Physics quiz question: As2S3 wavelength in air

Physics 205B Quiz 1, spring semester 2013
Cuesta College, San Luis Obispo, CA

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

"Orpiment 1"
Parent Géry
commons.wikimedia.org/wiki/File:Orpiment_1.JPG

Light of wavelength 218 nm in arsenic trisulfide (As₂S₃) (index of refraction[*] of 2.66) is incident at the interface between arsenic trisulfide and air (index of refraction 1.000). The wavelength of this light in air is:
(A) 82.0 nm.
(B) 218 nm.
(C) 362 nm.
(D) 580 nm.

[*] nvlpubs.nist.gov/nistpubs/jres/59/jresv59n2p83_A1b.pdf.

Correct answer (highlight to unhide): (D)

The relations between the index of refraction and the speed of light, for arsenic trisulfide (medium 1) and for air (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 arsenic trisulfide is the same as the frequency it has in air, such that:

f₁ = f₂,

(v₁/λ₁) = (v₂/λ₂),

λ₂ = λ₁·(v₂/v₁),

λ₂ = λ₁·((c/n₂)/(c/n₁)),

λ₂ = λ₁·(n₁/n₂) = (218 nm)·(2.66/1.000) = 580 nm.

(Response (A) is (218 nm)/(2.66); response (C) is (218 nm)·(1.66).)

Section 30882
Exam code: quiz01b3Es
(A) : 6 students
(B) : 3 students
(C) : 4 students
(D) : 21 students
(No response) : 1 student

Success level: 60%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.91