Basic Optics System OS-8515C

Transcription

1 T BASIC OPTICS RAY TABLE Instruction Manual with Experiment Guide and Teachers Notes B Basic Optics System OS-8515C Optics Bench OS-8465 NORMAL NORMAL COMPONENT COMPONENT

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3 Basic Optics System Table of Contents Introduction About the Equipment Storage Box About the Experiments Experiment 1: Color Addition Experiment 2: Prism Experiment 3: Reflection Experiment 4: Snell s Law Experiment 5: Total Internal Reflection Experiment 6: Convex and Concave Lenses Experiment 7: Hollow Lens Experiment 8: Lensmaker s Equation Experiment 9: Apparent Depth Experiment 10: Reversibility Experiment 11: Dispersion Experiment 12: Focal Length and Magnification of a Thin Lens Experiment 13: Focal Length and Magnification of a Concave Mirror Experiment 14: Virtual Images Experiment 15: Telescope Experiment 16: Microscope Experiment 17: Shadows Telescope and Microscope Test Pattern Teacher s Guide Storage Box Technical Support

4 T Basic Optics System OS-8515C 1 Optics Bench NORMAL NORMAL COMPONENT OS-8465 COMPONENT BASIC OPTICS RAY TABLE a d e f b c

5 Included Equipment Part Number 1. Viewing Screen OS Adjustable Lens Holder OS mm Mounted Lens mm Mounted Lens mm Mounted Lens mm Mounted Lens 7. Concave/convex Mirror 8. Half-screen OS-8456 OS-8519 OS Light Source OS m Optics Bench OS Ray Table with D-shaped Lens OS Ray Optics Kit with: OS-8516A a. Storage Box/Water Tank b. Mirror c. Hollow Lens OS-8511 d. Convex Lens e. Concave Lens f. Acrylic Trapezoid Storage Box 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 17 typical experiments. For an even greater variety, you can expand the system with any of the Basic Optics kits and components available from PASCO, including lasers, polarizers, diffraction slits, and light sensors. See the PASCO Physics catalog or visit for details. 5

6 Basic Optics System About the Equipment 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 adjustable 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. metric scale for measuring component positions 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. T-slots Mounted Lenses The Basic Optics System includes four lenses mounted in holders. 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 lenses. Mount the screen on the bench to view real images formed by Concave/convex Mirror and Half-screen The mounted mirror is concave on one side and convex on the other side. The radius of curvature of both surfaces is 200 mm. Use the half-screen to view real images formed by the concave side of the mirror. Ray Table and D-shaped Lens Use the ray table and D-shaped lens on a tabletop 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. 6

7 Model No. OS-8515C Storage Box Storage Box Use the foam-padded box to store, organize, and protect the system s components. Place the components in the fitted compartments as illustrated below. Extra compartments are included for additional components as spare parts. A full-page diagram appears on page 69. Remove or copy that page and attach it the box lid. Light Source AC Adapter Ray Optics Kit Concave/convex Mirror D-shaped Lens +100 mm +200 mm +250 mm -150 mm Ray Table and Adjustable Lens Holder Viewing Screen Half-screen Lenses 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 59. 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, protractor, and drawing compass. 1. Color Addition (page 9): Explore the results of mixing colored light and illuminating colored ink with colored light. 2. Prism (page 11): Show how a prism separates white light into its component colors and show that different colors are refracted at different angles through a prism. 3. Reflection (page 13): Show how rays are reflected from plane, concave, and convex mirrors. 4. Snell s Law (page 15): Determine the index of refraction of acrylic by measuring angles of incidence and refraction of a ray passing through the trapezoid. 5. Total Internal Reflection (page 17): Determine the critical angle at which total internal reflection occurs in the trapezoid. 7

8 Basic Optics System About the Experiments 6. Convex and Concave Lenses (page 19): Use ray tracing to determine the focal lengths of lenses. 7. Hollow Lens (page 21): Use the hollow lens and water to 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. 8. Lensmaker s Equation (page 23): Determine the focal length of a concave lens by measuring its radius of curvature. 9. Apparent Depth (page 25): Measure the apparent depth of the trapezoid 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 29): Explore how the relationship between the angles of incidence and refraction is related to the direction of propagation. 11. Dispersion (page 31): 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 17 also use the Light Source. 12. Focal Length and Magnification of a Thin Lens (page 33): Determine the focal length of a converging lens and measure the magnification for a certain combination of object and image distances. 13. Focal Length and Magnification of a Concave Mirror (page 37): Determine the focal length of a concave mirror and measure the magnification for a certain combination of object and image distances. 14. Virtual Images (page 41): Study virtual images formed by a diverging lens and a convex mirror. 15. Telescope (page 47): Construct a telescope and determine its magnification. 16. Microscope (page 51): Construct a microscope and determine its magnification. 17. Shadows (page 55): Show the umbra and the penumbra of a shadow. 8

