Physics quiz question: comparing emerald, turpentine wavelengths

Physics 205B Quiz 1, spring semester 2016
Cuesta College, San Luis Obispo, CA

Light of wavelength 480 nm in turpentine (index of refraction 1.472) is transmitted into emerald (index of refraction of 1.576).[*]

The wavelength of this light in emerald is __________ 480 nm.
(A) less than.
(B) equal to.
(C) greater than.
(D) (Not enough information is given.)

[*] physics.info/refraction/.

Correct answer (highlight to unhide): (A)

The relationship between the index of refraction n of a medium and the speed of light v traveling through that medium is given by:

n = c/v,

where c is the speed of light in vacuum. Since turpentine has a smaller index of refraction n₁ than the index of refraction n₂ of emerald, then:

n₁ < n₂,

(c/v₁) < (c/v₂),

v₂ < v₁,

and thus light travels with a slower speed through emerald than it does through turpentine.

The wavelength λ of light is a parameter dependent on both the wave speed v (which depends on the medium), and the frequency f (which depends on the source):

λ = v/f.

Since light that initially travels through turpentine then passes into emerald, then the frequency of this light remains constant as it comes from same given source, as this value does not depend on the medium. Then the frequency of this light f₁ in turpentine must be equal to the frequency of this light f₂ in emerald, such that:

f₁ = f₂,

(v₁/λ₁) = (v₂/λ₂),

and since v₂ < v₁, then λ₂ < λ₁, and the wavelength λ₂ in emerald will be shorter than 480 nm, the wavelength of light in turpentine.

Section 30882, 30883
Exam code: quiz01sN0w
(A) : 38 students
(B) : 2 students
(C) : 2 students
(D) : 0 students

Success level: 87%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.57