Question

A $0.50-mm$-diameter hole is illuminated by light of wavelength $550nm$. What is the width (in mm) of the central maximum on a screen $2.0m$ behind the slit?

Short answer

The Width of the cental screen is$4.8mm$

Step-by-step solution

Introduction

When light passes through a narrow opening, such as an aperture with a low f-number, it causes lens diffraction, which is an optical interference.

When the wavelength of light and the size of the opening are about the same, lens diffraction occurs.

Find width 

In a circular-aperture experiment, the central width is given by

$w=\frac{2.44\lambda L}{D}$

where$D$is the aperture diameter and $L$is the distance to the screen

Find width 

In our scenario, we'll be able to

$w=\frac{2.44\lambda L}{D}$

localid="1650215942766" $w=\frac{2.44\times 5\times {10}^{-7}m\times 2m}{5\times {10}^{-4}m}$

$=4.88\times {10}^{-3}\mathrm{m}$

$=4.88\mathrm{mm}$