9 Model No. OS-8515C Experiment 1: Color Addition Experiment 1: Color Addition 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 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. Light source Convex lens Part 1: Addition of Colored Light Folded paper 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. Red, green, and blue rays Figure 1.1: Color addition Combined colors 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 observation in Table Now block the green ray with a pencil. What color results from adding red and blue light? Record the result in Table Block each color in succession to see the addition of the other two colors and complete Table 1.1. Table 1.1: Results of Colored Light Addition Colors Added Resulting Color red + blue + green red + blue red + green green + blue 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. 9

10 Basic Optics System Experiment 1: Color Addition 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 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.) 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 Red Light A B 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 Red Light A B C D 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? 10

11 Model No. OS-8515C Experiment 2: Prism Experiment 2: Prism Required Equipment from Basic Optics System Light Source Trapezoid from Ray Optics Kit Blank white paper Purpose Incident ray Normal to surface 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. n 1 q 1 Surface Theory n 2 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, q 2 Refracted ray (n 1 > n 2 ) n 1 sin θ 1 = n 2 sin θ 2 Figure 2.1: Refraction of Light the angle of refraction (θ 2 ) depends on the angle of incidence (θ 1 ) and the indices of refraction of both media (n 1 and n 2 ), 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 frequency is bent a different amount. The trapezoid is made of acrylic which has an index of refraction of for light of wavelength 486 nm in a vacuum (blue light), for wavelength 589 nm (yellow), and for wavelength 651 nm (red). In general for visible light, index of refraction 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. Color spectrum Single white ray q Normal to surface Figure Position the trapezoid as shown in Figure 2.2. The acute-angled end of the trapezoid is used as a prism in this experiment. Keep the ray near the point of the trapezoid for maximum transmission of the light. 11

12 Basic Optics System Experiment 2: Prism 3. Rotate the trapezoid 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 trapezoid at the same angle that the white ray did. Do the colored rays emerge from the trapezoid parallel to each other? Why or why not? 12

13 Model No. OS-8515C Experiment 3: Reflection Experiment 3: Reflection Required Equipment from Basic Optics System Light Source Mirror from Ray Optics Kit Other Required Equipment Drawing compass Protractor Metric ruler White paper Purpose In this experiment, you will study how rays are reflected from different types of mirrors. You will measure the focal length and determine the radius of curvature of a concave 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). Normal to surface Incident ray Reflected ray Figure Measure the angle of incidence and the angle of reflection. Measure these angles from the normal. Record the angles in the first row Table 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. Table 3.1: Plane Mirror Results Angle of Incidence Angle of Reflection 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 13

14 Basic Optics System Experiment 3: Reflection 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 center of the mirror surface. The radius of curvature (R) of the mirror is twice the focal length. See Figure 3.2. R focal point f mirror 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.) Figure The place where the five reflected rays cross each other is the focal point of the mirror. Mark the focal point. Incident rays 3. Measure the focal length from the center of the concave mirror surface (where the middle ray hit the mirror) to the focal point. Record the result in Table 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. Figure 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. Table 3.2: Cylindrical Mirror Results Concave Mirror Convex Mirror Focal Length Radius of Curvature (determined using compass) 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? 14

15 Model No. OS-8515C Experiment 4: Snell s Law Experiment 4: Snell s Law Required Equipment from Basic Optics System Light Source Trapezoid from Ray Optics Kit Other Required Equipment Protractor White paper Purpose The purpose of this experiment is to determine the index of refraction of the acrylic trapezoid. For rays entering the trapezoid, you will measure the angles of incidence and refraction and use Snell s Law to calculate the index of refraction. Incident ray q 1 Normal to surface Theory n 1 n 2 Surface For light crossing the boundary between two transparent materials, Snell s Law states n 1 sin θ 1 = n 2 sin θ 2 where θ 1 is the angle of incidence, θ 2 is the angle of refraction, and n 1 and n 2 are the respective indices of refraction of the materials (see Figure 4.1). q 2 Figure 4.1 Refracted ray (n 1 > n 2 ) 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 trapezoid on the paper and position it so the ray passes through the parallel sides as shown in Figure 4.2. q i Incident ray 3. Mark the position of the parallel surfaces of the trapezoid and trace the incident and transmitted Figure 4.2 rays. Indicate the incoming and the outgoing rays with arrows in the appropriate directions. Carefully mark where the rays enter and leave the trapezoid. 4. Remove the trapezoid and draw a line on the paper connecting the points where the rays entered and left the trapezoid. This line represents the ray inside the trapezoid. 5. Choose either the point where the ray enters the trapezoid or the point where the ray leaves the trapezoid. At this point, draw the normal to the surface. 6. Measure the angle of incidence (θ i ) 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

