PASCO OS-8515B Instruction Manual

OS-8515B Instruction Manual with Experiment Guide and Teachers’ Notes 012-09614B ������������ �� �� �� �� �� �� �� �� �� �� �� �� �� � �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� � �� �� �� �� �� ��������� ��������� ������ ������ ������������ ��������� ������� � � � ������

Table of Contents Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 About the Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 About the Experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Experiment 1: Color Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Experiment 2: Prism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Experiment 3: Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Experiment 4: Snell’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Experiment 5: Total Internal Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Experiment 6: Convex and Concave Lenses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Experiment 7: Hollow Lens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Experiment 8: Lensmaker’s Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Experiment 9: Apparent Depth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Experiment 10: Reversibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Experiment 11: Dispersion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Experiment 12: Focal Length and Magnification of a Thin Lens . . . . . . . . . . . . . . . . . . 31 Experiment 13: Telescope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Experiment 14: Microscope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Experiment 15: Shadows. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Telescope and Microscope Test Pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Teacher’s Guide. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Technical Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

OS-8515B � 3 Introduction The PASCO Basic Optics System contains the optics components you will need for a variety of experiments and demonstrations. This manual includes student instructions and teacher’s notes for 15 typical experiments. For an even greater variety, you can expand the system with any of the Basic Optics kits and components avail- able from PASCO, including lasers, polarizers, diffraction slits, and light sensors. See the PASCO Physics cata- log or visit www.pasco.com for details. ������������ �� �� �� �� �� �� �� �� �� �� �� �� �� � �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� � �� �� �� �� �� ��������� ��������� ������ ������ ������������ ��������� ������� � � � ������ 1 2 3 4 5 6 7 8 a d e f c b Included Equipment Part Number 1. 1.2 m Optics Bench OS-8508 2. Viewing Screen OS-8467 3. +100 mm Mounted Lens 003-07204 4. +200 mm Mounted Lens 003-07205 5. Adjustable Lens Holder OS-8474 6. Light Source OS-8470 7. Ray Table with D-shaped Lens OS-8465 8. Ray Optics Kit with: OS-8516A a. Storage Box/Water Tank 740-177 b. Mirror 636-05100 c. Hollow Lens OS-8511 d. Convex Lens 636-05501 e. Concave Lens 636-05502 f. Acrylic Rhombus 636-05611

About the Equipment 4 About the Equipment For detailed information on the Light Source, Ray Table, Adjustable Lens Holder, and Ray Optics Kit, see the instruction sheets included with those components. Optics Bench Basic Optics components, such as mounted lenses and the adjust- able lens holder, snap into the wide central channel of the optics bench. Place the base of the component on the bench and push down firmly to snap it in place. To move it, squeeze the tab on base and slide it along the bench. Components that include a square bolt and a thumb screw are designed to be fasted to the T-slots on the sides and center of the bench. Slide the bolt into the T-slot, insert the thumb screw through the component’s mounting hold, thread the screw into the bolt and tighten it down. Use the metric scale on the bench to measure the positions of components. Light Source The included light source can be used on a tabletop or mounted on the bench. It functions as a bright point source, an illuminated crossed-arrow object, a primary-color source, and a ray box with up to five parallel rays. Mounted Lenses The Basic Optics System includes two lenses mounted in hold- ers. Use them on the optics bench with the light source, viewing screen, and other Basic Optics components. Adjustable Lens Holder To use an unmounted lens on the bench, place it in the adjustable lens holder. It will hold any round lens between 20 and 75 mm in diameter. Viewing Screen Mount the screen on the bench to view real images formed by lenses. Ray Table and D-shaped Lens Use the ray table and D-shaped lens on a table- top with the light source (in ray-box mode) to study angles of incidence, reflection and refraction. Ray Optics Kit The ray optics kit is a set of optics components designed for use with the light source in ray-box mode. To make the rays easy to see and trace, use the ray optics components on a white sheet of paper on a flat table top. The transparent storage box doubles as a water tank for studying lenses under water. About the Experiments The experiment instructions on the following pages are arranged and categorized according to which components of the Basic Optics System they use. See the table at the top of each experiment for a detailed list of required equipment. Teachers’ notes, including typical data and answers to questions, can be found starting on page 47. The experiments that call for the light source work best in a dimly lit room. Ray Optics Kit Experiments These experiments use the Ray Optics Kit, the Light Source (in ray-box mode), and may require blank white paper, a ruler, protrac- tor, and drawing compass. 1. Color Addition (page 7): Explore the results of mixing colored light and illumi- nating colored ink with colored light. ���������������� ������������������� ��������� �������

About the Experiments 5 2. Prism (page 9): Show how a prism separates white light into its component col- ors and show that different colors are refracted at different angles through a prism. 3. Reflection (page 11): Show how rays are reflected from plane, concave, and con- vex mirrors. 4. Snell’s Law (page 13): Determine the index of refraction of acrylic by measuring angles of incidence and refraction of a ray passing through the rhombus. 5. Total Internal Reflection (page 15): Determine the critical angle at which total internal reflection occurs in the rhombus. 6. Convex and Concave Lenses (page 17): Use ray tracing to determine the focal lengths of lenses. 7. Hollow Lens (page 19): Use the hollow lens and water to explore how the prop- erties of a lens are related to its shape, its index of refraction, and the index of refraction of the surrounding medium. 8. Lensmaker’s Equation (page 21): Determine the focal length of a concave lens by measuring its radius of curvature. 9. Apparent Depth (page 23): Measure the apparent depth of the rhombus and determine its index of refraction by comparing the apparent depth to the actual thickness. Ray Table Experiments These experiments use the Ray Table with the D-shaped Lens and the Light Source (in ray-box mode). 10. Reversibility (page 27): Explore how the relationship between the angles of inci- dence and refraction is related to the direction of propagation. 11. Dispersion (page 29): Show how white light is separated into colors by the acrylic D-shaped lens and determine the different indices of refraction for red and blue light. Optics Bench Experiments These experiments use the Optics Bench, Mounted Lenses, and Viewing Screen. Experiments 12 and 15 also use the Light Source. 12. Focal Length and Magnification of a Thin Lens (page 31): Determine the focal length of a converging lens by forming an image on the viewing screen. 13. Telescope (page 35): Construct a telescope and determine its magnification. 14. Microscope (page 39): Construct a microscope and determine its magnification. 15. Shadows (page 43): Show the umbra and the penumbra of a shadow.

Experiment 1: Color Addition 7 Experiment 1: Color Addition Purpose In Part 1 of this experiment, you will discover the results of mixing red, green, and blue light in different combinations. In Part 2, you will compare the appearance of red, blue, and black ink illuminated by red and blue light. Part 1: Addition of Colored Light Procedure 1. Turn the wheel on the light source to select the red, green, and blue color bars. Fold a blank, white sheet of paper, as shown in Figure 1.1. Lay the paper on a flat surface and put the light source on it so that the colored rays are projected along the horizontal part of the paper and onto the vertical part. 2. Place the convex lens near the ray box so it focuses the rays and causes them to cross at the vertical part of the paper. Note: The lens has one flat edge. Place the flat edge on the paper so the lens stands stably without rocking. 3. What is the resulting color where the three colors come together? Record your observa- tion in Table 1.1. 4. Now block the green ray with a pencil. What color results from adding red and blue light? Record the result in Table 1.1. 5. Block each color in succession to see the addition of the other two colors and com- plete Table 1.1. Questions 1. Is mixing colored light the same as mixing colored paint? Explain. 2. White light is said to be the mixture of all colors. In this experiment, did mixing red, green, and blue light result in white? Explain. Required Equipment from Basic Optics System Light Source Convex Lens from Ray Optics Kit Other Required Equipment Red, blue, and black pens Blank white paper ������������ ����������� ������������ ����������� ������������� �������� ������ Figure 1.1: Color addition Table 1.1: Results of Colored Light Addition Colors Added Resulting Color red + blue + green red + blue red + green green + blue

