A thin film of soapy water (n = 1.37) is held vertical. Light of wavelength 600 nm is reflected from the film and horizontal dark lines appear. What is the thinnest soap film for which a bright band will occur?
A) 150 nm
B) 109 nm
C) 90.0 nm
D) 438 nm
E) 219 nm

Question

Quizplus · Accepted Answer

For a bright band, the path length difference between the two reflected waves must be an integer multiple of the wavelength. For the thinnest film, this path length difference is equal to twice the thickness of the film. Therefore, the thinnest film for which a bright band will occur is:$$2t = m\lambda$$$$t = \frac{m\lambda}{2}$$For the first bright band, m = 1. Therefore, the thinnest film for which a bright band will occur is:$$t = \frac{1	imes 600 	ext{ nm}}{2} = 300 	ext{ nm}$$However, the question asks for the thinnest soap film, which means the film must be half of this thickness. Therefore, the thinnest soap film for which a bright band will occur is:$$t = \frac{300 	ext{ nm}}{2} = 150 	ext{ nm}$$Therefore, the correct answer is (A) 150 nm.

A Thin Film of Soapy Water (N = 1