16 Basic Optics System Experiment 4: Snell s Law 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. Table 4.1: Data and Results Angle of Incidence Angle of Refraction Calculated index of refraction of acrylic Average: 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 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 trapezoid relative to the ray that enters it? 16

17 Model No. OS-8515C Experiment 5: Total Internal Reflection Experiment 5: Total Internal Reflection Required Equipment from Basic Optics System Light Source Trapezoid from Ray Optics Kit Other Required Equipment Protractor White paper Purpose In this experiment, you will determine the critical angle at which total internal reflection occurs in the acrylic trapezoid and confirm your result using Snell s Law. Theory Incident ray Reflected ray For light crossing the boundary between two transparent materials, Snell s Law states q 1 n 1 sin θ 1 = n 2 sin θ 2 n 1 Surface where θ 1 is the angle of incidence, θ 2 is the angle of refraction, and n 1 and n 2 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 trapezoid, from acrylic (n =1.5) to air (n air =1). n 2 Figure 5.1 q 2 Refracted ray (n 1 > n 2 ) If the incident angle (θ 1 ) is greater than the critical angle (θ c ), there is no refracted ray and total internal reflection occurs. If θ 1 = θ c, the angle of the refracted ray (θ 2 ) is 90, as in Figure 5.2. In this case, Snell s Law states: n sin θ c = 1 sin 90 Incident ray q c Reflected ray Solving for the sine of critical angle gives: 1 sin θ c = -- n n n air = 1 90 Refracted ray Figure

18 Basic Optics System Experiment 5: Total Internal Reflection Procedure 1. Place the light source in ray-box mode on a sheet of white paper. Turn the wheel to select a single ray. Reflected ray 2. Position the trapezoid as shown in Figure 5.3, with the ray entering the trapezoid at least 2 cm from the tip. 3. Rotate the trapezoid until the emerging ray just barely disappears. Just as it disappears, the ray separates into colors. The trapezoid is correctly positioned if the red has just disappeared. 4. Mark the surfaces of the trapezoid. 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. Incident ray Figure 5.3 Refracted Ray 5. Remove the trapezoid and draw the rays that are incident upon and reflected from the inside surface of the trapezoid. 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: Exit point θ c = (experimental) Entrance point 2q c Reflection point 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: Figure 5.4 θ c = (theoretical) 7. Calculate the percent difference between the measured and theoretical values: Questions % difference = 1. How does the brightness of the internally reflected ray change when the incident angle changes from less than θ c to greater than θ c? 2. Is the critical angle greater for red light or violet light? What does this tell you about the index of refraction? 18

19 Model No. OS-8515C Experiment 6: Convex and Concave Lenses Experiment 6: Convex and Concave Lenses 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 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 Figure 6.1). Incoming rays 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 directions. Convex lens Figure 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. Table 6.1: Results Convex Lens Concave Lens Focal Length 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.) 19

20 Basic Optics System Experiment 6: Convex and Concave Lenses 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

21 Model No. OS-8515C Experiment 7: Hollow Lens Experiment 7: Hollow Lens 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) 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-concave 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. Figure 7.1: The hollow lens 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 parallel rays enter it through the flat side. Do the rays converge or diverge after passing through the lens? Record your observation in Table

22 Basic Optics System Experiment 7: Hollow Lens Repeat this step with water in different section of the lens to complete the first four rows of Table 7.1. 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) Water Air Air Air Air Water Air Air Air Water Water Air Water Air Water Water Water Water Air Water Water Water Air 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. Box Incident rays Hollow lens 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. Questions Repeat this step with air in different section of the lens to complete Table Under what conditions is a plano-convex lens converging? Under what conditions is it diverging? 2. If a plano-concave lens of an unknown material is a diverging lens when surrounded by air, is it possible to know whether the lens will be converging or diverging when placed in water? Explain. 22

