Question

An experiment is conducted in which red light is diffracted through a single slit.


Then, each of the following alterations to the original experiment is made, one at a time, and the experiment is repeated. After each alteration, the experiment is returned 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.

A. Which of these alterations decreases the angles at which the diffraction minima appear?

Answer 1

Concepts and reason

The concept used to solve this problem is diffraction grating.

Use the equation of the diffraction grating to find the alteration where the angle decreases.

Fundamentals

Expression for the diffraction grating equation is as follows:

Here, the order is , wavelength of the light is , slit width is , and the angle of incidence at which the diffraction minima occurs is .

The incorrect options are given below:

• 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.

Expression for the diffraction grating equation is as follows:

Rearrange the expression to get the expression for .

The angle of incidence is directly proportional to the wavelength of the light and inversely proportional to the slit width.

The slit width is inversely proportional to the angle of incidence. If the slit width decreases, then the angle decreases.

The slit width is being halved which means it is decreasing, so the angle increases.

There is no relationship between the angle and the distance between the slits and the screen.

The angle is independent of the distance between the slits and the screen.

Therefore, the angle will not be affected if the distance between the slits and the screen increases or decreases.

The correct option is given below:

• The slit width is doubled.

The correct option is given below:

• A green, rather than red, light source is used.

The red light has the longest wavelength than the wavelength of the green light.

The angle is directly proportional to the wavelength of the light.

The correct option is given below:

• The experiment is conducted in a water-filled tank.

If the experiment is conducted in a water-filled tank, then the light will travel from the rarer medium to the denser medium.

When the light moves into the water from air, the velocity and the wavelength of the light will change.

The wavelength of the light will decrease. Therefore, the angle will decrease.

Ans:

The diffraction minima decrease when the slit width is doubled.

The diffraction minima appear when a green light source is used rather than the red light source.

The diffraction minima occur when the experiment is conducted in water filled tank.