Book edition 1st Edition

Author(s) Paul Peter Urone

Pages 1272 pages

ISBN 9781938168000

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Short Answer

How many lines per centimeter are there on a diffraction grating that gives a first-order maximum for $470 ‐ nm$ blue light at an angle of $25 . 0^{\circ}$ ?

The lines per cm for the first-order maximum are $8929$ per centimeter.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given data

$λ = 470 nm (\frac{10^{‐ 9} m}{1 nm}) = 4 . 70^{,} 10^{‐ 7} m$

The wavelength of the blue light is

The order of maximum is 1.

The angle at which the first-order maximum is observed $_{25 . 0^{\circ}}$

Step 2: Evaluating the lines per centimeter for first-order maximum

The equation of the constructive interference can be expressed as

$d sinθ = mλ$ …………………(1)

Where, $d, λ, θ$ and m is the separation between slits, the wavelength of the incident light, and the angle made with the maximum and order of maximum, respectively.

Therefore, if we substitute the given data in equation (1) for m=1, we will get,

We then evaluate the number of lines per centimeter, $n$ , using the relation:

$n = \frac{1.0 cm}{d}$ .

Substitute the value in the above expression, and we get,

$n = (\frac{1.0 cm}{1.12 \times 10^{‐ 6} m}) (\frac{1 m}{100 cm}) \approx 8929$

Therefore, the lines for the first-order maximum are $^{8929}$ per centimeter.

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College Physics (Urone)

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Short Answer

How many lines per centimeter are there on a diffraction grating that gives a first-order maximum for $470 ‐ nm$ blue light at an angle of $25 . 0^{\circ}$ ?

Step by Step Solution

Step 1: Given data

Step 2: Evaluating the lines per centimeter for first-order maximum

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College Physics (Urone)

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Short Answer

How many lines per centimeter are there on a diffraction grating that gives a first-order maximum for 470‐nm blue light at an angle of 25.0∘?

Step by Step Solution

Step 1: Given data

Step 2: Evaluating the lines per centimeter for first-order maximum

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