Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

Answers without the blur.

Just sign up for free and you're in.

Short Answer

Show that the dispersion of a grating is $D = \frac{t a n θ}{λ}$

It is proved that the dispersion of a grating is $\frac{\tan θ}{λ}$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Definition and concept of diffraction from a grating

An optical element with a periodic structure that divides light into a number of beams that move in diverse directions is known as a diffraction grating.

The angular distance $θ$ of the $m_{t h}$ order diffraction pattern produced from a grating having line separation is

$d s i n θ = m λ$ …(i)

Here, $λ$ is the wavelength of the incident light.

Step 2: Showing that dispersion of a grating D=tanθλ

The dispersion is given by

$D = \frac{d θ}{d λ}$

Differentiate equation (i) with respect to $λ$ to get

$d \cos θ \frac{d θ}{d λ} = m \frac{d θ}{d λ} = \frac{m}{d \cos θ}$

Substitute form of $m$ from equation (i) to get

$\frac{d θ}{d λ} = \frac{\frac{d \sin θ}{λ}}{d \cos θ} \frac{d θ}{d λ} = \frac{\tan θ}{λ}$

Find Study Materials for

Create Study Materials

Select your language

Fundamentals Of Physics

Answers without the blur.

Short Answer

Show that the dispersion of a grating is $D = \frac{t a n θ}{λ}$

Step by Step Solution

Step 1: Definition and concept of diffraction from a grating

Step 2: Showing that dispersion of a grating D=tanθλ

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Select your language

Fundamentals Of Physics

Answers without the blur.

Short Answer

Show that the dispersion of a grating is D=tanθλ

Step by Step Solution

Step 1: Definition and concept of diffraction from a grating

Step 2: Showing that dispersion of a grating D=tanθλ

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Work Energy and Power

Radiation

Astrophysics

Physics of Motion

Scientific Method Physics

Fluids

Torque and Rotational Motion

Nuclear Physics

Fields in Physics

Measurements

Space Physics

Electricity

Physical Quantities and Units

Medical Physics

Electrostatics

Further Mechanics and Thermal Physics

Mechanics and Materials

Engineering Physics

Energy Physics

Force

Particle Model of Matter

Waves Physics

Magnetism

Modern Physics

Atoms and Radioactivity

Dynamics

Electricity and Magnetism

Conservation of Energy and Momentum

Fundamentals of Physics

Kinematics Physics

Circular Motion and Gravitation

Linear Momentum

Rotational Dynamics

Oscillations

Translational Dynamics

Geometrical and Physical Optics

Thermodynamics

Magnetism and Electromagnetic Induction

Electromagnetism

Electric Charge Field and Potential

Turning Points in Physics

Show that the dispersion of a grating is $D = \frac{t a n θ}{λ}$