Experiment 1: Law of Geometrical Optics Objectives: Verify the law of reflection using experiments. Verify the law of refraction using experiments. Measure the index of refraction of water. Pre Lab: 1. Find the definition and equations of the reflection and refraction laws. 2. What is the difference between an internal reflection and an external reflection? 3. Define and provide an equation for the critical angle. 4. Define total internal reflection (TIR). 5. Find the refractive index for the following media: water, plastic, glass. 6. Calculate the critical angle for an air-water interface assuming nair = 1. 7. Can internal reflection be used to determine the refractive index of a medium? If so, how? 8. Complete the following table: find the theoretical refracted angles corresponding to the following incident angles. Your TA will identify the media. Incident angles (deg) Refracted angles (deg) 10 20 30 50 70 90 9. Use your knowledge of trigonometric functions to find an expression for r, the angle between the laser beam direction and the reflected beam direction, using lengths x and y in the Figure 1. Does your formula work for oblique angles r too? If not, explain why, and how would you modify it to work? Figure 1. Reflection diagram for question 7 [Source: Projects in Optics: Applications Workbook, Newport Corporation] Note on data taking: The measurements and recording of data for these experiments are as important as the effects you will be exploring. Good record keeping is fundamental to good science and engineering. Part A: Law of Reflection Equipment Required: Laser Assembly (LA) Beam Steering Assembly (BSA-I) Rotation Stage (R) Sheet of paper Masking tape Experiment setup: 1. Place the Beam Steering Assembly on a Rotation Stage (R). 2. Locate the Laser and BSA as shown in Fig. 2. 3. Tape a sheet of paper on the wall at the same height at which you set the Laser. Fig. 2: Setup for the Law of Reflection experiment (view from above) [Source: Projects in Optics: Applications Workbook, Newport Corporation] 4. Adjust the beam steering mirror to reflect the laser beam back onto itself. a. Record the position of the rotation stage as 0 in Table 1 below. b. Note that there are two reflections to line up as you aim the beam back onto itself. Explain these. (Why isn't there just one?) 5. Scan the angle of the mirror by turning (R) such that the laser beam is reflected onto the piece of paper on the wall. a. Record the new angle in Table 1 (column A). b. Mark on the paper on the wall the location of the center of the beam. c. Repeat this process for 4 more different rotation stage angles that produce beam positions separated by at least an inch on the wall. 6. Refer back to Figure 1. Measure and record lengths corresponding to x and y. 7. Using the equation found in Pre Lab section, determine the angle r for the previous positions on the wall. Complete Table 1. Rotation stage initial angle Perp. distance from BSA-I to wall Position Rotation stage reflection angle Incident angle ∆ = - 0 Distance x (cm) from Fig. 1 Reflected angle r Table 1 0: _______ y: _______ (cm) A B C D E 8. Given the results in the table, what can you say about the relation between the incident and reflected angle? a. What is the theoretical relation between the incident angle and the reflected angle? b. Does the experiment verify the theory? If not, explain why. Part B: Law of Refraction Equipment Required: Laser Assembly (LA) 2 Beam Steering Assembly (BSA-I) Beam Steering Assembly with a variable angle holder (BSA-III) Plastic Tank Experiment set up: 9. IMPORTANT: Look ahead at the placement of the water tank in Figure 3, and look at the current location of your laser’s power supply. Is it close to where you will set up the tank? To avoid electrical hazards, place the power supply for your laser in a location where it will be unlikely to come in contact with an accidental water spill from the tank. 10. Set the Laser at the maximum height. 11. Place the different elements as shown in Figures 3 and 4. Fig. 3: Setup for Law of Refraction experiment (view from above) [Source: Projects in Optics: Applications Workbook, Newport Corporation] 12. Rotate the mirror on the BSA-III to direct the laser beam approximately at an angle of 45 degrees (see Fig. 4). Record the angle i. 13. Measure the distances, H1 and V1 (with no water into the plastic box). Fig. 4: Setup for the Law of Refraction experiment (side view) [Source: Projects in Optics: Applications Workbook, Newport Corporation] 14. Fill the plastic box with water to within 1cm of the top. 15. Measure H2 and V2. 16. Calculate i the incident angle and r, the refracted angle in Figure 4, using trigonometry. Show your work. 17. Given the fact that the refractive index of the air is 1, calculate the refractive index of the water using the law of refraction for an air-water interface. 18. Does the experimental value of the refractive index of the water close to the theoretical value? How well can you repeat this measurement? Give the major sources of error. Suggest ways to improve the accuracy of the results. Part C: Internal Reflection 19. Can you find the refractive index of the water using the internal reflection phenomenon? Explain an experimental setup and describe any difficulties you would encounter. Considerations: 1. Describe the difficulties you encountered in this lab. 2. What did you learn? 3. What do you think could be improved in this lab?