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MR. SURRETTE VAN NUYS HIGH SCHOOL CHAPTER 15: REFLECTION AND REFRACTION WORKSHEET SOLUTIONS 1. Light in air enters a diamond (n = 2.42) at an angle of incidence of 30.0o. What is the angle of refraction inside the diamond? 1A. (1) n = sin1 / sin2 (2) sin2 = sin1 / n (3) sin2 = sin 30o / 2.42 (4) sin2 = 0.2066 (5) 2 = arcsin2 = 11.9o 2. An underwater scuba diver sees the sun at an apparent angle of 35.0o from the vertical. How far is the sun above the horizon? (nwater = 1.33) 2A. (1) n = sin2 / sin1 (2) (n)(sin1) = sin2 (3) (1.33)(sin 35o) = sin2 (4) sin2 = 0.7629 (5) 2 = arcsin2 = 49.7o 3. Dispersion occurs when: (A) some materials bend light more than other materials (B) a material slows down some wavelengths more than others (C) a material changes some frequencies more than others (D) light has different speeds in different materials (E) a material changes the color of incoming light 4. If the velocity of light through an unknown liquid is measured at 1.85 x 108 m/s, what is the index of refraction of this liquid? 4A. (1) n = c / v (2) n = 3.00 x 108 m/s / 1.85 x 108 m/s (3) n = 1.62 1|Page PHYSICS MR. SURRETTE VAN NUYS HIGH SCHOOL 5. If the critical angle for internal reflection inside a certain transparent material is found to be 56.0o, what is the index of refraction of the material? (Air is outside the material). 5A. (1) sin c = n2 / n1 (2) n1 = n2 / sinc (3) n1 = 1.00 / sin 56o (4) n1 = 1.21 6. Which of the following describes what will happen to a light ray incident on an air-to-glass boundary at less than the critical angle? (A) total reflection (B) total transmission (C) total dispersion (D) partial reflection, total transmission (E) partial reflection, partial transmission 6A. 7. A beam of light in air is incident at an angle of 35.0o to the surface of a rectangular block of clear plastic (n = 1.49). The light beam first passes through the block and re-emerges from the opposite side into air at what angle to the surface? Example 7. Diagram 7A. 35o 8. A beam of light in air is incident on the surface of a rectangular block of clear plastic (n = 1.49). If the velocity of the beam before it enters the plastic is 3.00 x 108 m/s, what is its velocity after emerging from the block? 8A. 3.00 x 108 m/s 2|Page PHYSICS MR. SURRETTE VAN NUYS HIGH SCHOOL 9. A ray of light in air is incident on an air-to-glass boundary at an angle of 41.5o with the normal. If the index of refraction of the glass is 1.47, what is the angle of the refracted ray within the glass with respect to the normal? 9A. (1) n = sin1 / sin2 (2) sin2 = sin1 / n (3) sin2 = sin 41.5o / 1.47 (4) sin2 = 0.4508 (5) 2 = arcsin2 = 26.8o 10. A light in air is incident on an air-to-glass boundary at an angle of 45.0o and is refracted in the glass at an angle of 30.0o with the normal. What is the index of refraction of the glass? 10A. (1) n = sin1 / sin2 (2) n = sin 45o / sin 30o (3) n = 0.7071 / 0.5 (4) n = 1.41 11. A laser beam, incident at 30 degrees onto the surface of a block of glass, is partially reflected and partially transmitted (with refraction) at the block’s upper surface. The index of refraction of the glass is 1.5. Example 11. Diagram 11a. What is the speed of light in the glass expressed as a fraction of c? A. (1) n = c / v (2) v = c / n (3) v = (1 c) / (1.5) (4) v = 0.67 c 11b. Is the angle of refraction greater than, less than, or equal to 30 degrees? A. less than 11c. Calculate the angle of refraction in degrees. A. (1) n1sin1 = n2sin2 (2) sin2 = (n1)(sin1) / (n2) (3) sin2 = (1.0)(sin30o) / (1.5) (4) sin2 = 0.333 (5) 2 = arcsin2 = 19.5o 3|Page PHYSICS MR. SURRETTE VAN NUYS HIGH SCHOOL 11d. What is the angle the reflected beam makes with the normal? A. 30 degrees. The angle of reflection = the angle of incidence. 12. A beam of light in water strikes a boundary with air. The index of refraction of water is 1.33. 