Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

If, in a two-slit interference pattern, there are $8$ bright fringes within the first side peak of the diffraction envelope and diffraction minima coincide with two-slit interference maxima, then what is the ratio of slit separation to slit width?

The ratio of the slit separation to the slit width is $9 : 1$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given data

In a two-slit interference pattern, there are $8$ bright fringes within the first side peak of the diffraction envelope.

Step 2: Diffraction and interference from a double slit

The angular distance of the $m_{t h}$ order diffraction minima is given by

$a s i n θ = m λ$ …(i)

Here, $λ$ is the wavelength of the incident light and $a$ is the slit width.

The angular distance of the $n_{t h}$ order interference maxima is given by

$d s i n θ = n λ$ …(ii)

Here, $λ$ is the wavelength of the incident light and $d$ is the separation between the two slits.

Step 3: Determining the ratio of the slit separation to the slit width

The $9_{t h}$ interference maxima coincide with the $1_{s t}$ diffraction minima. From equations (i) and (ii) the angular distance of the $1_{s t}$ diffraction minima and the $9_{t h}$ interference maxima is

$\begin{array}{l} d \sin θ = 9 λ \\ a \sin θ = λ \end{array}$

Divide the two equations to get

$\frac{d}{a} = \frac{9}{1}$

Thus, the required ratio is $9 : 1$ .

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Fundamentals Of Physics

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Short Answer

If, in a two-slit interference pattern, there are $8$ bright fringes within the first side peak of the diffraction envelope and diffraction minima coincide with two-slit interference maxima, then what is the ratio of slit separation to slit width?

Step by Step Solution

Step 1: Given data

Step 2: Diffraction and interference from a double slit

Step 3: Determining the ratio of the slit separation to the slit width

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If, in a two-slit interference pattern, there are8 bright fringes within the first side peak of the diffraction envelope and diffraction minima coincide with two-slit interference maxima, then what is the ratio of slit separation to slit width?

Step by Step Solution

Step 1: Given data

Step 2: Diffraction and interference from a double slit

Step 3: Determining the ratio of the slit separation to the slit width

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If, in a two-slit interference pattern, there are $8$ bright fringes within the first side peak of the diffraction envelope and diffraction minima coincide with two-slit interference maxima, then what is the ratio of slit separation to slit width?