Geometric Optics with Lenses PURPOSE: To observe the refraction of light off through lenses; to investigate the relationship between objects and images; to study the relationship between object distance, image distance, and focal length and to investigate magnification. EQUIPMENT: Ray box with power supply, lens kit, white paper, ruler, protractor, colored pencils, optics bench with component holders, 100 mm focal length convex lenses, viewing screen, calculator. Part 1 Investigating Snell s Law Light waves refract (bend) if they pass through a transparent medium which causes them to change speed. Snell s Law describes the relationship of incident and refracted rays when the medium changes. We shall investigate what occurs when light rays go from air to acrylic. The speed of light through acrylic is 2.00 x 10 8 m/s. Assume the speed of light in air = c. What is the index of refraction for: a. air, (n 1 in Fig.1)? Fig.1 b. acrylic (n 2 in Fig. 1) Procedure ➀ Place the ray box, on a white sheet of paper on the table. Slide the ray mask until only one white ray is showing. This will be the incident ray, as shown on the diagram, right. ➁ Place the rhombus from the lens kit on the table and position it so the ray passes through the parallel sides as shown in Fig. 2. ➂ Trace the parallel surfaces of the rhombus, the incident ray, Fig.2 and the transmitted ray (leaves the rhombus). Indicate the incoming and the outgoing rays with arrows in the appropriate directions. ➃ Remove the rhombus and draw a line connecting the points where the ray entered and left the rhombus. This represents the refracted ray inside the rhombus. ➄ At the point where the ray enters the rhombus, draw the normal to the incident surface with a dashed line. Continue it all the way through to the parallel side, as shown in Fig 2. ➅ Measure the angle of incidence (θ1) and the angle of refraction (θ2) with a protractor. Both these angles should be measured from the normal. Record the values in the data table, below. Repeat for another angle. ➆ Use Snell s Law to calculate a theoretical angle of refraction (θ2-th). Record the values in the data table. Calculate the percent difference between theoretical and measured (experimental) values for θ 2. 1
Data Table for Snell s Law Angle of incidence (θ1) Angle of Refraction (θ2) Experimental Angle of Refraction (θ2-th) Theoretical Percent difference Questions: 1. Explain how your data support Snell s Law: 2. What is the angle of the ray that leaves the rhombus (transmitted ray) relative to the incident ray? Explain why this is the case? Part 2 Concave and Convex Lens Procedure ➀ Place the ray box on a white piece of paper. Using five white rays from the ray box, shine the rays straight into the Fig. 3 convex lens from the lens kit. 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. ➁ The ray box simulates light rays coming from a long distance and striking the lens parallel to the principal axis. Measure the length from the center of the convex lens to where the refracted rays cross. Record the result in the data table below. What is the place called where the five refracted rays cross each other? ➂ Repeat the procedure for the concave lens. Note that in Step 2, the rays leaving the lens are diverging and they will not cross. Use a ruler to extend the outgoing rays straight back through the lens to find where these extended rays cross. ➃ What is different about where the focal point for the concave lens is located, relative to the focal point of the convex lens? 2
➄Nest the convex and concave lenses together and place them in the path of the parallel rays. the rays. What does this tell you about the relationship between the focal lengths of these two lenses? Part 3 Image Formation for the Convex Lens PROCEDURE: 1. Set up the optics bench as shown below. Note that in this picture the light source (ray box) and the object (crossed arrow target) are the same. 2. Use the lens labeled 100 mm. Please note that this is a nominal focal length, and they are all somewhat different. Assume 100 mm is the true focal length for the time being, choose a distance, d o, that is greater than twice the focal length (i.e. greater than 200mm). Predict the following for this value of d o : Fig.4 a. Will the image be larger, smaller, or the same size? b. Will the image be upright or inverted? c. Will the image be real or virtual? d. Will the value for d i be greater than, equal to, or less than d o? 3. Do it! Put the lens at your chosen distance of d o from the crossed arrow target and slide the screen to the place where the image is the most sharply focused. Now calculate the actual focal length for your 100mm lens. Is d o greater than the true value of 2f? If not, change your d o value so that it is and find the new image. Enter your results in the table, below. You may get a slightly different value of f for each measurement. When measuring the size of the object, choose something easily seen in the image (e.g. the arrow, or the inner target). 3
Distance of lens from object d o > 2f f < d o < 2f d o = 2f d o < f d o = f d o mm d i mm f mm (calculate) size of object mm size of image mm Actual magnification h i /h 0 4. How did your predictions compare with the experiment? Explain: 5. Repeat the process for a value of d o which is greater than f, but less than 2f. Predict the following for this value of d o : a. Will the image be larger, smaller, or the same size? b. Will the image be upright or inverted? c. Will the image be real or virtual? d. Will the value for d i be greater than, equal to, or less than d o? 5. Do it! Enter the results in the table. How was this image different than the previous case? How was it similar? 6. Based on the previous two experiments, predict the magnification of the image when the lens is placed at a distance of exactly 2f from the crossed arrow target. m = 7. Do it! Enter the results in the table. What do you notice about the values of d o and d i compared to each other? Did the actual magnification agree with your prediction? 8. Predict the following for a value of d o that is less than the focal length: 4
a. Will the image be larger, smaller, or the same size? b. Will the image be upright or inverted? c. Will the image be real or virtual? d. Will the value for d i be greater than, equal to, or less than d o? 9. Do it! In this case, it is not possible to obtain the value of d i by finding a focused image on the screen. Determine where the image should be and how you should go about finding it. 10. Put the lens at the focal length (use the average of all the calculated focal lengths). Can you find an image with the screen? By looking through the lens? Where should the image be? Fill in the table with the values that you can obtain, either by measurement or by calculation. 11. Which of these arrangements (d o > 2f, f < d o < 2f, etc.) is used to make a slide projector show an image on a screen. How do you make the screen image appear upright? 12. Which of these arrangements (d o > 2f, f < d o < 2f, etc.) is used to make the image at the back of a camera? 13. When you take a picture, you often use an adjustment to get the object in focus. What do you think is happening inside of the camera when you do this? 14. Use the 3 special rays for the thin lens configurations that follow. 5
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