12a. If the angle of incidence is 41 degrees what is the angle of refraction? A. (1) n1 sin 1 = n2 sin 2 (2) sin2 = (n1)(sin 1) / (n2) (3) sin2 = (1.33)(sin 41o) / (1.00) (4) sin2 = 0.8726 (5) 2 = arcsin2 = 60.8o 12b. Calculate the critical angle for these rays. A. (1) n1sin1 = n2sin2 (2) sin1 = (n2)(sin2) / (n1) (3) sin1 = (1.00)(sin 90o) / (1.33) (4) sin1 = 0.752 (5) 1 = arcsin1 = 48.8o 12c. If the angle of incidence is 61 degrees what happens to the light at the boundary? A. It is totally reflected. 4|Page PHYSICS MR. SURRETTE VAN NUYS HIGH SCHOOL CHAPTER 15: REFLECTION AND REFRACTION QUIZ SOLUTIONS 1. Light in air enters a diamond (n = 2.42) at an angle of incidence of 41.2o. What is the angle of refraction inside the diamond? 1A. (1) n = sin1 / sin2 (2) sin2 = sin1 / n (3) sin2 = sin 41.2o / 2.42 (4) sin2 = 0.2722 (5) 2 = arcsin2 = 15.8o 2. If the velocity of light through an unknown liquid is measured at 1.97 x 108 m/s, what is the index of refraction of this liquid? (c = 3.00 x 108 m/s) 2A. (1) n = c / v (2) n = 3.0 x 108 m/s / 1.97 x 108 m/s (3) n = 1.52 3. If the critical angle for internal reflection inside a certain transparent material is found to be 46.5o, what is the index of refraction of the material? (Air is outside the material). 3A. (1) sinc = n2 / n1 (2) n1 = n2 / sinc (3) n1 = 1.00 / sin 46.5o (4) n1 = 1.38 4. A ray of light in air is incident on an air-to-glass boundary at an angle of 12.8o with the normal. If the index of refraction of the glass is 1.87, what is the angle of the refracted ray within the glass with respect to the normal? 4A. (1) n = sin1 / sin2 (2) sin2 = sin1 / n (3) sin2 = sin 12.8o / 1.87 (4) sin2 = 0.1185 (5) 2 = arcsin2 = 6.8o 5. A light in air is incident on an air-to-glass boundary at an angle of 48.7o and is refracted in the glass at an angle of 27.5o with the normal. What is the index of refraction of the glass? 5A. (1) n = sin 1 / sin 2 (2) n = sin 48.7o / sin 27.5o (3) n = 1.63 5|Page PHYSICS MR. SURRETTE VAN NUYS HIGH SCHOOL 6. A laser beam, incident at 35 degrees to the normal on the surface of a glass block, is partially reflected and partially transmitted (with refraction) at the block’s upper surface. The index of refraction of the glass is 1.6. 6a. The speed of light in a vacuum is c = 3.0 x 108 m/s. What is the speed of light in this glass expressed as a fraction of c? A. (1) n = c/v (2) v = c/n (3) v = (1 c) / (1.6) (4) v = 0.625 c 6b. Is the angle of refraction greater than, less than, or equal to 35 degrees? A. less than 6c. A. (1) (2) (3) (4) (5) Calculate the angle of refraction in degrees. n1sin1 = n2sin2 sin2 = (n1)(sin1) / (n2) sin2 = (1.0)(sin35o) / (1.6) sin2 = 0.3585 2 = arcsin2 = 21.0o 6d. What is the angle the reflected beam makes with the normal? A. 35 degrees. = ’ 7. A beam of light in water strikes a boundary with air. The index of refraction of water is 1.33. 7a. A. (1) (2) (3) (4) (5) If the angle of incidence is 32.7 degrees what is the angle of refraction? n1sin1 = n2sin2 sin2 = (n1)(sin1) / (n2) sin2 = (1.33)(sin 32.7o) / (1.00) sin2 = 0.7185 2 = arcsin2 = 43.9o 6|Page PHYSICS MR. SURRETTE 7b. A. (1) (2) (3) (4) (5) VAN NUYS HIGH SCHOOL Calculate the critical angle for these rays. n1 sin 1 = n2sin2 sin 1 = (n2)(sin 2) / (n1) sin 1 = (1.00)(sin 90o) / (1.33) sin 1 = 0.752 1 = arcsin1 = 48.8o 7c. If the angle of incidence is 10 degrees, what happens to the light at the boundary? A. refracted outside to the air. 8. Dispersion occurs when: 8A. a material slows down some wavelengths more than others 9. A beam of light in an unknown medium is incident on the surface of a rectangular block of clear plastic (n = 1.49) If the velocity of the beam before it enters the plastic is 1.54 x 108 m/s, what is its velocity after emerging from the block? 9A. 1.54 x 108 m/s 10. A beam of light in air is incident at an angle of 40.0o to the surface of a rectangular block of clear plastic ( n = 1.49). The light beam first passes through the block and re-emerges from the opposite side into air at what angle to the normal to that surface? 10A. 40.0o 7|Page PHYSICS