# A soap film (n=1.33) is 782 nm thick. White light strikes the film at normal incidence. What...

## Question:

A soap film (n=1.33) is 782 nm thick. White light strikes the film at normal incidence. What visible wavelengths will be constructively reflected if the film is surrounded by air on both sides?

## Constructive reflection from a soap film.

An interference effect occurs when there are at least two waves overlap. When they overlap crest to crest, we have constructive interference; when they overlap crest to trough, we have distructive interference. What this also means is that when the path difference of two waves is a multiple of wavelength, we have constructive interference; while when the path difference is some odd multiple of half-wavelength, we have distructive interference.

## Answer and Explanation:

When path difference is the multiple of wavelengths, there will be constructive reflected waves. Therefore, we have

{eq}\begin{align*} \Delta d&=m\lambda=2t,\\ \lambda&=\frac{2t}{m}, \end{align*} {/eq}

where {eq}\Delta d {/eq} is the path difference, {eq}t {/eq} is the thickness of the soap film, and {eq}m {/eq} is an integer. We have constructive reflected waves in wavelengths:

{eq}\begin{align*} \lambda_1&=1564 \;\text{nm},\\ \lambda_2&=782 \;\text{nm},\\ \lambda_3&=521 \;\text{nm},\\ \lambda_4&=391 \;\text{nm}\cdots \end{align*} {/eq}

Visible wavelengths usually range from 380 nm to 750 nm. Hence, 521 nm and 391 nm, which are green light and violet light, respectively, will be reflected constructively. 