Physics quiz question: water wavelength in spharelite

Physics 205B Quiz 1, spring semester 2018
Cuesta College, San Luis Obispo, CA

Light of wavelength 476 nm in water (index of refraction[*] of 1.33) with an incident angle of 16.0° 
is transmitted into sphalerite (index of refraction of 2.43). (Drawing is not to scale.) The wavelength of this light traveling through sphalerite is:
(A) 196 nm.
(B) 261 nm.
(C) 358 nm.
(D) 870 nm.

[*] physics.info/refraction/.

Correct answer (highlight to unhide): (B)

The relations between the index of refraction and the speed of light, for water (medium 1) and for spharelite (medium 2) are:

n₁ = c/v₁,

n₂ = c/v₂,

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:

λ₁ = v₁/f₁,

λ₂ = v₂/f₂.

However, the frequency of the light in spharelite is the same as the frequency it has in water, such that:

f₁ = f₂,

(v₁/λ₁) = (v₂/λ₂),

λ₂ = λ₁·(v₂/v₁),

λ₂ = λ₁·((c/n₂)/(c/n₁)),

λ₂ = λ₁·(n₁/n₂) = (476 nm)·(1.33/2.43) = 261 nm.

(Response (A) is (476 nm)/(1.33); response (C) is (218 nm)/(2.43); response (D) is (476 nm)⋅(2.43/1.33).)

Sections 30882, 30883
Exam code: quiz01AM0l
(A) : 4 students
(B) : 28 students
(C) : 1 student
(D) : 2 students

Success level: 80%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.64