Physics quiz question: polarized light transmitted through two polarizers

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

Polarized light passes through two polarizers with polarization axes turned as shown below.


The total fraction of the incident light intensity transmitted through both polarizers is:
(A) 0.
(B) 0.19.
(C) 0.38.
(D) 0.56.

Correct answer (highlight to unhide): (B)

The fraction of the diagonally polarized light that passes through the vertical polarizer 1 is cos²θ, where the angle θ = 60° is measured between the diagonal polarization of the light entering polarizer 1 (60° clockwise from vertical) and the transmission axis of polarizer 1 (vertical). The light after passing through polarizer 1, but before passing through polarizer 2 is now vertically polarized, having a polarization that matches the transmission axis of polarizer 1.


The fraction of this vertically polarized light that passes through polarizer 2 is again cos²θ, but where the angle θ = 30° is measured between the polarization of the light entering polarizer 2 (vertical) and the transmission axis of polarizer 2 (30° counterclockwise from the vertical).


Thus the fraction of light that passes through both polarizer 1 and polarizer 2 is:

cos²(60°)·cos²(30°) = (1/4)⋅(3/4) = (3/16) = 0.1875,

or to two significant figures, 0.19 of the original unpolarized intensity.

(Response (C) is (1/2)·cos²(30°), which would be the fraction of unpolarized light that would pass through both polarizers; and response (D) is cos²(30°)⋅cos²(30°).)

Student responses
Sections 30882, 30883
Exam code: quiz01AM0l
(A) : 4 students
(B) : 25 students
(C) : 5 students
(D) : 1 student

Success level: 71%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.45