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Found in: Page 997

### College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

# What is the wavelength of light falling on double slits separated by 2.00 µm if the third-order maximum is at an angle of 60.0º ?

The wavelength of the light is${}^{577\mathrm{nm}}$.

See the step by step solution

## Step 1: Given data

The angle for the third minimum is${}^{\mathbf{60}\mathbf{.}{\mathbf{0}}^{\mathbf{0}}}$

The separation of the double slits is $\mathrm{d}=2.00\mathrm{\mu m}\left(\frac{{10}^{-6}\mathrm{m}}{1\mathrm{\mu m}}\right)=2.00×{10}^{-6}\mathrm{m}$

## Step 2: Finding the wavelength of the light

A formula for the angle of the third-order maximum can be expressed as,

$\mathrm{dsin\theta }=3\mathrm{\lambda }...............................\left(1\right)$

Substituting the given data in equation (1), we get,

$2.00×{10}^{-6}\mathrm{m}×\mathrm{sin}\left(60.{0}^{0}\right)=3×\mathrm{\lambda }\phantom{\rule{0ex}{0ex}}\mathrm{\lambda }=\left(\frac{1.732×{10}^{-6}\mathrm{m}}{3}\right)\phantom{\rule{0ex}{0ex}}\mathrm{\lambda }=0.577×{10}^{-6}\mathrm{m}\left(\frac{1\mathrm{nm}}{{10}^{-9}\mathrm{m}}\right)\phantom{\rule{0ex}{0ex}}\mathrm{\lambda }=577\mathrm{nm}$

Thus, the distance between two slits is ${}^{\mathbf{577}\mathbf{}\mathbf{nm}}$.