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:
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.
As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
Nearly correct, but argument has conceptual errors, or is incomplete.
Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner.
Implementation/application of ideas, but credit given for effort rather than merit.
Irrelevant discussion/effectively blank.
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: