Question

A double-slit diffraction pattern is formed on a distant screen. If the separation between the slits decreases, what happens to the distance between interference fringes? Assume the angles involved remain small.

	The distance between interference fringes remains the same.
	The effect cannot be determined unless the distance between the slits and the screen is known.
	The distance between interference fringes also decreases.
	The distance between interference fringes increases.

Answer 1

Concepts and reason

The concept which is used to solve this problem is double-slit diffraction.

Use the relation between wavelength, slit widths, screen distance to find the expression for the distance from the centerline for minimum intensity.

Use the relation between the distance from the centerline for minimum intensity and screen distance to find the correct option from the given statement.

Fundamentals

Diffraction and interference are the phenomenon that differentiates between waves and particles.

Particles do not diffract and interfere but waves do.

When the light passes through the slit, the pattern of the resulting waves can be calculated by considering each point in the gap as a point source from which new waves spread out.

The condition for minimum diffraction pattern is as follows:

Here, is the slit width, n is the order, is the wavelength, and is the angle.

By small angle approximation,

Here, y is the distance from the center for minimum intensity and D is the screen distance.

The condition for minimum diffraction is as follows:

…… (1)

By small angle approximation,

Substitute for in Equation (1).

Rearrange Equation (1) to get y,

The incorrect options are as follows:

• The distance between interference fringes remains the same.

• Unless the distance between the slits and the screen is known, the effect cannot be determined.

• There will be a decrease in the distance between interference fringes.

Expression for the distance from the centerline for minimum intensity is as follows:

From the above expression,

Hence, the correct option is, the distance between the interference fringes increases.

Ans:

Thus, the distance between the interference fringes increases.