Physics midterm question: unpolarized light, different polarizer sets

Physics 205B Midterm 1, spring semester 2013
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. Discuss why a greater fraction of the incident light passes through polarizer set 1 than through polarizer set 2. Explain your reasoning using the properties of polarizers and polarization.


Solution and grading rubric:

• p:
  Correct. One-half of the unpolarized light will pass through the first polarizer in either set, but the first polarizer in set 1 will let vertically polarized light pass through, while the first polarizer in set 2 will let horizontally polarized light pass through. From Malus' law, the fraction of polarized light that passes through a polarizer is given by cos²θ, where θ (the angle between the polarization of light and the transmission axis of the polarizer) would be 15° for set 1, and 75° for set 2. Since (1/2)·cos²(15°) > (1/2)·cos²(75°), more light will pass through the set 1 than through set 2.
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Section 30882
Exam code: midterm01p0C4
p: 26 students
r: 3 students
t: 4 students
v: 0 students
x: 0 students
y: 0 students
z: 0 student

A sample "p" response (from student 1337):
Another sample "p" response (from student 3698):