Question

Light from a helium-neon laser passes (λ = 633nm) through a circular aperture and is observed on a screen 5.60 m behind the aperture. The width of the central maximum is 1.20 cm.

What is the diameter (in mm) of the hole?

Answer 1

Concepts and reason

The concept required to solve this problem is diffraction.

First, obtain the expression for the diameter of the hole by using the expression for the width of the airy disk and expression for the angular width in terms of diameter of the hole. Finally, calculate the value of the diameter of the hole by using the values of the wavelength of the light, distance from the hole to the screen, and the width of the central maximum.

Fundamentals

The expression for the angular width in terms of diameter of the hole is,

$=2.44 $

Here, is the wavelength of the light and is the diameter of the circular aperture.

The width of the central maximum is expressed as follows;

Here, is the distance from the hole to the screen.

The expression for the angular width in terms of diameter of the hole is,

$=2.44 $ …… (1)

The width of the airy disk is expressed as follows;

Rearrange the above equation for.

…… (2)

Compare the equations (1) and (2) and solve for the diameter of the hole.

The expression for the diameter of the hole is,

Substitute for , 5.60 m for L, and 1.20 cm for w.

Ans:

The diameter of the hole is .