## 20180324

### Physics midterm question: wavelengths at total internal reflection interface

Physics 205B Midterm 1, spring semester 2018
Cuesta College, San Luis Obispo, CA Light of wavelength 533 nm in a unknown material (index of refraction n1) undergoes total internal reflection from an interface with a different unknown material (index of refraction n2). (Drawing is not to scale.) Show that the wavelength in the n2 material would be longer than 533 nm (assuming that light could eventually be transmitted out in the n2 material). Explain your reasoning using the properties of light and refraction.

• p:
Discusses/demonstrates that the wavelength λ2 in the second n2 material would be longer than 533 nm by:
1. qualitatively or quantitatively showing that n2 < n1 by appealing to the critical angle θ2 = sin−1(n2/n1) (where n2 < n1 in order to avoid a domain error in the inverse sine function); or Snell's law n1⋅sinθ1 = n2⋅sinθ2 where θ2 = 90°, and thus n2 < n1; and
2. that since index of refraction n = c/v, a smaller index of refraction n2 results in a faster speed of light v2; and
3. since the wavelength λ = v/f, since the second material has a faster speed of light v2, and the frequency of light is independent of the medium it travels through, then it will have a longer wavelength in that material.
May combine arguments in (1)-(2) by arguing that total internal reflection occurs when light traveling in a slower material is "frustrated" in trying to travel out into a faster material.
• r:
As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. Typically one of arguments (1)-(3) missing, incomplete, or problematic.
• t:
Nearly correct, but argument has conceptual errors, or is incomplete. Typically two of arguments (1)-(3) missing, incomplete, or problematic.
• 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, indices of refraction, wave speed, frequency and wavelengths.
• x:
Implementation/application of ideas, but credit given for effort rather than merit. No clear attempt at applying Snell's law and/or critical angles, indices of refraction, wave speed, frequency and wavelengths.
• y:
Irrelevant discussion/effectively blank.
• z:
Blank.
Sections 30882, 30883
Exam code: midterm01cVdP
p: 17 students
r: 6 students
t: 9 students
v: 3 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 3673): A sample "p" response (from student 1929): 