A soap film is illuminated by white light normal to its surface. the index of refraction of the film is 1.50. wavelengths of 480 nm and 800 nm and no wavelengths between are intensified in the reflected beam. the thickness of the film is:

Question

Ethen Stewart

Physics

8 February, 01:54

A soap film is illuminated by white light normal to its surface. the index of refraction of the film is 1.50. wavelengths of 480 nm and 800 nm and no wavelengths between are intensified in the reflected beam. the thickness of the film is:

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Kenneth Ritter · Answer 1

Since the index of refraction of the film is larger than that of air (n = 1) there is an additional phase shift for the reflection in the soap film.

The formula for constructive interference is

2L = (m + 0.5) λ/n

Where,

L = thickness of the film

m = order number

λ = wavelength

n = index of refraction = 1.50

Rewriting in terms of λ:

λ = 3L / (m + 0.5)

The information that λ = 800 nm and λ = 480 nm are consecutive maximum means that if λ = 800 nm refers to m, then λ = 480 nm refers to m + 1. Using the m dependence on λ, this implies that:

800 / (m + 1 + 0.5) = 480 / (m + 0.5)

800 (m + 0.5) = 480 (m + 1.5)

800 m + 400 = 480 m + 720

320 m = 320

m = 1

In other words for m = 1 and λ = 800 nm:

L = (m + 0.5) λ/3 = (1.5) * 800/3 = 400 nm