Refraction, Snell’s Law, and Total Internal Reflection Example 1: A beam of light, going from air to water, has an angle of incidence is 30°. What is the angle of refraction, in the water? Example 2: What is the refractive medium if a ray coming from air at an angle of incidence of 50° is refracted through an angle of 35°. Example 3: A certain material has a critical angle of 52.0°. What is its index of refraction? Example 4: What is the critical angle for a glass that has an index of refraction of 1.500?

Snell’s Law:

(n1)(sin Θ1) = (n2)( (sin Θ2)

Snell’s Law Practice 1) A ray of light enters the top of a glass of water at an angle of 36 ° with the

normal. What is the angle between the refracted ray and the normal? (26°)

2) When light passes from air into water at an angle of 60° from the normal, what is the angle of refraction? (40.6°)

3) A block of amber is placed in water and a laser beam travels from the water through the amber. The angle of incidence is 35° while the angle of refraction is 24°. What is the index of refraction of amber? (n = 1.88)

4) The angles of incidence and refraction for light going from air into a material with a higher index of refraction are 63.5 ° and 42.9 °, respectively. What is the index of refraction of this material? (n = 1.31)

5) A person shines a light at a friend who is underwater. If the ray in the water makes an angle of 36.2° with the normal, what is the angle of incidence? (51.9°)

6) Calculate the critical angle for light going from glycerin into air. (42.8°)

7) A fiber-optic cable has an index of refraction of 1.53. For total internal reflection, what is the minimum angle of incidence to the inside wall of the cable if the cable is in the following: Air (40.8°), Water (60.6°)

8) You buy some land in Nunavut. A strange crystal is found all over your land. To determine what it is, you pass a beam of light through it. You observe that the light enters the crystal at a 30° angle from the normal, and is bent 11.776° from the normal. What is the strange crystal? (n = 2.45)

9) You set up a mining operation in Nunavut. A worker brings you some crystals. You pass a beam of light through one of the crystals. You observe that the light enters the crystal at 30° from the normal, and is bent 19.47° from the normal. What has the worker brought you? (n = 1.5)

10) Find the critical angle for light traveling from ice (n = 1.309) into air. (49.81°) 11) Which has a smaller critical angle in air, diamond (n = 2.419) or cubic zirconia

(n = 2.2)? Show your work. (diamond 24.42°, cubic zirconia 27.0°) 12) A laser beam travels from flint glass into lemon oil. The angle of incidence is 40°

and the angle of reflection is 44°. What is the refractive index of lemon oil? (1.49)

Table 1: Indices of Refraction (n) for Selected Media Medium (n) Medium (n) Medium (n)

Vacuum 1.0000 Pyrex glass 1.47 Crown glass 1.52 Air 1.00029 Glycerin 1.47 Flint Glass 1.61 or 1.66 CO2 1.0005 Vegetable oil 1.47 Ruby 1.779 ice 1.309 Plexiglass 1.49 Sapphire 1.794 Water 1.33 Glass 1.5 Cubic Zirconia 2.17 Ethyl Alcohol 1.36 Table Salt 1.51 Diamond 2.42

Solutions: 1) A ray of light enters the top of a glass of water at an angle of 36 ° with the

normal. What is the angle between the refracted ray and the normal? (26°)

2) When light passes from air into water at an angle of 60° from the normal, what is the angle of refraction? (40.6°)

3) A block of amber is placed in water and a laser beam travels from the water through the amber. The angle of incidence is 35° while the angle of refraction is 24°. What is the index of refraction of amber? (n = 1.88)

4) The angles of incidence and refraction for light going from air into a material with a higher index of refraction are 63.5 ° and 42.9 °, respectively. What is the index of refraction of this material? (n = 1.31)

Solutions: 5) A person shines a light at a friend who is underwater. If the ray in the water

makes an angle of 36.2° with the normal, what is the angle of incidence? (51.9°)

6) Calculate the critical angle for light going from glycerin into air. (42.8°)

7) A fiber-optic cable has an index of refraction of 1.53. For total internal reflection, what is the minimum angle of incidence to the inside wall of the cable if the cable is in the following: Air (40.8°), Water (60.6°)

8) You buy some land in Nunavut. A strange crystal is found all over your land. To determine what it is, you pass a beam of light through it. You observe that the light enters the crystal at a 30° angle from the normal, and is bent 11.776° from the normal. What is the strange crystal? (n = 2.45)

Solutions: 9) You set up a mining operation in Nunavut. A worker brings you some crystals. You

pass a beam of light through one of the crystals. You observe that the light enters the crystal at 30° from the normal, and is bent 19.47° from the normal. What has the worker brought you? (n = 1.5)

10) Find the critical angle for light traveling from ice (n = 1.309) into air. (49.81°)

11) Which has a smaller critical angle in air, diamond (n = 2.419) or cubic zirconia (n = 2.2)? Show your work. (diamond 24.42°, cubic zirconia 27.0°)

12) A laser beam travels from flint glass into lemon oil. The angle of incidence is 40° and the angle of reflection is 44°. What is the refractive index of lemon oil? (1.49)