Experiment 1: Color Addition 8 Part 2: Observing Colored Ink Under Colored Light Procedure 1. While you look away, have your partner draw two lines—one red and one black—on a sheet of white paper. One of the lines should be labeled A, and the other B, but you should not know which is which. Before you look at the paper, have your partner turn off the room lights and cover the red and green bars so the paper is illuminated only with blue light. Now look. What colors do the two lines appear to be? Do they appear to be different colors? Record your observations in Table 1.2. Finally, observe the lines under white light and record their actual colors in Table 1.2. 2. Repeat step 1, but this time have your partner draw lines using blue and black ink (labeled C and D), and observe them under red light. 3. For Trial 2, switch roles and repeat steps 1 and 2 with your partner observing lines that you have drawn. Record the results in Table 1.2. (For this trial, you may try to trick your partner by drawing both lines the same color—both red or both black, for instance.) 4. Look at red and black lines under red light. Which line is easier to see? _________________________ Questions 1. What makes red ink appear red? When red ink is illumined by blue light, is most of the light absorbed or reflected? 2. When illumined with red light, why is red ink on white paper more difficult to see than black ink? Table 1.2: Colored Ink Observed Under Colored Light Trial 1: Name of observer: ______________________________________ Color of Light Line Apparent Color of Ink Do they look different? Actual Color of Ink Blue Light A B Red Light C D Trial 2: Name of observer: ______________________________________ Color of Light Line Apparent Color of Ink Do they look different? Actual Color of Ink Blue Light A B Red Light C D

Experiment 2: Prism 9 Experiment 2: Prism Purpose The purpose of this experiment is to show how a prism separates white light into its component colors and to show that different colors are refracted at different angles through a prism. Theory When a monochromatic light ray crosses from one medium (such as air) to another (such as acrylic), it is refracted. According to Snell’s Law, n1sin θ1 = n2sin θ2 the angle of refraction (θ2) depends on the angle of incidence (θ1) and the indices of refraction of both media (n1 and n2), as shown in Figure 2.1. Because the index of refraction for light varies with the frequency of the light, white light that enters the material (at an angle other than 0°) will separate into its component colors as each fre- quency is bent a different amount. The rhombus is made of acrylic which has an index of refraction of 1.497 for light of wavelength 486 nm in a vacuum (blue light), 1.491 for wavelength 589 nm (yellow), and 1.489 for wavelength 651 nm (red). In general for visible light, index of refrac- tion increases with increasing frequency. Procedure 1. Place the light source in ray-box mode on a sheet of blank white paper. Turn the wheel to select a single white ray. 2. Position the rhombus as shown in Figure 2.2. The acute-angled end of the rhom- bus is used as a prism in this experiment. Keep the ray near the point of the rhom- bus for maximum transmission of the light. Required Equipment from Basic Optics System Light Source Rhombus from Ray Optics Kit Blank white paper ����������������� ������� ������������� ��������� ������������ �� �� �� �� Figure 2.1: Refraction of Light � ���������������� ����������������� ����� �������� Figure 2.2

Experiment 2: Prism 10 3. Rotate the rhombus until the angle (θ) of the emerging ray is as large as possible and the ray separates into colors. (a) What colors do you see? In what order are they? (b) Which color is refracted at the largest angle? (c) According to Snell’s Law and the information given about the frequency dependence of the index of refraction for acrylic, which color is predicted to refract at the largest angle? 4. Without repositioning the light source, turn the wheel to select the three primary color rays. The colored rays should enter rhombus at the same angle that the white ray did. Do the colored rays emerge from the rhombus parallel to each other? Why or why not?

Experiment 3: Reflection 11 Experiment 3: Reflection Purpose In this experiment, you will study how rays are reflected from different types of mir- rors. You will measure the focal length and determine the radius of curvature of a con- cave mirror and a convex mirror. Part 1: Plane Mirror Procedure 1. Place the light source in ray-box mode on a blank sheet of white paper. Turn the wheel to select a single ray. 2. Place the mirror on the paper. Position the plane (flat) surface of the mirror in the path of the incident ray at an angle that allows you to clearly see the incident and reflected rays. 3. On the paper, trace and label the surface of the plane mirror and the incident and reflected rays. Indicate the incoming and the outgoing rays with arrows in the appropriate directions. 4. Remove the light source and mirror from the paper. On the paper, draw the normal to the surface (as in Figure 3.1). 5. Measure the angle of incidence and the angle of reflection. Measure these angles from the normal. Record the angles in the first row Table 3.1. 6. Repeat steps 1–5 with a different angle of incidence. Repeat the procedure again to complete Table 3.1 with three different angles of incidence. 7. Turn the wheel on the light source to select the three primary color rays. Shine the colored rays at an angle to the plane mirror. Mark the position of the surface of the plane mirror and trace the incident and reflected rays. Indicate the colors of Required Equipment from Basic Optics System Light Source Mirror from Ray Optics Kit Other Required Equipment Drawing compass Protractor Metric ruler White paper Table 3.1: Plane Mirror Results Angle of Incidence Angle of Reflection ������������ ��������� ������� ������������� Figure 3.1

Experiment 3: Reflection 12 the incoming and the outgoing rays and mark them with arrows in the appropriate directions. Questions 1. What is the relationship between the angles of incidence and reflection? 2. Are the three colored rays reversed left-to-right by the plane mirror? Part 2: Cylindrical Mirrors Theory A concave cylindrical mirror focuses incoming parallel rays at its focal point. The focal length ( f ) is the distance from the focal point to the cen- ter of the mirror surface. The radius of curvature (R) of the mirror is twice the focal length. See Figure 3.2. Procedure 1. Turn the wheel on the light source to select five parallel rays. Shine the rays straight into the concave mirror so that the light is reflected back toward the ray box (see Figure 3.3). Trace the surface of the mirror and the incident and reflected rays. Indicate the incoming and the outgoing rays with arrows in the appropriate directions. (You can now remove the light source and mirror from the paper.) 2. The place where the five reflected rays cross each other is the focal point of the mirror. Mark the focal point. 3. Measure the focal length from the center of the concave mirror sur- face (where the middle ray hit the mirror) to the focal point. Record the result in Table 3.2. 4. Use a compass to draw a circle that matches the curvature of the mirror (you will have to make several tries with the compass set to different widths before you find the right one). Measure the radius of curvature and record it in Table 3.2. 5. Repeat steps 1–4 for the convex mirror. Note that in step 3, the reflected rays will diverge, and they will not cross. Use a ruler to extend the reflected rays back behind the mirror’s surface. The focal point is where these extended rays cross. Questions 1. What is the relationship between the focal length of a cylindrical mirror and its radius of curvature? Do your results confirm your answer? 2. What is the radius of curvature of a plane mirror? Table 3.2: Cylindrical Mirror Results Concave Mirror Convex Mirror Focal Length Radius of Curvature (determined using compass) � � ����� ����� ������ Figure 3.2 ������������� Figure 3.3

Experiment 4: Snell’s Law 13 Experiment 4: Snell’s Law Purpose The purpose of this experiment is to determine the index of refraction of the acrylic rhombus. For rays entering the rhombus, you will measure the angles of incidence and refraction and use Snell’s Law to calculate the index of refraction. Theory For light crossing the boundary between two transparent materials, Snell’s Law states n1sin θ1 = n2sin θ2 where θ1 is the angle of incidence, θ2 is the angle of refraction, and n1 and n2 are the respective indices of refraction of the materials (see Figure 4.1). Procedure 1. Place the light source in ray-box mode on a sheet of white paper. Turn the wheel to select a single ray. 2. Place the rhombus on the paper and position it so the ray passes through the parallel sides as shown in Figure 4.2. 3. Mark the position of the parallel surfaces of the rhombus and trace the incident and transmitted rays. Indicate the incoming and the outgoing rays with arrows in the appropriate direc- tions. Carefully mark where the rays enter and leave the rhombus. 4. Remove the rhombus and draw a line on the paper connecting the points where the rays entered and left the rhombus. This line represents the ray inside the rhombus. 5. Choose either the point where the ray enters the rhombus or the point where the ray leaves the rhombus. At this point, draw the normal to the surface. 6. Measure the angle of incidence (θi) and the angle of refraction with a protractor. Both of these angles should be measured from the normal. Record the angles in the first row of Table 4.1. Required Equipment from Basic Optics System Light Source Rhombus from Ray Optics Kit Other Required Equipment Protractor White paper ����������������� ������� ������������� ��������� ������������ �� �� �� �� Figure 4.1 �� ������������ Figure 4.2

