Chapter 19, Problem 60A

To determine

To explain: The changes in the single slit diffraction pattern as the width of the slit is decreased.

Explanation of Solution

Introduction:

Diffraction of light waves is the bending of light waves around the ends of an obstacle. This illuminates the region where the geometrical shadow of the obstacle is expected. As the light wave encounters the slit there will be a diffraction of light waves from the slit and interference takes place between the light waves that are diffracted from the slit. The interference may be constructive or destructive. For constructive interference, the band produced in the pattern is bright and for the destructive interference, the region is dark in the pattern.

The single slit forms a diffraction pattern that contains bright and broad central band with blurred side bands.The expression for the central band width is given by,

  $\beta =\frac{2\lambda D}{d}$

Where, $\lambda$ is the wavelength of light $D$ is the distance between the slit and the screen $d$ is the slit width

Above expression indicates that bandwidth of the central band is inversely proportional to the slit width. Hence if the slit width is reduced, the bands in the pattern becomes wider and dimmer.