Monochromatic light ($\lambda$ = 500 nm)is incident on a soap bubble (n = 1.40).What is the wavelength of the light (in nm)in the bubble film?
A)255
B)500
C)700
D)357
E)422

Question

Quizplus · Accepted Answer

When monochromatic light enters a soap bubble film, it reflects from both surfaces of the film, causing interference. This interference leads to a pattern of bright and dark bands called interference fringes. The condition for constructive interference is given by 2nt = mλ, where n is the refractive index of the film, t is the thickness of the film, m is an integer (1, 2, 3, etc.), and λ is the wavelength of the incident light. For the first-order maximum, m = 1. Therefore, λ = 2nt/m = 2n(t/1) = 2nt, where t is the thickness of the film at the point of incidence of the light. For a soap bubble, the thickness of the film varies from zero (at the top) to some maximum value (at the bottom), so the wavelength of the light in the bubble film will also vary. However, we can use the average value of the thickness to get an approximation. The average thickness of a soap bubble is about 250 nm. Thus, the wavelength of the light in the bubble film is approximately 2n(250 nm) = 2(1.40)(250 nm) = 700 nm. Answer choice D is the closest to this value.

Monochromatic Light λ\lambdaλ = 500 Nm)is Incident on a Soap Bubble (N =

Monochromatic Light $\lambda$ = 500 Nm)is Incident on a Soap Bubble (N =