Answered: two parralel slits are illuminated by…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

two parralel slits are illuminated by light of two wavelengths, one of which is (5.8*10^-7 )m. on the screen the fourth dark line of known wavelength coincides with fifth bright line of unkown wavelegth. find the unkown wavelegth.

Expert Solution

Step 1

Given data:

Value of known wavelength is, $λ_{1} = 5.8 \times 10^{- 7} m$ .

Order of fringes of light of known wavelength is, $n_{1} = 4$ .

Order of fringes of light of unknown wavelength is, $n_{2} = 5$ .

Step 2

Expression for angular position for constructive interference $(θ_{2})$ is given as,

$d \sin θ_{2} = m λ_{2} \sin θ_{2} = \frac{m λ_{2}}{d}$

Here, m denotes the order of fringes. And d is the width of slit.

For destructive interference, the expression for the angular position is given as,

$d \sin θ_{1} = (m + \frac{1}{2}) λ_{1}$

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