20170207

Physics quiz question: wavelength in unknown material

Physics 205B Quiz 1, spring semester 2017
Cuesta College, San Luis Obispo, CA

Light of wavelength 550 nm in calcite (index of refraction[*] of 1.486) with an incident angle of 37.0° is transmitted into an unknown material with an angle of 30.5°. (Drawing is not to scale.) The wavelength of this light in the unknown material is __________ 550 nm.
(A) shorter than.
(B) equal to.
(C) longer than.
(D) (Not enough information is given.)

[*] physics.info/refraction/.

Correct answer (highlight to unhide): (A)

Snell's law relates the indices of refraction with the incident and transmitted angles:

ncalcite·sin(θcalcite) = nunknown·sin(θunknown).

Since the incident angle in calcite (θcalcite = 37.0°) is greater than the transmitted angle in the unknown material (θunknown = 30.5°), then the calcite index of refraction must be less than that of the unknown material:

θcalcite > θunknown,
ncalcite < nunknown.

The relationships between the indices of refraction and speed of light for calcite and the unknown material are given by:

ncalcite = c/vcalcite,
nunknown = c/vunknown,

where c is the speed of light in vacuum. Since calcite has a lower index of refraction, then the speed of light in calcite must be faster:

ncalcite < nunknown,
vcalcite > vcalcite.

The relationships between the speed of light, the frequency and wavelength in a material are given by:

λcalcite = vcalcite/fcalcite,
λunknown = vunknown/funknown.

Since the frequency of a wave depends on its source and not on the material it travels through, the frequency remains constant as the light starts in calcite and is then transmitted into the unknown material:

fcalcite = funknown.

And because the speed of light in calcite is faster than the unknown material, then the wavelength of light in calcite (λcalcite = 550 nm) must be greater than the wavelength of light in the unknown material:

vcalcite > vcalcite,
∴λcalcite > λunknown.

Student responses
Sections 30882, 30883
Exam code: quiz01Om6A
(A) : 19 students
(B) : 2 students
(C) : 7 students
(D) : 0 students

Success level: 68%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.50