Experiment 4: Snell’s Law 14 7. On a new sheet of paper, repeat steps 2–6 with a different angle of incidence. Repeat these steps again with a third angle of incidence. The first two columns of Table 4.1 should now be filled. Analysis 1. For each row of Table 4.1, use Snell’s Law to calculate the index of refraction, assuming the index of refraction of air is 1.0. 2. Average the three values of the index of refraction. Compare the average to the accepted value (n = 1.5) by calculating the percent difference. Question What is the angle of the ray that leaves the rhombus relative to the ray that enters it? Table 4.1: Data and Results Angle of Incidence Angle of Refraction Calculated index of refraction of acrylic Average:

Experiment 5: Total Internal Reflection 15 Experiment 5: Total Internal Reflection Purpose In this experiment, you will determine the critical angle at which total internal reflec- tion occurs in the acrylic rhombus and confirm your result using Snell’s Law. Theory For light crossing the boundary between two transpar- ent materials, Snell’s Law states n1sin θ1 = n2sin θ2 where θ1 is the angle of incidence, θ2 is the angle of refraction, and n1 and n2 are the respective indices of refraction of the materials (see Figure 5.1). In this experiment, you will study a ray as it passes out of the rhombus, from acrylic (n = 1.5) to air (nair = 1). If the incident angle (θ1) is greater than the critical angle (θc), there is no refracted ray and total internal reflection occurs. If θ1 = θc, the angle of the refracted ray (θ2) is 90°, as in Figure 5.2. In this case, Snell’s Law states: n sin θc = 1 sin 90° Solving for the sine of critical angle gives: Required Equipment from Basic Optics System Light Source Rhombus from Ray Optics Kit Other Required Equipment Protractor White paper ������� ������������� ��������� ������������ �� �� �� �� ������������� Figure 5.1 ������������� ������������ � ������� �� ������������� ��� Figure 5.2 sin θc 1 n-- =

Experiment 5: Total Internal Reflection 16 Procedure 1. Place the light source in ray-box mode on a sheet of white paper. Turn the wheel to select a single ray. 2. Position the rhombus as shown in Figure 5.3, with the ray entering the rhombus at least 2 cm from the tip. 3. Rotate the rhombus until the emerging ray just barely disappears. Just as it disappears, the ray separates into colors. The rhombus is correctly posi- tioned if the red has just disappeared. 4. Mark the surfaces of the rhombus. Mark exactly the point on the surface where the ray is internally reflected. Also mark the entrance point of the incident ray and the exit point of the reflected ray. 5. Remove the rhombus and draw the rays that are incident upon and reflected from the inside surface of the rhombus. See Figure 5.4. Measure the angle between these rays using a protractor. (Extend these rays to make the protractor easier to use.) Note that this angle is twice the critical angle because the angle of incidence equals the angle of reflection. Record the critical angle here: θc = _______ (experimental) 6. Calculate the critical angle using Snell’s Law and the given index of refraction for Acrylic (n = 1.5). Record the theoretical value here: θc = _______ (theoretical) 7. Calculate the percent difference between the measured and theoretical values: % difference = _______ Questions 1. How does the brightness of the internally reflected ray change when the incident angle changes from less than θc to greater than θc? 2. Is the critical angle greater for red light or violet light? What does this tell you about the index of refraction? �������� ��� ��������� ��� ��������� ��� Figure 5.3 ��� ���������� �������� ����� ���������� ����� ��� ����� �� �� �� Figure 5.4

Experiment 6: Convex and Concave Lenses 17 Experiment 6: Convex and Concave Lenses Purpose In this experiment, you will explore the difference between convex and concave lenses and determine their focal lengths. Theory When parallel light rays pass through a thin lens, they emerge either converging or diverging. The point where the converging rays (or their extensions) cross is the focal point of the lens. The focal length of the lens is the distance from the center of the lens to the focal point. If the rays diverge, the focal length is negative. Procedure 1. Place the light source in ray-box mode on a white sheet of paper. Turn the wheel to select three parallel rays. Shine the rays straight into the convex lens (see Fig- ure 6.1). Note: The lenses used in this experiment have one flat edge. Place the flat edge on the paper so the lens stands stably without rocking. 2. Trace around the surface of the lens and trace the incident and transmitted rays. Indicate the incoming and the outgoing rays with arrows in the appropriate direc- tions. 3. The point where the outgoing rays cross is the focal point of the lens. Measure the focal length from the center of the lens to the focal point. Record the result in Table 6.1. 4. Repeat the procedure with the concave lens. Note that in step 3, the rays leaving the lens are diverging and do not cross. Use a ruler to extend the outgoing rays straight back through the lens. The focal point is where these extended rays cross. (Remember to record the focal length as a negative number.) Required Equipment from Basic Optics System Light Source Convex Lens from Ray Optics Kit Concave Lens from Ray Optics Kit Other Required Equipment Metric ruler Table 6.1: Results Convex Lens Concave Lens Focal Length ������������� ����������� Figure 6.1

Experiment 6: Convex and Concave Lenses 18 5. Nest the convex and concave lenses together and place them in the path of the parallel rays (see Figure 6.2). Trace the rays. Are the outgoing rays converging, diverging or parallel? What does this tell you about the relationship between the focal lengths of these two lenses? 6. Slide the convex and concave lenses apart by a few centimeters and observe the effect. Then reverse the order of the lenses. Trace at least one pattern of this type. What is the effect of changing the distance between the lenses? What is the effect of reversing their positions? Figure 6.2

Experiment 7: Hollow Lens 19 Experiment 7: Hollow Lens Purpose In this experiment you will explore how the properties of a lens are related to its shape, its index of refraction, and the index of refraction of the surrounding medium. Background A conventional lens is made of a material whose index of refraction is higher than that of the surrounding medium. For instance, the lenses in a pair of eyeglasses are usually made from glass or plastic with an index of refraction of 1.5 or higher, while the air surrounding the lenses has an index of refraction of 1.0. However, a lens can also have a lower index of refraction than the surrounding medium, as is the case when a hollow lens is “filled with air” and surrounded by water. (The index of refraction of water is about 1.3.) The hollow lens in this experiment has three sections: a plano-con- cave section and two plano-convex sections. We will refer to these as sections 1, 2, and 3 (see Figure 7.1). You will determine whether each section acts as a converging or diverging lens when it is a) filled with water and surrounded by air and b) filled with air and surrounded by water. Procedure 1. Before you test the hollow lens, make some predictions: For every configuration in Table 7.1, predict whether incoming parallel rays will converge or diverge after passing through the lens. Record your predictions in the table. 2. Place the light source in ray-box mode on a white sheet of paper. Turn the wheel to select five parallel rays. 3. Fill section 1 with water and place the lens in front of the light source so the par- allel rays enter it through the flat side. Do the rays converge or diverge after pass- ing through the lens? Record your observation in Table 7.1. Required Equipment from Basic Optics System Light Source Hollow Lens from Ray Optics Kit Box from Ray Optics Kit (with lenses and foam insert removed) White Plastic Sheet from Ray Optics Kit Other Equipment Water Paper towels White paper Small weight (to stop lens from floating) Eye-dropper (optional, for removing water from the hollow lens) � � � Figure 7.1: The hollow lens

Experiment 7: Hollow Lens 20 Repeat this step with water in different section of the lens to complete the first four rows of Table 7.1. 4. Put the white plastic sheet in the transparent ray-optics box. Put the hollow lens in the box on top of the sheet as shown in Figure 7.2. Place a small weight on top of the lens to stop it from floating. Position the light source outside of the box so that the rays enter the hollow lens through the flat side. Figure 7.2: Hollow lens set up for testing surrounded by water 5. Fill the box with water to just below the top of the lens. Fill sections 2 and 3 of the lens with water (leaving section 1 “filled” with air). Record your observation in Table 7.1. Repeat this step with air in different section of the lens to complete Table 7.1. Questions 1. Under what conditions is a plano-convex lens converging? Under what condi- tions is it diverging? 2. If a plano-concave lens of an unknown material is a diverging lens when sur- rounded by air, is it possible to know whether the lens will be converging or diverging when placed in water? Explain. Table 7.1: Predictions and Observations Lens surrounded by: Section 1 filled with: Section 2 filled with: Section 3 filled with: Prediction (converging or diverging) Observation (converging or diverging) Air Water Air Air Air Water Air Air Air Water Water Air Water Water Air Water Water Water Air Water Water Water Air ������������� ��� �����������

