# 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?

(Answer in nm)

## 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.

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from CLEP Natural Sciences: Study Guide & Test Prep

Chapter 8 / Lesson 16