Question

Light passes through a single slit. If the width of the slit is reduced, what happens to the width of the central bright fringe? (a) The width of the central bright fringe does not change, because it depends only on the wavelength of the light and not on the width of the slit. (b) The central bright fringe becomes wider, because the angle that locates the first dark fringe on either side of the central bright fringe becomes smaller. (c) The central bright fringe becomes wider, because the angle that locates the first dark fringe on either side of the central bright fringe becomes larger. (d) The central bright fringe becomes narrower, because the angle that locates the first dark fringe on either side of the central bright fringe becomes larger. (e) The central bright fringe becomes narrower, because the angle that locates the first dark fringe on either side of the central bright fringe becomes smalle

Answer 1

Answer:

(c) The central bright fringe becomes wider, because the angle that locates the first dark fringe on either side of the central bright fringe becomes larger.

Explanation:

The formula that gives the angle of the first minimum of the diffraction pattern from a single-slit is

$sin \theta = \frac{\lambda}{w}$

where

$\lambda$ is the wavelength of the light

w is the width of the slit

We see that the angle is inversely proportional to the width of the slit: therefore, if the width of the slit is reduced (so, w is decreased), the angle that locates the first minimum $\theta$ increases, and so the central bright fringe becomes wider.