Experiment 8: Lensmaker’s Equation 21 Experiment 8: Lensmaker’s Equation Purpose In this experiment you will determine the focal length of a concave lens in two ways: a) by direct measurement using ray tracing and b) by measuring the radius of curva- ture and using the lensmaker’s equation. Theory The lensmaker’s equation is used to calculate the focal length (in air or a vacuum), f, of a lens based on the radii of curvature of its surfaces (R1 and R2) and the index of refraction (n) of the lens material: (eq. 8.1) In this notation, R is positive for a convex surface (as viewed from outside the lens) and R is negative for a concave surface (as in Figure 8.1). Figure 8.1 Procedure 1. Place the light source in ray-box mode on a white sheet of paper. Turn the wheel to select three parallel rays. Shine the rays straight into the convex lens (see Fig- ure 8.2). Note: The lens has one flat edge. Place the flat edge on the paper so the lens stands stably without rocking. Required Equipment from Basic Optics System Light Source Concave Lens from Ray Optics Kit Other Required Equipment Metric ruler 1 f-- n – 1 ( ) 1 R1 ------ 1 R2 – ------ ⎝ ⎠ ⎜ ⎟ ⎛ ⎞ = ������ ������� ���� �� �� ������������� ������������ Figure 8.2

Experiment 8: Lensmaker’s Equation 22 2. Trace around the surface of the lens and trace the incident and transmitted rays. Indicate the incoming and the outgoing rays with arrows in the appropriate direc- tions. 3. Remove the lens. To measure the focal length, use a ruler to extend the outgoing diverging rays straight back through the lens. The focal point is where these extended rays cross. Measure the distance from the center of the lens to the focal point. Record the result as a negative value: f = _______________ (measured directly) 4. To determine the radius of curvature, put the concave lens back in the path of the rays and observe the faint reflected rays off the first surface of the lens. The front of the lens can be treated as a concave mirror having a radius of curvature equal to twice the focal length of the effective mirror (see Figure 8.3). Trace the surface of the lens and mark the point where the central ray hits the surface. Block the central ray and mark the point where the two outer rays cross. Measure the distance from the lens surface to the point where the reflected rays cross. The radius of curvature is twice this distance. Record the radius of curvature: R = _______________ 5. For this lens, it is not necessary to measure the curvature of both sides because they are equal (R1 = R2 = R). Calculate the focal length of the lens using the lens- maker’s equation (Equation 8.1). The index of refraction is 1.5 for the acrylic lens. Remember that a concave surface has a negative radius of curvature. f = _______________ (calculated) 6. Calculate the percent difference between the two values of f from step 3 and step 5: % difference = _______________ ������������ ����� Figure 8.3: Reflected rays from the lens surface

Experiment 9: Apparent Depth 23 Experiment 9: Apparent Depth Purpose In this experiment, you will use two different methods to measure the apparent depth of the acrylic rhombus. You will also determine the index of refraction of acrylic by comparing the apparent depth to the actual depth. Theory Light rays originating from the bottom surface of a block of transparent material refract at the top surface as the rays emerge from the material into the air (see Figure 9.1). When viewed from above, the apparent depth, d, of the bottom sur- face of the block is less than the actual thickness, t, of the block. The apparent depth is given by (eq. 9.1) d = t/n where n is the index of refraction of the material. Part 1: Parallax Method Background Place this page flat on the table in front of you. Hold a pencil horizontally a few centi- meters above the paper. With one eye closed or covered, look down at the pencil and move your head side to side (without moving the pencil). Notice how the pencil appears to move relative to the words printed on the paper; this phenomenon is known as parallax. Now hold the tip of the pencil on the paper and check for parallax. When there is no parallax between to objects, they are at the same distance from you. Procedure 1. Place a blank sheet of paper flat on the table. Use a straight edge and pencil to draw a vertical line on the paper. Place the rhombus on the paper over the line as shown in Figure 9.2. Required Equipment from Basic Optics System Light Source Rhombus from Ray Optics Kit Convex Lens from Ray Optics Kit Mirror from Ray Optics Kit (used to block rays) Other Required Equipment Metric ruler White paper Very sharp pencil �������� ����� � � ����� � � ������ ��� Figure 9.1

Experiment 9: Apparent Depth 24 Figure 9.2 2. With both eyes, look down through the top of the rhombus. Does the line viewed through the rhombus appear to be closer? Close or cover one eye, and move your head side to side. Do you see parallax between the line viewed through the rhom- bus and the line viewed directly? 3. In this step, you will hold a pencil near the rhombus to determine the position of the apparent line. When the pencil and the apparent line are at the same distance from your eye, there will be no parallax between them. While looking down through the rhombus (with one eye), hold a very sharp pencil as shown in Figure 9.3 so it appears to be lined up with the line inside the rhombus. Move your head left and right to check for parallax. Move the pencil up or down and check again. When there is no parallax, mark that point. (Hold the rhombus with your free hand, press the pencil tip gently against the side of the rhombus and twist the pencil to make a light mark. Erase the mark after you have finished this experiment.) Analysis 1. Measure the distance from the top of the rhombus to your pencil mark. Record this apparent depth, d, in the first row of Table 9.1. 2. Measure the thickness, t, of the rhombus and record it in Table 9.1. 3. Use Equation 9.1 to calculate the index of refraction and record your result in Table 9.1. Part 2: Ray-tracing Method Procedure 1. Place the light source in ray-box mode on a white sheet of paper. Turn the wheel to select five parallel rays. Shine the rays straight into the convex lens. Place the mirror on its edge between the ray box and the lens so that it blocks the middle three rays, leaving only the outside two rays (as in Figure 9.4, but do not put the rhombus there yet). Note: The lens has one flat edge. Place the flat edge on the paper so the lens stands stably without rocking. Table 9.1: Results d t n Part 1: Parallax method Part 2: Ray-tracing method ����� ������� ���� ���� ���� ����������� ����� �������� ������������ Figure 9.3

Experiment 9: Apparent Depth 25 2. Mark the place on the paper where the two rays cross each other. 3. Position the rhombus as shown in Figure 9.4. The “bottom” surface of the rhombus must be exactly at the point where the two rays cross. The crossed rays simulate rays that originate at an object on the “bottom” of the block. 4. Trace the rhombus and trace the rays diverging from the “top” surface. 5. Remove the rhombus and light source. Trace the diverging rays back into the rhombus. The point where these rays cross (inside the rhombus) is the appar- ent position of the “bottom” of the rhombus when viewed through the “top”. Analysis 1. Measure the apparent depth, d, and record it in Table 9.1. 2. Use Equation 9.1 to calculate the index of refraction and record your result in Table 9.1. Questions 1. Of the two methods that you used to determine d, which one is more precise? Explain. 2. The accepted value of the index of refraction of acrylic is n = 1.49. What was the percent difference between the accepted value and each of your two results? � � ������ ���� ������ ������� �������� �������� ����� �������� Figure 9.4

Experiment 10: Reversibility 27 Experiment 10: Reversibility Purpose In Trial 1 of this experiment, you will determine the relationship between the angle of incidence and the angle of refraction for light passing from air into a more optically dense medium (the acrylic of the D-shaped lens). In Trial 2, you will determine whether the same relationship holds between the angles of incidence and refraction for light passing out of a more optically dense medium back into air. That is to say, if the light is traveling in the opposite direction through the lens, is the law of refraction the same or different? By comparing the results of both trials, you will find the answer to this question. In Figure 10.1, notice that refraction occurs only at the flat surface of the D-shaped lens, not at the curved surface. Figure 10.1: Refraction of light passing into the lens (Trial 1) and out of the lens (Trial 2) Setup 1. Place the light source in ray-box mode on a flat tabletop. Turn the wheel to select a single ray. 2. Put the ray table in front of the light source so the ray from the light source crosses the exact center of the ray table. 3. Put the D-shaped lens on the ray table exactly centered in the marked outline. Required Equipment from Basic Optics System Ray Table D-shaped Lens Light Source �� �� �� �� �� �� �� �� �� �� �� �� �� � �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� � �� �� �� �� �� ��������� ��������� ������ ������ ������������ ��������� ������� � � � ������ �� �� �� �� �� �� �� �� �� �� �� �� �� � �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� � �� �� �� �� �� ��������� ��������� ������ ������ ������������ ��������� ������� � � ��� Angle of refraction θr1 Angle of incidence θi2 Angle of refraction θr2 Trial 1 Trial 2 Angle of incidence θi1 �� �� �� �� �� �� �� �� �� �� �� �� �� � �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� � �� �� �� �� �� ��������� ��������� ������ ������ ������������ ��������� ������� �� �� �� �� �� �� �� �� �� �� �� �� �� �� � �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� � �� �� �� �� �� ��������� ��������� ������ ������ ������������ ��������� ������� �� ������������ ��������� ������ ��� Figure 10.2: Initial setup for Trial 1

