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Question: 
  1. What is the smallest thickness of a soap film (n = 1.33) that would appear black if illuminated with 480-nm light? Assume there is air on both sides of the soap film.
  2. What are two other possible thicknesses for the film to appear black?
  3. If the thickness $t$ was much less than $\lambda$, why would the film also appear black?

Source: Giancoli, Douglas C., Physics: Principles with Applications, 7th Edition, 2014.

Quick Answer: 
  1. $x_1 = 180 \textrm{ nm}$
  2. $x_2 = 360 \textrm{ nm, } x_3 = 540 \textrm{ nm}$
  3. there would be only a phase difference of one half wavelength, which is destructive.

Giancoli 7th Edition, Chapter 24, Problem 46

(3:20)

Chapter 24, Problem 46 is solved.

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