Physics quiz question: air-Pyrex® refraction

Physics 205B Quiz 1, spring semester 2011
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 22.8

"Ides of March Haul - Pyrex Patented May 27, 1919"
Fearless Stumbler
flic.kr/p/9qK4PZ

A beam of light strikes the interface between air (index of refraction 1.000) and Pyrex® (index of refraction[*] 1.474), with a transmitted angle of 38.0°. (Drawing is not to scale.) The incident angle in air is:
(A) 25.8°.
(B) 42.7°.
(C) 56.0°.
(D) 65.2°.

Correct answer (highlight to unhide): (D)

[*] physics.info/refraction/.

Snell's law relates the indices of refraction with the incident and transmitted angles:

n_air·sin(θ_air) = n_Pyrex®·sin(θ_Pyrex®),

where the given (or assumed to be known) quantities, unknown quantities, and quantities to be explicitly solved for are denoted.

Directly solving for the incident angle in air:

sin(θ_air) = (n_Pyrex®/n_air)·sin(θ_Pyrex®),

θ_air = sin^{– 1}(n_Pyrex®/n_air)·sin(θ_Pyrex®)) = sin^–1((1.474/1.000)·sin(38.0°)) = 65.1600804828°,

or to three significant figures, the incident angle in air is 65.2°.

(Response (A) is θ_Pyrex®/n_Pyrex®; response (B) is sin^–1(1/n_Pyrex®); and response (C) is (n_Pyrex®/n_air)·θ_Pyrex®.)

Section 30882
Exam code: quiz01w4v3
(A) : 0 students
(B) : 1 student
(C) : 0 students
(D) : 7 students

Success level: 88%
Discrimination index (Aubrecht & Aubrecht, 1983): 0