Physics quiz question: possible total internal reflection?

Physics 205B Quiz 1, fall semester 2010
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Comprehensive Problem 23.78

A beam of light strikes the interface between glycerin (index of refraction[*] 1.473) and air (index of refraction 1.000), with an incident angle 44.0°. (Drawing is not to scale.) As a result, this light is:
(A) reflected back into glycerin.
(B) transmitted into air.
(C) (Both of the above choices.)
(D) (Not enough information is given.)

[*] physics.info/refraction/.

Correct answer (highlight to unhide): (A)

The critical angle for light incident on a glycerine-air interface (where medium 1 is glycerin, and medium 2 is air) is given by:

θ_c = sin^–1(n₂/n₁) = sin^–1(1.000/1.473) = 42.76°.

Since the incident angle of 44.0° is greater than the critical angle, then the light in glycerin will experience total internal reflection back down into the glycerin, with none of it transmitted out into air.

Student responses
Section 70856
(A) : 12 students
(B) : 0 students
(C) : 1 student
(D) : 0 students

Success level: 92%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.13