23 Model No. OS-8515C Experiment 8: Lensmaker s Equation Experiment 8: Lensmaker s Equation Required Equipment from Basic Optics System Light Source Concave Lens from Ray Optics Kit Other Required Equipment Metric ruler 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 curvature 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 (R 1 and R 2 ) and the index of refraction (n) of the lens material: (eq. 8.1) ( n 1) = f R 1 R 2 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). Double Concave Lens R 1 R 2 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 Figure 8.2). Incoming rays Note: The lens has one flat edge. Place the flat edge on the paper so the lens stands stably without rocking. Concave lens Figure

24 Basic Optics System Experiment 8: Lensmaker s Equation 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 directions. 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: 1/2 R Concave lens Figure 8.3: Reflected rays from the lens surface R = 5. For this lens, it is not necessary to measure the curvature of both sides because they are equal (R 1 = R 2 = R). Calculate the focal length of the lens using the lensmaker 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 = 24

25 Model No. OS-8515C Experiment 9: Apparent Depth Experiment 9: Apparent Depth Required Equipment from Basic Optics System Light Source Trapezoid 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 Purpose In this experiment, you will use two different methods to measure the apparent depth of the acrylic trapezoid. 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 surface of the block is less than the actual thickness, t, of the block. The apparent depth is given by n air = 1 n > 1 d t top (eq. 9.1) d = t/n where n is the index of refraction of the material. Part 1: Parallax Method Background Figure 9.1 bottom Place this page flat on the table in front of you. Hold a pencil horizontally a few centimeters 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 trapezoid on the paper over the line as shown in Figure

26 Basic Optics System Experiment 9: Apparent Depth Trapezoid Figure With both eyes, look down through the top of the trapezoid. Does the line viewed through the trapezoid 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 trapezoid and the line viewed directly? 3. In this step, you will hold a pencil near the trapezoid 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 trapezoid (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 trapezoid. 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 trapezoid with your free hand, press the pencil tip gently against the side of the trapezoid and twist the pencil to make a light mark. Erase the mark after you have finished this experiment.) Figure 9.3 Look down Move eye side to side Hold pencil still Analysis 1. Measure the distance from the top of the trapezoid to your pencil mark. Record this apparent depth, d, in the first row of Table Measure the thickness, t, of the trapezoid and record it in Table Use Equation 9.1 to calculate the index of refraction and record your result in Table 9.1. Part 1: Parallax method Part 2: Ray-tracing method Table 9.1: Results d t n 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 trapezoid there yet). Note: The lens has one flat edge. Place the flat edge on the paper so the lens stands stably without rocking. 26

27 Model No. OS-8515C Experiment 9: Apparent Depth 2. Mark the place on the paper where the two rays cross each other. 3. Position the trapezoid as shown in Figure 9.4. The bottom surface of the trapezoid 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. t d top surface 4. Trace the trapezoid and trace the rays diverging from the top surface. bottom surface 5. Remove the trapezoid and light source. Trace the diverging rays back into the trapezoid. The point where these rays cross (inside the trapezoid) is the apparent position of the bottom of the trapezoid when viewed through the top. Convex lens Analysis Mirror on edge 1. Measure the apparent depth, d, and record it in Table Use Equation 9.1 to calculate the index of refraction and record your result in Table 9.1. Figure 9.4 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 = What was the percent difference between the accepted value and each of your two results? 27

28 Basic Optics System Experiment 9: Apparent Depth 28

29 COMPONENT COMPONENT COMPONENT COMPONENT Model No. OS-8515C Experiment 10: Reversibility Experiment 10: Reversibility Required Equipment from Basic Optics System Ray Table D-shaped Lens Light Source 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. Trial 1 Trial 2 Angle of incidence θ i OS NORMAL NORMAL COMPONENTT C COMPONENT BASIC OPTICS RAY TABLE Angle of refraction θ r1 Angle of incidence θ i NORMAL NOR NORMAL COMPONENT T BASIC OPTICS RAY TABLE C COMPONENT OS Angle of refraction θ r2 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. Light Source Ray Table NORMAL NORMAL BASIC OPTICS RAY TABLE OS Put the D-shaped lens on the ray table exactly centered in the marked outline. Single Ray Figure 10.2: Initial setup for Trial 1 29

