Physics quiz question: polarized light transmitted through two polarizers

Physics 205B Quiz 1, spring semester 2019
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) 0.017.
(B) 0.063.
(C) 0.23.
(D) 0.87.

Correct answer (highlight to unhide): (A)

The fraction of the diagonally polarized light that passes through the polarizer 1 is cos²θ, where the angle θ = 75° is measured between the horizontal polarization of the light entering polarizer 1, and the transmission axis of polarizer 1 (15° clockwise from vertical). The light after passing through polarizer 1, but before passing through polarizer 2 is now diagonally polarized, having a polarization that matches the transmission axis of polarizer 1 (15° clockwise from vertical).


The fraction of this diagonally polarized light that passes through polarizer 2 is again cos²θ, but where the angle θ = 60° is measured between the diagonal polarization of the light entering polarizer 2 (15° clockwise from vertical) and the transmission axis of polarizer 2 (15° counterclockwise from the horizontal).


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

cos²(75°)·cos²(60°) = (0.067)⋅(0.25) = 0.017,

of the original unpolarized intensity, to two significant figures.

(Response (B) is cos²(75°)·cos²(15°); response (C) is cos²(15°)·cos²(60°); and response (D) is cos²(15°)⋅cos²(15°).)

Student responses
Sections 30882, 30883
Exam code: quiz01aN7u
(A) : 11 students
(B) : 12 students
(C) : 3 students
(D) : 11 students

Success level: 32%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.25