Physics quiz question: wavelength of light in air

Physics 205B Quiz 1, spring semester 2014
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 22.19(a)

Light of wavelength 440 nm in crown glass (index of refraction[*] of 1.51) is incident at an angle of 30.0° at the interface between crown glass and air (index of refraction 1.000). (Drawing is not to scale.) The wavelength of this light in air is:
(A) 290 nm.
(B) 440 nm.
(C) 660 nm.
(D) 860 nm.

[*] physics.info/refraction/.

Correct answer (highlight to unhide): (C)

The relations between the index of refraction and the speed of light, for crown glass and for air, are:

n_{crown glass} = c/v_{crown glass},

n_air = c/v_air,

where the given (or assumed to be known) quantities, unknown quantities, and quantities to be explicitly solved for are denoted. Also the relations between wavelength, speed, and frequency are:

λ_{crown glass} = v_{crown glass}/f_{crown glass},

λ_air = v_air/f_air.

However, the frequency of the light in crown glass is the same as the frequency it has in air, such that:

f_{crown glass} = f_air,

v_{crown glass}/λ_{crown glass} = v_air/λ_air,

λ_air = λ_{crown glass}·v_air/v_{crown glass},

λ_air = λ_{crown glass}·n_{crown glass}/n_air = (440 nm)·(1.51)/(1.000) = 664.4 nm,

or to two significant figures, 660 nm.

(Response (A) is (440 nm)/(1.51); response (D) is (440 nm)/(0.51).)

Sections 30882, 30883
Exam code: quiz01ksB4
(A) : 8 students
(B) : 4 students
(C) : 27 students
(D) : 2 students

Success level: 66%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.58