Experiment 10: Reversibility 28 Record Data Trial 1 1. Turn the ray table so the incoming ray enters the lens through the flat sur- face (see Figure 10.2). 2. Rotate the ray table to set the angle of incidence to each of the values listed in the first column of Table 10.1. For each angle of incidence (θi1), observe the corresponding angle of refraction (θr1) and record it in the second column of the table. Trial 2 1. Copy all of the values in the second column to the third column of the table. (In other words, the angles of refraction that you observe in Trial 1 will be the angles of incidence that you use in Trial 2.) 2. Turn the ray table so the incoming ray enters the lens through the curved surface. 3. For the angles of incidence (θi2) that you wrote in the third column of the table, observe the corresponding angles of refraction (θr2) and record them in the fourth column. Analysis 1. Using your values for θi1 and θr1 and Snell’s Law (Equation 10.1), determine the index of refraction of acrylic (nacrylic). Assume the index of refraction of air (nair) is 1.0. (eq. 10.1) nacrylic = ___________ (from θi1 and θr1) 2. Determine nacrylic again, this time using your values of θi2 and θr2. nacrylic = ___________ (from θi2 and θr2) Questions 1. Is the law of refraction the same for light rays going in either direction between the two media? 2. Does the principle of optical reversibility hold for reflection as well as refraction? Explain. Table 10.1: Data Trial 1 Ray Incident on Flat Surface Trial 2 Ray Incident on Curved Surface Angle of Incidence θi1 Angle of Refraction θr1 Angle of Incidence θi2 Angle of Refraction θr2 0° 10° 20° 30° 40° 50° 60° 70° 80° nair (θi1 ) sin nacrylic (θr1 ) sin =

Experiment 11: Dispersion 29 Experiment 11: Dispersion Purpose The purpose of this experiment is to determine the index of refraction of acrylic at two different wavelengths. Theory When light crosses the boundary between two transparent media, it is refracted. Snell’s Law expresses the relationship between index of refraction of the first medium (n1), the index of refraction of the second medium (n2), the angle of incidence (θ1), and the angle of refraction (θ2): (eq. 11.1) Figure 11.1 We can assume the index of refraction of air (n2 in this experiment) is always equal to 1.0. However, the index of refraction of acrylic (n1) depends on the wavelength, or color, of the light. Therefore, the different wavelengths present in an incident ray of white light will be refracted at different angles. The wavelength dependence of a material’s index of refraction is known as dispersion. Setup 1. Place the light source in ray-box mode on a flat tabletop. Turn the wheel to select a single ray. 2. Put the ray table in front of the light source so the ray from the light source crosses the exact center of the ray table (see Figure 11.2). 3. Put the acrylic D-shaped lens on the ray table in the marked outline. Turn the ray table so Required Equipment from Basic Optics System Ray Table D-shaped Lens Light Source n1 sinθ1 n2 sinθ2 = ������������� ��������� ������������ �� �� �� �� ������� ��� �� �� �� �� �� �� �� �� �� �� �� �� �� � �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� � �� �� �� �� �� ��������� ��������� ������ ������ ������������ ��������� ������� �� �� �� �� �� �� �� �� �� �� �� �� �� �� � �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� � �� �� �� �� �� ��������� ��������� ������ ������ ������������ ��������� ������� �� ������������ ��������� ������ ��� Figure 11.2

Experiment 11: Dispersion 30 the ray enters the lens through the curved surface, and the angle of incidence is 0°. Procedure 1. Hold a piece of white paper vertically near the edge of the Ray Table so the out- going ray is visible on the paper. 2. Slowly rotate the ray table to increase the angle of incidence. Notice that the ray is refracted only at the flat surface of the lens, not at the curved surface. As you continue to increase the angle of incidence, watch the refracted light on the paper. Analysis 1. At what angle of refraction do you begin to notice color separation in the refracted light? 2. At what angle of refraction does the maximum color separation occur? 3. What colors are present in the refracted ray? (Write them in the order of mini- mum to maximum angle of refraction.) 4. Use Snell’s Law (Equation 11.1) to calculate the index of refraction of acrylic for red light (nred) and the index of refraction for blue light (nblue).

Experiment 12: Focal Length and Magnification of a Thin Lens 31 Experiment 12: Focal Length and Magnification of a Thin Lens Purpose The purpose of this experiment is to determine the focal length of a thin lens, and to measure the magnification for a certain combination of object and image distances. Theory For a thin lens: (eq. 12.1) where f is focal length, do is the distance between the object and the lens, and di is the distance between the image and the lens. By measuring do and di the focal length can be determined. Magnification, M, is the ratio of image size to object size. If the image is inverted, M is negative. Part I: Object at Infinity In this part, you will determine the focal length of the lens by making a single mea- surement of di with . Procedure 1. Hold the lens in one hand and the screen in the other hand. Focus the image of a distant bright object (such as a window or lamp across the room) on the screen. 2. Have your partner measure the distance from the lens to the screen. This is the image distance, di. di = _______________ Analysis 1. As do approaches infinity, what does 1/do approach? Required Equipment from Basic Optics System Light Source Bench Converging lens of unknown focal length1 1Instructors: see note on page 51. Screen Other Equipment Metric ruler Optics Caliper (optional, for measuring image sizes), PASCO part OS-8468 1 f-- 1 do ----- 1 di + ---- = do ∞ ≅

Experiment 12: Focal Length and Magnification of a Thin Lens 32 2. Use the Thin Lens Formula (Equation 12.1) to calculate the focal length. f = _______________ Part II: Object Closer Than Infinity In this part, you will determine the focal length by measuring several pairs of object and image distances and plotting 1/do versus 1/di. Figure 12.1 Procedure 1. Place the light source and the screen on the optics bench 1 m apart with the light source’s crossed arrow object toward the screen. Place the lens between them (see Figure 12.1). 2. Starting with the lens close to the screen, slide the lens away from the screen to a position where a clear image of the crossed-arrow object is formed on the screen. Measure the image distance and the object distance. Record these measurements (and all measurements from the following steps) in Table 12.1. 3. Measure the object size and the image size for this position of the lens. 4. Without moving the screen or the light source, move the lens to a second position where the image is in focus. Measure the image distance and the object distance. 5. Measure the object size and image size for this position also. Note that you will not see the entire crossed-arrow pattern. Instead, measure the image and object sizes as the distance between two index marks on the pattern (see Figure 12.2 for example). 6. Repeat steps 2 and 4 with light source-to-screen distances of 90 cm, 80 cm, 70 cm, 60 cm, and 50 cm. For each light source-to-screen distance, find two lens positions where clear images are formed. (You don’t need to measure image and object sizes.). Analysis Part A: Focal Length 1. Calculate 1/do and 1/di for all 12 rows in Table 12.1. 2. Plot 1/do versus 1/di and find the best-fit line (linear fit). This will give a straight line with the x- and y-intercepts equal to 1/f. Record the intercepts (including units) here: y-intercept = 1/f = _______________ x-intercept = 1/f = _______________ Note: You can plot the data and find the best-fit line by hand on paper or on a computer. ������������ ���� ������ ��� ����������������������� ���������������� ���������������� Figure 12.2

Experiment 12: Focal Length and Magnification of a Thin Lens 33 3. For each intercept, calculate a value of f and record it in Table 12.2. 4. Find the percent difference between these two values of f and record them in Table 12.2. 5. Average these two values of f. Find the percent difference between this average and the focal length that you found in Part I. Record these data in Table 12.2. Analysis Part B: Magnification 1. For the first two data points only (the first two lines of Table 12.2), use image and object distances to calculate the magnification, M, at each position of the lens. Record the results in Table 12.3. (eq. 12.2) Table 12.1: Image and Object Distances Distance from light source to screen do di 1/do 1/di Image Size Object Size 100 cm 90 cm 80 cm 70 cm 60 cm 50 cm Table 12.2: Focal Length f Result from x-intercept Result from y-intercept % difference between results from intercepts Average of results from intercepts Result from Part I % difference between Average of results from intercepts and result from Part I M di do ----- ⎝ ⎠ ⎜ ⎟ ⎛ ⎞ – =

