Physics midterm question: incident angle less than critical angle

Physics 205B Midterm 1, spring semester 2012
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Comprehensive Problem 23.91

A beam of light strikes the interface between vegetable oil and air with an incident angle equal to the critical angle of 42.9°, such that the beam undergoes total internal reflection. (Drawing is not to scale.) If the incident angle of the beam of light in vegetable oil is decreased slightly from 42.9° to 42.8°, describe what will happen to the beam. Explain your reasoning using the properties of light and refraction.

Solution and grading rubric:

• p:
  Correct. With an incident angle less than the critical angle, light will be transmitted instead of totally internally reflected (there will also be a partially reflected ray as well). Discusses definition of the critical angle, or explicitly solves for the transmitted angle in air using Snell's law.
  
• 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: midterm01o1Ls
p: 21 students
r: 2 students
t: 3 students
v: 1 student
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 0928) appeals to the definition of the critical angle:
Another sample "p" response (from student 0801), explicitly solving for the index of refraction for cooking oil, then calculating the transmitted angle in air: