Question

An experiment isconducted in which red light is diffracted through a singleslit.

Then, each of the following alterationsto the original experiment is made, one at a time, and theexperiment is repeated. After each alteration, the experiment isreturned to its original configuration.

A	The slit width is halved.
B	The distance between the slits and the screen is halved.
C	The slit width is doubled.
D	A green, rather than red, light source is used.
E	The experiment is conducted in a water-filled tank.
F	The distance between the slits and the screen is doubled.

Part A

Which of these alterations decreases theangles at which the diffraction minima appear?

Answer 1

Concepts and reason

The concept of diffraction minima is required to solve the problem.

First, find the wrong alterations which will not decreases the angles at which the diffraction minima appear by using the expression of first diffraction minimum. Then find the correct alterations which decreases the angles at which the diffraction minima appear by using the expression of first diffraction minimum.

Fundamentals

Bending of waves is called diffraction. Around the obstacles the light bends and causes the single slit diffraction pattern.

When light passes through the slit the pattern of the wave is calculated by treating each point in the aperture as a point source from where the new waves spread.

The expression for the angle at which the first diffraction minimum occurs is given as,

$\begin{array}{c}\\\sin \theta = \left( {\frac{{m\lambda }}{a}} \right)\\\\\theta = {\sin ^{ - 1}}\left( {\frac{{m\lambda }}{a}} \right)\\\end{array}$

Here, $\lambda$ is the wavelength of the light, $\theta$ is the diffraction angle, $m$ is the order of the minima, and $a$ is the slit width.

The angles at which the diffraction minima appear increases with when the slit width is decreased. Hence, when the slit width is halved, the angle at which diffraction minimum appears will not decrease.

The angle at which diffraction minimum appears does not depend on the distance between the slits and the screen. Hence, the angle will not increase with any alteration in the distance between the slit and the screen

Thus, the alteration which will not decreases the angles at which the diffraction minima appear are,

• The slit width is halved.

• The distance between the slits and the screen is halved.

• The distance between the slits and the screen is doubled.

(C)

The angle at which the diffraction minimum appears is given as,

$\theta = {\sin ^{ - 1}}\left( {\frac{{m\lambda }}{a}} \right)$

Here, $\lambda$ is the wavelength of the light, $\theta$ is the diffraction angle, $m$ is the order of the minima, and $a$ is the slit width.

From the above expression, the slit width is inversely proportional to the angle between central maxima and diffraction minima. Thus, the angle at which diffraction minimum appears will decrease when the slit width is increased.

Hence, the angles at which the diffraction minima appear will decrease when the slit width is doubled.

(D)

The expression for the diffraction angle is,

$\theta = {\sin ^{ - 1}}\left( {\frac{{m\lambda }}{a}} \right)$.

The diffraction angle is directly proportional to the wavelength.

The wavelength of the green light source is less when comparing with the red light. Green light is used because it reduces the angle by half.

Hence, the angles at which the diffraction minima appear will decrease when a green light source is used.

(E)

Inside the denser medium, the wavelength of the light is reduced, speed is reduced and the frequency remains constant.

When light travels in denser medium the wavelength of light will get decreased.

The angle is proportional to the wavelength of light used. Decreasing the wavelength by using different lights will decrease the angle.

Hence, the angles at which the diffraction minima appear will decrease when the experiment is conducted in a water-filled tank.

Ans: Part C

The alteration which decreases the angles at which the diffraction minima appear is when the slit width is doubled.

Part D

The alteration which decreases the angles at which the diffraction minima appear is a green, rather than red, light source is used.

Part E

The alteration which decrease the angles at which the diffraction minima appear is the experiment is conducted in water filled tank.