## 20140214

### Physics quiz question: unpolarized light, different polarizer sets

Physics 205B Quiz 1, spring semester 2014
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 22.45

Unpolarized light is incident on two sets of ideal polarizers. Compared to polarizer set 1, polarizer set 2 will transmit __________ light.
(A) less.
(B) the same (non-zero) amount of.
(C) more.
(D) (Both polarizer sets will have no light transmitted through them.)

Correct answer (highlight to unhide): (B)

An ideal polarizer will transmit one-half of unpolarized light through it, where the transmitted light would be fully polarized in the same direction as the transmission axis of the polarizer.

From Malus' law, the fraction of polarized light passing through a polarizer is given by cos2θ, where θ is the angle between the original polarization and the transmission axis of the polarizer.

For polarizer set 1, the fraction of light passing through the first polarizer is 0.5, and will have a vertical polarization. The fraction of this light passing through the second polarizer is cos2(45°) = 0.5, and will have a polarization that is at a clockwise angle of 45° with respect to the vertical. Thus the fraction of the original light that passes through both polarizers of polarizer set 1 is the product 0.5·cos2(45°) = 0.25.

For polarizer set 2, the fraction of light passing through the first polarizer is also 0.5, but the resulting light that passes through will have a polarization that is at a clockwise angle of 45° with respect to the vertical. The fraction of this light passing through the second polarizer is cos2(45°) = 0.5, and will have a vertical polarization. Thus the fraction of the original light that passes through both polarizers of polarizer set 2 is the product 0.5·cos2(45°) = 0.25, and thus will transmit the same (non-zero) amount of light as compared to polarizer set 1.

Sections 30882, 30883
Exam code: quiz01ksB4
(A) : 12 students
(B) : 22 students
(C) : 6 students
(D) : 1 student

Success level: 54%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.83