Cuesta College, San Luis Obispo, CA
Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 25.20
[20 points.] A soap film (n = 1.41) of thickness 320 nm is surrounded by air above and below. Which visible (400-700 nm) wavelength(s) in air reflects with constructive interference? Show your work and explain your reasoning. Solution and grading rubric:
- p = 20/20:
Correct. Recognizes (a) reflection off of top of soap film causes 180° phase shift, while reflection off of bottom of soap film causes no phase shift, such that the two reflected rays are out-of-phase with each other; (b) the path difference is 2*t = 640 nm; (c) for constructive interference of two out-of-phase reflected rays, delta(l) = (m + 1/2)*lambda = odd*lambda/2, where lambda is the wavelength in oil; (d) wavelength in oil is related to the wavelength in air by lambda = lambda_0/n_oil, such that lambda_0 = 4*n*t/odd = 1800 nm, 600 nm, 360 nm, of which only 600 nm is in the visible light range. Minor algebraic errors okay, as long as (a)-(d) are all accounted for. - r = 16/20:
Nearly correct, but includes minor math errors. Omission of one or two of concepts (a)-(d) outlined above. - t = 12/20:
Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Demonstrates some understanding of at least one of concepts (a)-(d) outlined above. - v = 8/20:
Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. - x = 4/20:
Implementation of ideas, but credit given for effort rather than merit. - y = 2/20:
Irrelevant discussion/effectively blank. - z = 0/20:
Blank.
Grading distribution:
Section 31988
p: 2 students
r: 3 students
t: 7 students
v: 1 student
x: 0 students
y: 0 students
z: 0 students
A sample "p" response (from student 1987), with a minor algebraic error in dividing 640 nm by a factor of (1/2), resulting in a wavelength (in soap) of 320 nm instead of 1280 nm:
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