Physics quiz question: finding incident angle from transmitted angle

Physics 205B Quiz 1, Spring Semester 2010
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 23.11

Sunlight strikes the surface of a lake (index of refraction 1.33). A fish sees the sun underwater at an angle of 30.0° with respect to the normal. What angle do the sun's rays in air make with respect to the normal? (Drawing is not to scale.)
(A) 22.1 degrees.
(B) 40.6 degrees.
(C) 41.7 degrees.
(D) 48.8 degrees.

Correct answer: (C)

From Snell's law, n_i*sin(theta_i) = n_t*sin(theta_t), where n_i = 1.000 (given), n_t = 1.33, and theta_t = 30.0 degrees. Then solving for the incident angle in air:

theta_i = Arcsin(n_t*sin(theta_t)/n_i) = 41.7 degrees.

Response (A) is Arcsin(sin(theta_t)/n_t); response (B) is Arcsin(sin(90 degrees - theta_t)/n_t); response (D) is Arcsin(n_i/n_t), which is the critical angle for water incident on air.

Student responses
Section 31988
(A) : 2 students
(B) : 0 students
(C) : 10 students
(D) : 1 student

Success level: 76%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.50