Question

- In a single slit diffraction experiment, the width of the slit is made double its original width. Then the central maximum of the diffraction pattern will become
A. narrower and fainter
B. narrower and brighter
C. broader and fainter
D. broader and brighter

Answer 1

This question is based on a single slit diffraction experiment. The single slit diffraction is the study of the intensity distribution due to diffraction from a single slit and to determine the slit width. And it occurs when the light moving within a single slit is of the order of wavelength of light, then a slit pattern can be observed.

Complete step by step answer:
In this question, if the width of the slit is made double its original width, so the central maximum of the diffraction pattern will become narrower and brighter.

The angular width of the central maximum is given by,
$w = \dfrac{{2D\lambda }}{a}$
Here, $a$ is the width of the slit and $\lambda$ is the wavelength.

If the value of $a$ becomes doubled, then the angular width of the central maximum decreases to half its previous value. This is because of the inverse relationship between width of slit and angular width.
This implies that the central maximum becomes much sharper. Moreover, if $a$ is doubled, then the intensity of the central maximum becomes four times. Therefore, the central maximum becomes much narrower and brighter.

Thus, the option (B) is correct.

Note:
In this question, we must have the knowledge regarding the single slit experiment and the formula for finding the angular width. So that we can easily make a relation between the angular width and the width of the slit.