Experiment 12: Focal Length and Magnification of a Thin Lens 34 2. Calculate the absolute value of M (for each of the two lens positions) using your measurements of the image size and object size. Record the results in Table 12.3. (eq. 12.3) 3. Calculate the percent differences between the absolute values of M found using the two methods. Record the results in Table 12.3. Questions 1. Is the image formed by the lens upright or inverted? 2. Is the image real or virtual? How do you know? 3. Explain why, for a given screen-to-object distance, there are two lens positions where a clear image forms. 4. By looking at the image, how can you tell that the magnification is negative? 5. You made three separate determinations of f (by measuring it directly with a dis- tant object, from the x-intercept of your graph, and from the y-intercept). Where these three values equal? If they were not, what might account for the variation? M image size object size ------------------------- = Table 12.3: Magnification Point 1 Point 2 calculated from image and object distances calculated from image and object sizes % difference M M

Experiment 13: Telescope 35 Experiment 13: Telescope Purpose In this experiment, you will construct a telescope and determine its magnification. Theory Figure 13.1 An astronomical telescope consists of two convex lenses. The astronomical telescope in this experiment will form an image in the same place as the object (see Figure 13.1). The lenses are thin compared to the other distances involved, which allows the Thin Lens Formula to be used: (eq. 13.1) where f is focal length, do is the distance between the object and the lens, and di is the distance between the image and the lens. The magnification, M, of a two-lens system is equal to the product of the magnifica- tions of the individual lenses: (eq. 13.2) Set Up 1. Tape the paper grid pattern to the screen to serve as the object. 2. The +200 mm lens is the objective lens (the one closer to the object). The +100 mm lens is the eyepiece lens (the one closer to the eye). Place the lenses near one Required Equipment from Basic Optics System Bench 2 Convex Lenses (+100 mm and +200 mm) Screen Paper grid pattern (see page 45), or a 14 × 16 grid of 1 cm squares ��� ���� ��� ��� ������ ����� ���� ������� ���� ������� ��� 1 f-- 1 do ----- 1 di + ---- = M M1M2 di1 – do1 ---------- ⎝ ⎠ ⎜ ⎟ ⎛ ⎞ di2 – do2 ---------- ⎝ ⎠ ⎜ ⎟ ⎛ ⎞ = =

Experiment 13: Telescope 36 end of the optics bench and place the screen on the other end (see Figure 13.2). Their exact positions do not matter yet. Figure 13.2 Procedure 1. Put your eye close to the eyepiece lens and look through both lenses at the grid pattern on the screen. Move the objective lens to bring the image into focus. Figure 13.3 2. In this step, you will adjust your telescope to make the image occur in the same place as the object. To do this, you will look at both image and object at the same time and judge their relative positions by moving your head side to side. If the image and object are not in the same place, then they will appear to move relative to each other. This effect is known as parallax. Open both eyes. Look with one eye through the lenses at the image and with the other eye past the lenses at the object (see Figure 13.3). The lines of the image (solid lines shown in Figure 13.4) will be superimposed on the lines of the object (shown as dotted lines in Figure 13.4). Move your head left and right or up and down by about a centimeter. As you move your head, the lines of the image may move relative to the lines of the object due to the parallax. Adjust the eyepiece lens to eliminate parallax. Do not move the objective lens. When there is no parallax, the lines in the center of the lens appear to be stuck to the object lines. Note: You will probably have to adjust the eyepiece lens by no more than a few centimeters. 3. Record the positions of the lenses and screen in Table 13.1. 4. Estimate the magnification of your telescope by counting the number of object squares that lie along one side of one image square. To do this, you must view the image through the telescope with one eye while looking directly at the object with the other eye. Remember that magnification is negative for an inverted image. Record the observed magnification in Table 13.1. Analysis To calculate the magnification, complete the following steps and record the results in Table 13.1: ������ ������� �������������� ������� ������������� �������� ��������� ������ ��������� ���� �������� ���� ����������� Figure 13.4

Experiment 13: Telescope 37 1. Measure do1, the distance from the object (paper pat- tern on screen) to the objective lens. 2. Determine di2, the distance from the eyepiece lens to the image. Since the image is in the plane of the object, this is equal to the distance between the eye- piece lens and the object (screen). Remember that the image distance for a virtual image is negative. 3. Calculate di1 using do1 and the focal length of the objective lens in the Thin Lens Formula (Equation 13.1). 4. Calculate do2 by subtracting di1 from the distance between the lenses. 5. Calculate the magnification using Equation 13.2. 6. Calculate the percent difference between the calcu- lated magnification and the observed value. Questions 1. Is the image inverted or upright? 2. Is the image that you see through the telescope real or virtual? Further Study Image Formed by the Objective Lens Where is the image formed by the objective lens? Is it real or virtual? Use a desk lamp to brightly illuminate the paper grid (or replace the screen with the light source’s crossed-arrow object). Hold a sheet of paper vertically where you think the image is. Do you see the image? Is it inverted or upright? Remove the sheet of paper and hold a pencil in the same place. Look through eyepiece lens; you will see two images, one of the pencil and one of the grid pattern. Are both images inverted? Use parallax to determine the location of the pencil image. Object at Infinity Remove the screen and look through the lenses at a distant object. Adjust the distance between the lenses to focus the telescope. Estimate the observed magnification. Now calculate the magnification by taking the ratio of the focal lengths of the lenses. Compare the calculated magnification to the observed magnification. How is the distance between the lenses related to their focal lengths? Table 13.1: Results Position of Objective Lens Position of Eyepiece Lens Position of Screen Observed magnification do1 di2 di1 do2 Calculated Magnification Percent Difference

Experiment 14: Microscope 39 Experiment 14: Microscope Purpose In this experiment, you will construct a microscope and determine its magnification. Theory Figure 14.1 A microscope magnifies an object that is close to the objective lens. The microscope in this experiment will form an image in the same place as the object (see Figure 14.1). The lenses are thin compared to the other distances involved, which allows the Thin Lens Formula to be used: (eq. 14.1) where f is focal length, do is the distance between the object and the lens, and di is the distance between the image and the lens. The magnification, M, of a two-lens system is equal to the product of the magnifica- tions of the individual lenses: (eq. 14.2) Set Up 1. Tape the paper grid pattern to the screen to serve as the object. 2. The +100 mm lens is the objective lens (the one closer to the object). The +200 mm lens is the eyepiece lens (the one closer to the eye). Place the lenses near the Required Equipment from Basic Optics System Bench 2 Convex Lenses (+100 mm and +200 mm) Screen Paper grid pattern (see page 45), or a 14 × 16 grid of 1 cm squares ��� ��� ��� ��� ������ ����� ���� ������� ���� ������� ��� 1 f-- 1 do ----- 1 di + ---- = M M1M2 di1 – do1 ---------- ⎝ ⎠ ⎜ ⎟ ⎛ ⎞ di2 – do2 ---------- ⎝ ⎠ ⎜ ⎟ ⎛ ⎞ = =

Experiment 14: Microscope 40 middle of the optics bench and place the screen near the end of the bench (see Figure 14.2). Figure 14.2 Procedure 1. Put your eye close to the eyepiece lens and look through both lenses at the grid pattern on the screen. Move the objective lens to bring the image into focus. Figure 14.3 2. In this step, you will adjust your microscope to make the image occur in the same place as the object. To do this, you will look at both image and object at the same time and judge their relative positions by moving your head side to side. If the image and object are not in the same place, then they will appear to move relative to each other. This effect is known as parallax. Open both eyes. Look with one eye through the lenses at the image and with the other eye past the lenses at the object (see Figure 14.3). The lines of the image (solid lines shown in Figure 14.4) will be superimposed on the lines of the object (shown as dotted lines in Figure 14.4). Move your head left and right or up and down by about a centimeter. As you move your head, the lines of the image may move relative to the lines of the object due to the parallax. Adjust the eyepiece lens to eliminate parallax. Do not move the objective lens. When there is no parallax, the lines in the center of the lens appear to be stuck to the object lines. Note: Even when there is no parallax, the lines may appear to move near the edges of the lens because of lens aberrations. Concentrate on the part of the image seen through the centers of the lenses. Be sure that the eye looking at the object (the left eye in Figure 14.3) is looking directly at the object and not through the objective lens. 3. Record the positions of the lenses and the object in Table 14.1. 4. Estimate the magnification of your microscope by counting the number of object squares that lie along one side of one image square. To do this, you must view the image through the microscope with one eye while looking directly at the object with the other eye. Remember that magnification is negative for an inverted image. Record the observed magnification in Table 14.1. ������ ������� �������������� ������� ������������� �������� ��������� ������ ��������� ���� �������� ���� ����������� Figure 14.4

