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

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