30 Basic Optics System Record Data Table 10.1: Data Experiment 10: Reversibility Trial 1 Trial 1 Ray Incident on Flat Surface Trial 2 Ray Incident on Curved Surface 1. Turn the ray table so the incoming ray enters the lens through the flat surface (see Figure 10.2). Angle of Incidence θ i Angle of Refraction θ r1 Angle of Incidence θ i2 Angle of Refraction θ r2 2. Rotate the ray table to set the angle of incidence to each of the values listed in the first column of Table For each angle of incidence (θ i1 ), observe the corresponding angle of refraction (θ r1 ) 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 (θ i2 ) that you wrote in the third column of the table, observe the corresponding angles of refraction (θ r2 ) and record them in the fourth column. Analysis 1. Using your values for θ i1 and θ r1 and Snell s Law (Equation 10.1), determine the index of refraction of acrylic (n acrylic ). Assume the index of refraction of air (n air ) is 1.0. (eq. 10.1) n air sin( θ i1 ) = n acrylic sin( θ r1 ) n acrylic = (from θ i1 and θ r1 ) 2. Determine n acrylic again, this time using your values of θ i2 and θ r2. Questions n acrylic = (from θ i2 and θ r2 ) 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. 30

31 COMPONENT COMPONENT COMPONENT COMPONENT Model No. OS-8515C Experiment 11: Dispersion Experiment 11: Dispersion Required Equipment from Basic Optics System Ray Table D-shaped Lens Light Source 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 (n 1 ), the index of refraction of the second medium (n 2 ), the angle of incidence (θ 1 ), and the angle of refraction (θ 2 ): (eq. 11.1) n 1 sinθ 1 = n 2 sinθ 2 Incident ray q 1 n 1 n 2 acrylic air q 2 Refracted ray (n 1 > n 2 ) Figure 11.1 We can assume the index of refraction of air (n 2 in this experiment) is always equal to 1.0. However, the index of refraction of acrylic (n 1 ) 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 Light Source Ray Table 1. Place the light source in ray-box mode on a flat tabletop. Turn the wheel to select a single ray 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) BASIC OPTICS RAY TABLE OS-8465 NORMAL NORMAL Put the acrylic D-shaped lens on the ray table in the marked outline. Turn the ray table so Single Ray Figure

32 Basic Optics System Experiment 11: Dispersion Procedure the ray enters the lens through the curved surface, and the angle of incidence is Hold a piece of white paper vertically near the edge of the Ray Table so the outgoing 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 minimum to maximum angle of refraction.) 4. Use Snell s Law (Equation 11.1) to calculate the index of refraction of acrylic for red light (n red ) and the index of refraction for blue light (n blue ). 32

33 Model No. OS-8515C Experiment 12: Focal Length and Magnification of a Thin Lens Experiment 12: Focal Length and Magnification of a Thin Lens Required Equipment from Basic Optics System Light Source Bench Converging lens of unknown focal length 1 Screen Other Equipment Metric ruler Optics Caliper (optional, for measuring image sizes), PASCO part OS Instructors: see note on page 63. 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) 1 -- f = d o d i where f is focal length, d o is the distance between the object and the lens, and d i is the distance between the image and the lens. By measuring d o and d i 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 measurement of d i with d o. 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, d i. Analysis d i = 1. As d o approaches infinity, what does 1/d o approach? 33

34 Basic Optics System Experiment 12: Focal Length and Magnification of a Thin Lens 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/d o versus 1/d i. 1 m Screen Light source Lens 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 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). Measure object or image size between two pattern features 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/d o and 1/d i for all 12 rows in Table Plot 1/d o versus 1/d i 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: Figure 12.2 y-intercept = 1/f = x-intercept = 1/f = Note: You can plot the data and find the best-fit line on paper or on a computer. 34

35 Model No. OS-8515C Experiment 12: Focal Length and Magnification of a Thin Lens Table 12.1: Image and Object Distances Distance from light source to screen d o d i 1/d o 1/d i Image Size Object Size 100 cm 90 cm 80 cm 70 cm 60 cm 50 cm 3. For each intercept, calculate a value of f and record it in Table Find the percent difference between these two values of f and record them in Table 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 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 Analysis Part B: Magnification 1. For the first two data points only (the first two lines of Table 12.2), use the image and object distances to calculate the magnification, M, at each position of the lens. Record the results in Table (eq. 12.2) d i M = ---- d o 35