Experiment 14: Microscope 41 Analysis To calculate the magnification complete the following steps and record the answers in Table 14.1: 1. Measure do1, the distance from the object (paper pat- tern on screen) to the objective lens. 2. Determine di2, the distance from the eyepiece lens to the image. Since the image is in the plane of the object, this is equal to the distance between the eye- piece lens and the object (screen). Remember that the image distance for a virtual image is negative. 3. Calculate di1 using do1 and the focal length of the objective lens in the Thin Lens Formula (Equation 14.1). 4. Calculate do2 by subtracting di1 from the distance between the lenses. 5. Calculate the magnification using Equation 14.2. 6. Calculate the percent difference between the calcu- lated magnification and the observed value. Questions 1. Is the image inverted or upright? 2. Is the image that you see through the microscope real or virtual? Further Study Image Formed by the Objective Lens Where is the image formed by the objective lens? Is it real or virtual? Us a desk lamp to brightly illuminate the paper grid (or replace the screen with the light source’s crossed-arrow object). Hold a sheet of paper vertically where you think the image is. Do you see the image? Is it inverted or upright? Remove the sheet of paper and hold a pencil in the same place. Look through eyepiece lens; you will see two images, one of the pencil and one of the grid pattern. Are both images inverted? Use parallax to determine the location of the pencil image. Increasing Magnification While looking through your microscope, move the objective lens a few centimeters closer to the object. Which way do you have to move the eyepiece lens to keep the image in focus? How close can you move the objective lens and still see a clear image? (Make a pencil mark on the paper grid so you have something very small to focus on.) What is the theoretical limit to how close you can move the objective lens? Table 14.1: Results Position of Objective Lens Position of Eyepiece Lens Position of Screen Observed magnification do1 di2 di1 do2 Calculated Magnification Percent Difference

Experiment 15: Shadows 43 Experiment 15: Shadows Purpose The purpose of this experiment is to show the umbra (darker part) and the penumbra (lighter part) of the shadow. Set Up 1. Place the two optics benches beside each other. 2. Put one light source on each bench with the point source (circular hole) facing the other end of the bench. 3. Place the screen on one of the benches at the opposite end to the light sources. Procedure 1. Plug in only one of the light sources. 2. Hold a pencil about 5 cm away from the screen so its shadow is cast on the screen. Now turn the light source around so the crossed-arrow illuminates the pencil and screen. How does the shadow change? 3. Rotate the light source back to the point-source position. Plug in the second light source. Make a sketch of the shadow of the pencil. Label the umbra and the pen- umbra. 4. Move the pencil away and toward the screen. How does the shadow change? 5. Block the light from each point source in succession to determine which part of the shadow is caused by each light source. Indicate your observation on your sketch. Required Equipment from Basic Optics System (2 systems needed) 2 Benches 2 Light Sources 1 Screen

Telescope and Microscope Test Pattern 45 Telescope and Microscope Test Pattern Attach a copy of this pattern to the viewing screen for experiments 13 and 14. 1 cm grid

Teacher’s Guide 47 Teacher’s Guide Experiment 1: Color Addition Note on procedure: Student’s expectation may differ from actual results. Encourage them to carefully observe the resulting colors and describe them accurately. Part 1, typical results: Part 1, answers to questions: 1. Mixing light is not the same as mixing paint. The mixing of colored light is additive mixing; the mixing of paint is subtractive mixing. 2. In this experiment the mixture of red, green, and blue does not look pure white to most people. To produce white light, the three colors must be present in a spe- cific ratios of intensities. Part 2, typical results: (Step 4) Under red light, black ink is easier to see than red; red ink appears nearly the same color as white paper. Part 2: answers to questions: 1. Red ink appears red because it reflects red light and absorbs other colors. Under blue light, red ink absorbs most of the visible light. 2. Under red light, red ink is difficult to see because both ink and paper reflect most of the visible light. Experiment 2: Prism Notes on procedure: (Step 3) (a) Red, Orange, Yellow, Green and Blue are seen in that order. (b) Blue is refracted at the largest angle.(c) Blue is predicted to refract at the largest angle because its index of refraction is largest. (Step 4) When colored rays enter the prism, they do not emerge parallel to each other because of their differing indices of refraction. Table 1.1: Results of Colored Light Addition Colors Added Resulting Color red + blue + green slightly bluish-white red + blue pink-purple red + green yellow-orange green + blue bluish-green Table 1.2: Colored Ink Observed Under Colored Light Color of Light Line Apparent Color of Ink Do they look different? Actual Color of Ink Blue Light A Black Yes, slightly Red B Black Black Red Light C Black Yes, slightly Blue D Black Black

Teacher’s Guide 48 Experiment 3: Reflection Part 1, typical results: Part 1, answers to questions: 1. The angle of incidence and the angle of reflection are equal. 2. The three colored rays are not reversed by the mirror. Part 2, typical results: The actual radius of both curved mirrors is about 12.5 cm. Part 2, answers to questions: 1. The radius of curvature is twice the focal length for a cylindrical mirror. The typical experimental results confirm this. 2. The radius of curvature of a plane mirror approaches infinity. Experiment 4: Snell’s Law Typical results: Answer to question: The ray leaves the rhombus at the same angle it entered. Experiment 5: Total Internal Reflection Typical results: (Step 5) Measured critical angle: θc = 41.0° (Step 6) Calculated critical angle: θc = sin−1(1/n) = sin−1(1/1.5) = 41.8° (Step 7) % Difference = 1.9% Answers to questions: 1. The internally reflected ray becomes much brighter when the incident angle is larger than the critical angle. 2. The critical angle is greater for red light. This tells us that the index of refraction is smaller. Table 3.1: Plane Mirror Results Angle of Incidence Angle of Reflection 9.0° 9.2° 16.8° 16.5° 19.0° 37.8° Table 3.2: Cylindrical Mirror Results Concave Mirror Convex Mirror Focal Length 6.2 cm 6.4 cm Radius of Curvature (determined using compass) 13.3 cm 13.2 cm Table 4.1: Data and Results Angle of Incidence Angle of Refraction Calculated index of refraction of acrylic 38.0° 26.0° 1.40 51.2° 33.8° 1.40 22.0° 14.4° 1.51 Average:1.44 (4% deviation from accepted value)

Teacher’s Guide 49 Experiment 6: Convex and Concave Lenses Typical results: (Step 5) When the lenses are nested together, parallel rays entering the lenses emerge nearly parallel; this tells us that the focal lengths are of approximately equal magnitude and opposite sign. (Step 6) By moving the lenses apart, the spacing of the rays can be changed, but they remain nearly parallel. Experiment 7: Hollow Lens Typical results: Answers to questions: 1. A plano-convex lens is converging when it has a higher index of refraction than the surrounding medium. It is diverging when it has a lower index of refraction. 2. It is not possible to predict whether a plano-concave lens of unknown material will be diverging or converging under water because its index of refraction may be less than or greater than that of water. Experiment 8: Lensmaker’s Equation Typical results: (Step 3) Measured focal length: f = −12.0 cm (Step 4) Measured focal distance of reflected rays: R/2 = 6.0 cm. Radius of curvature: R = −12.0 cm (Step 5) Calculated focal length: (Step 6) % Difference: 0.8% The actual radius of curvature or the lens is about −12.7 cm. Table 6.1: Results Convex Lens Concave Lens Focal Length 13.75 cm -12.1 cm Table 7.1: Predictions and Observations Lens surrounded by: Section 1 filled with: Section 2 filled with: Section 3 filled with: Prediction (converging or diverging) Observation (converging or diverging) Air Water Air Air diverging Air Water Air converging Air Air Water converging Water Air Water diverging Water Air Water Water converging Water Air Water diverging Water Water Air diverging f n – 1 ( ) 1 R ⁄ 1 R ⁄ + ( ) [ ] 1 – 1.5 – 1 ( ) 1 –12.0 cm ( ) ⁄ 1 –12.0 cm ( ) ⁄ + ( ) [ ] 1 – –12.1 cm = = =

