Cuesta College, San Luis Obispo, CA
Vertically polarized light is incident on a set of two ideal polarizers.
If the total fraction of the incident light intensity transmitted through both polarizers is 0.15, then the angle θ of the second polarizer is:
(A) 23°.
(B) 44°.
(C) 67°.
(D) 81°.
Correct answer (highlight to unhide): (C)
The fraction of the vertically polarized light that passes through polarizer 1 is cos2θ, where the angle θ = 0° is measured between the vertical polarization of the light entering polarizer 1, and the transmission axis of polarizer 1 (which is also vertical). The light after passing through polarizer 1, but before passing through polarizer 2 is still vertical (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, where the angle θ measured between the vertical polarization of the light entering polarizer 2 and the transmission axis of polarizer 2 (rotated clockwise from the vertical) is unknown.
Since the total fraction of the light that passes through both polarizers is given, then this is the result of multiplying together the fractions that passed through each polarizer:
total fraction = (fraction 1)×(fraction 2),
0.15 = (1)×(cos2θ),
√(0.15) = cosθ
cos–1(√(0.15)) = θ = 67.213502000402852°,
or to two significant figures, the clockwise angle θ that the transmission axis of polarizer 2 is rotated from vertical is 67°.
(Response (A) is cos–1(√(0.85)); response (B) is (1/0.15)2; and response (D) is cos–1(0.15).)
Student responses
Sections 30882, 30883
Exam code: quiz01PxP7
(A) : 2 students
(B) : 1 student
(C) : 30 students
(D) : 2 students
Success level: 86%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.25
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