Physics quiz question: vertically polarized light, different polarizer sets

Physics 205B Quiz 1, spring semester 2013
Cuesta College, San Luis Obispo, CA

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

Polarized light is incident on two sets of ideal polarizers.

More light will be transmitted through:
(A) polarizer set 1.
(B) polarizer set 2.
(C) (Both polarizer sets will have the same non-zero amount of light transmitted through them.)
(D) (Both polarizer sets will have no light transmitted through them.)

Correct answer (highlight to unhide): (A)

For 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 cos²(0°) = 1, and will still have a vertical polarization. The fraction of this light passing through the second polarizer is cos²(15°) = 0.93301270189, or 0.93 to two significant figures, and have a polarization that is at a clockwise angle of 15° with respect to the vertical. Thus the fraction of the original light that passes through both polarizers of polarizer set 1 is the product cos²(0°)·cos²(15°) = 0.93.

For polarizer set 2, the fraction of light passing through the first polarizer is cos²(15°) = 0.93, and the resulting light that passes through will have a polarization that is at a clockwise angle of 15° with respect to the vertical. The fraction of this light passing through the second polarizer is cos²(15°) = 0.93 (and will again have a vertical polarization). Thus the fraction of the original light that passes through both polarizers of polarizer set 2 is the product cos²(15°)·cos²(15°) = 0.87051270189, or 0.87 to two significant figures.

Section 30882
Exam code: quiz01b3Es
(A) : 22 students
(B) : 2 students
(C) : 11 students
(D) : 0 students

Success level: 63%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.54