Physics midterm question: total internal reflection at fluorite-water interface?

Physics 205B Midterm 1, spring semester 2015
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Comprehensive Problem 23.78

Light in fluorite (index of refraction of 1.39) is incident at an ethyl alcohol interface (index of refraction of 1.36), and this light is totally internally reflected back down into fluorite. (Drawing is not to scale.) Then the ethyl alcohol is replaced with a layer of water (index of refraction of 1.33) poured onto the fluorite. Discuss whether or not total internal reflection also occurs at the fluorite-water interface, if the angle in fluorite is the same as before. Explain your reasoning using the properties of light and refraction.

Solution and grading rubric:

• p:
  Correct. Discusses/demonstrates:
  1. because the critical angle for fluorite up into ethyl alcohol is 78.1°, the incident angle in fluorite must be greater than 78.1° for total internal reflection to occur at the fluorite-ethyl alcohol interface;
  2. with this same angle in fluorite (any value at or greater than 78.1°), this is larger than the critical angle for fluorite up into water (73.1°), such that total internal reflection also occurs at the fluorite-ethyl alcohol interface. (May instead put any angle at or greater than 78.1° as the incident angle in fluorite in Snell's law to find that the transmitted angle in water is undefined, and interprets this as total internal reflection occurring at the fluorite-water interface.)
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. Typically solves for the two critical angles, but either does not sufficiently explain total internal reflection for the fluorite-water interface, or explains that total internal reflection will not occur.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. Some attempt at solving for the critical angles, but switches the incident and transmitted indices of refraction (resulting in an calculator error), or because the incident and transmitted indices are switched, discusses how total internal reflection will not occur.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some garbled attempt at applying Snell's law and/or critical angles.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. Approach other than that of applying Snell's law and/or critical angles.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 30882, 30883
Exam code: midterm01p34K
p: 24 students
r: 7 students
t: 11 students
v: 4 students
x: 1 student
y: 0 students
z: 0 student

A sample "p" response (from student 0203):
Another sample "p" response (from student 1828):
A sample "t" response (from student 0550):