Physics quiz question: unpolarized light transmitted through two polarizers

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

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


The fraction of the incident light intensity transmitted is:
(A) 0.29.
(B) 0.38.
(C) 0.48.
(D) 0.97.

Correct answer (highlight to unhide): (C)

The intensity of light that passes through polarizer 1 is one-half of the original unpolarized intensity, and this light is then diagonally polarized, having a polarization that matches the transmission axis of that polarizer, at an angle of 30° measured clockwise from the vertical (the convention followed in this class is to depict transmission axes of polarizers).

The fraction of this diagonally polarized light that passes through polarizer 2 is cos²θ, where the angle θ = 10° is measured between the diagonal polarization of the light entering polarizer 2 (30° clockwise from vertical) and the transmission axis of polarizer 2 (40° clockwise from the vertical).


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

(1/2)·cos²(10°) = 0.48492315519...,

or to two significant figures, 0.48 of the original unpolarized intensity.

(Response (A) is (1/2)·cos²(40°); response (B) is (1/2)·cos²(30°); and response (D) is cos²(10°).)

Student responses
Sections 30882, 30883
Exam code: quiz01Om6A
(A) : 15 students
(B) : 3 students
(C) : 7 students
(D) : 3 students

Success level: 25%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.43