Physics midterm question: dichroic mirror

Physics 205B Midterm 1, Fall Semester 2010
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Comprehensive Problem 25.67

[10 points.] A thin transparent film (n = 1.60) is coated onto a glass plate (n = 1.51). If this film is to minimize the transmitted intensity for a given wavelength, which equation should be used: ∆lmλ, or ∆l = (m + 1/2)*λ (where λ is the wavelength value in the film)? Explain your reasoning using the properties of phase shifts and interference.

Solution and grading rubric:
  • p = 10/10:
    Correct. (1) Minimize transmission means strong (constructive interference) reflections. (2) The reflection of light in air off of the film has a 180° phase shift, while the reflection of light in the film off of the glass has no phase shift, thus the reflections are out of phase. (3) Thus for constructive interference delta(l) = (m + 1/2)*lambda should be used (where delta(l) = 2*t, and lambda is the wavelength in the film = lambda_air/n_film, but further work using these is not necessary).
  • 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. One argument missing or switched.
  • 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:

Grading distribution:
Section 70856
p: 7 students
r: 3 students
t: 1 student
v: 0 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 7111):

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