Teacher’s Guide 50 Experiment 9: Apparent Depth Typical results: Typical ray-tracing results are represented at 50% scale in Figure TG.1. The gray regions represent the actual light beams; the black lines and dots represent the student’s actual marks. Notice that this student traced along the edges of the light beams. The actual thickness of the rhombus is t = 3.175 ± 0.025 cm. Based on the accepted value of n = 1.49, the theoretical apparent depth is d = 2.13. Answers to questions: 1. Of the two methods, the parallax method is the more precise. Using that method, both d and t could be measured with a precision of less than 1 mm. Using the ray-tracing method, the points at which the rays crossed had a larger uncertainty due to the thickness of the light beams. 2. For the typical data above, the percent differences between the accepted and experimental values of n are 0.7% for Part 1 and 5% for Part 2. Experiment 10: Reversibility Typical results: Table 1.1: Results d t n Part 1: Parallax method 2.12 cm 3.18 cm 1.50 Part 2: Ray-tracing method 2.23 cm 3.18 cm 1.43 Table 10.1: Data Trial 1 Ray Incident on Flat Surface Trial 2 Ray Incident on Curved Surface Angle of Incidence θi1 Angle of Refraction θr1 Angle of Incidence θi2 Angle of Refraction θr2 0° 0 0 1.0 10° 7.0 7.0 7.5 20° 13.5 13.5 19.5 30° 20.0 20.0 30.0 40° 25.5 25.5 39.0 50° 31.0 31.0 49.0 60° 35.5 35.5 59.0 70° 39.5 39.5 70.0 80° 41.0 41.0 77.0 ������� Figure TG.1

Teacher’s Guide 51 Notes on analysis: 1. One way to find nacrylic is to plot sin(θi1) versus sin(θr1) and find the best-fit line. The slope of the line is equal to 1/nacrylic. Using this method and the data above, nacrylic= 1.498 for Trial 1. 2. For Trial 2, nacrylic is the slope of sin(θi2) versus sin(θr2), thus nacrylic= 1.50. Answers to questions: 1. Yes, the law of refraction is the same for light going in either direction between the two media. 2. Yes, the principle of optical reversibility holds for both reflection and refraction, thus the law that the angle of incidence equals the angle of reflection. Experiment 11: Dispersion Typical results from analysis: 1. Color separation was first noted at about 40°, although it may be noticeable before then depending on the light in the room. 2. Maximum separation occurs at about 85°; beyond that the violet is totally internally reflected. 3. In order, the colors seen are: red, orange, yellow, green, cyan, blue, violet (though not all colors may be resolvable depending on the room light). 4. With an incident angle of 40°, the violet refracted at 76° and the red at 73°; therefore nred = 1.488 and nblue = 1.510 Experiment 12: Focal Length and Magnification of a Thin Lens Note on equipment: Provide students with the +100 mm mounted lens. Cover the focal length indicated on the label. Other converging lenses will work, but you may have to modify the light source-to-screen values given in Table 12.1. Part 1: For a distant object, 1/do approaches zero, therefore the image will form clearly with a lens-to-screen distance of di = f ≅ 10 cm. ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� Trial 2 slope = 1.498 ± 0.009 Trial 1 slope = 0.666 ± 0.013 1/slope = 1.50 ± 0.03

Teacher’s Guide 52 Part 2: Typical results. y-intercept = 1/f = 0.0977 cm-1 x-intercept = 1/f = 0.103 cm-1 Answers to questions: 1. The image if inverted. 2. The image is real because it can be viewed on a screen. 3. For a given object-to-image distance, the two object distance-image distance pairs are the inverse of each other, which demonstrates the reversibility of light through a lens. 4. The magnification is negative because the image is inverted. 5. The three determined values of f are unlikely to be exactly equal, primarily due to measure- ment error. Table 12.1: Image and Object Distances Distance from light source to screen do (cm) di (cm) 1/do (cm-1) 1/di (cm-1) Image Size Object Size 100 cm 88.5 11.5 0.0113 0.0870 5.5 mm 42 mm 11.0 89.0 0.0909 0.0112 81 mm 10 mm 90 cm 78.3 11.7 0.0128 0.0855 11.3 78.7 0.0885 0.0127 80 cm 68.0 12.0 0.0147 0.0833 11.5 68.5 0.0870 0.0146 70 cm 57.7 12.3 0.0173 0.0813 11.9 58.1 0.0840 0.0172 60 cm 47.1 12.9 0.0212 0.0775 12.3 47.7 0.0813 0.0210 50 cm 36.0 14.0 0.0278 0.0714 13.4 36.6 0.0746 0.0273 Table 12.2: Focal Length f Result from x-intercept 9.75 cm Result from y-intercept 10.2 cm % difference between results from intercepts 4.4% Average of results from intercepts 9.98 cm Result from Part I 10.0 cm % difference between Average of results from intercepts and result from Part I 0.2% Table 12.3: Magnification Point 1 Point 2 calculated from image and object distances -0.130 -8.09 calculated from image and object sizes 0.13 8.1 % difference 0% 0.1% M M

Teacher’s Guide 53 Experiment 13: Telescope Typical results: Answers to questions: 1. The image is inverted. 2. It is a virtual image. Further study, Image Formed by the Objective Lens: The objective lens forms a real, upright image; to see it, hold a sheet of paper at distance di1 from the objective. When a pencil is placed at this location, it’s vir- tual image, viewed through the eyepiece lens, coincides with the virtual image of the grid pattern viewed through both lenses. Further study, Object at Infinity: When adjusted for a distant object, the distance between the lenses is equal to the sum of the focal lengths. Experiment 14: Microscope Typical results: Answers to questions: 1. The image is inverted. 2. It is a virtual image. Further study, Image Formed by the Objective Lens: The objective lens forms a real, upright image; to see it, hold a sheet of paper at distance di1 from the objective. When a pencil is placed at this location, it’s vir- Table 13.1: Results Position of Objective Lens 63.4 cm Position of Eyepiece Lens 102.2 cm Position of Screen 0.0 cm Observed magnification -5 do1 63.4 cm di2 -102.2 cm di1 29.2 cm do2 9.6 cm Calculated Magnification -4.9 Percent Difference 2% Table 14.1: Results Position of Objective Lens 20.9 cm Position of Eyepiece Lens 54.9 cm Position of Screen 0.0 cm Observed magnification -3 do1 20.9 cm di2 -54.9 cm di1 19.2 cm do2 14.8 cm Calculated Magnification -3.41 Percent Difference 12%

Teacher’s Guide 54 tual image, viewed through the eyepiece lens, coincides with the virtual image of the grid pattern viewed through both lenses. Further study, Increasing Magnification: As the objective lens is moved closer to the object, the eye- piece must be moved further away. In practice, the objective can be moved to within about 13 cm before distor- tion from lens aberrations becomes significant. The theoretical limit is 10 cm, or the focal length of the objective lens. Experiment 15: Shadows When the pencil is illuminated by the point source, the shadow appears sharper than when illuminated by a dis- tributed light source (the crossed-arrow object). When illuminated by both point sources, the pencil casts two shadows. The area where the shadows overlap is the umbra. The areas of partial shadow are the penumbra. By moving the pencil toward the screen, the relative size of the umbra is increased. By moving the pencil away from the screen, the umbra is decreased until the two shadow separate entirely.

Technical Support 55 Technical Support For assistance with any PASCO product, contact PASCO at: Limited Warranty For a description of the product warranty, see the PASCO catalog. Copyright The PASCO scientific 012-09614B Basic Optics System Instruction Manual is copyrighted with all rights reserved. Permission is granted to non-profit educational institutions for reproduction of any part of this manual, providing the reproductions are used only in their laboratories and classrooms, and are not sold for profit. Reproduction under any other circumstances, without the written con- sent of PASCO scientific, is prohibited. Trademarks PASCO and PASCO scientific are trademarks or registered trademarks of PASCO scientific, in the United States and/or in other coun- tries. All other brands, products, or service names are or may be trademarks or service marks of, and are used to identify, products or services of, their respective owners. For more information visit www.pasco.com/legal. Address: PASCO scientific 10101 Foothills Blvd. Roseville, CA 95747-7100 Phone: 916-786-3800 (worldwide) 800-772-8700 (U.S.) Fax: (916) 786-3292 Web: www.pasco.com Email: [email protected] Authors: Ann Hanks Dave Griffith Alec Ogston