20110330

Physics midterm question: three-layer refraction

Physics 205B Midterm 1, Spring Semester 2011
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Comprehensive Problem 23.97

[10 points.] A beam of light strikes an air-oil interface with an incident angle of 41°. The beam travels through the oil and emerges from a parallel oil-glass interface below. Ignore reflections, and this diagram is not drawn to scale. 
Is the angle of the exiting ray in glass greater than, less than, or equal to 41°? Explain your reasoning using the properties of light and refraction.

Solution and grading rubric:
  • p = 10/10:
    Correct. Solves for theta_3 after first solving for theta_2 using Snell's law twice; or solves for theta_3 by noting that the oil layer can be ignored mathematically in n_1*sin(theta_1) = n_3*sin(theta_3); or argues that since the indices of refraction increase, the angles will decrease such that theta_3 > (theta_2) > theta_1.
  • r = 8/10:
    As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
  • t = 6/10:
    Nearly correct, but argument has conceptual errors, or is incomplete.
  • v = 4/10:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner.
  • x = 2/10:
    Implementation/application of ideas, but credit given for effort rather than merit.
  • y = 1/10:
    Irrelevant discussion/effectively blank.
  • z = 0/10:
    Blank.

Grading distribution:
Section 30882
Exam code: midterm01g74S
p: 8 students
r: 0 students
t: 0 students
v: 0 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 7503), eliminating n_2*sin(theta_2) in the two Snell's law equations:

A sample "p" response (from student 3373), explicitly solving for theta_2, and then for theta_3:

A sample "p" response (from student 1990), arguing qualitatively for theta 1 > theta_2 > theta_3:

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