Question

A beam of light of wavelength $600\text{nm}$ from a distant source, falls on a single slit $1.00\text{mm}$ wide and the resulting diffraction pattern is observed on a screen $2\text{m}$ away. The distance between the first dark fringe, on either side of the central bright fringe is,

• A. $1.2\text{cm}$
• B. $1.2\text{mm}$
• C. $2.4\text{cm}$
• D. $2.4\text{mm}$

Answer 1

The correct option is D $2.4\text{mm}$

In a single slit diffraction setup, the width of central maximum is twice the width of secondary maximum/minimum.

The distance of first minimum, from central maximum, is,
$\beta =\frac{\lambda D}{a}$

$\therefore$ distance between the first minima, on either sides of the central maximum, is given by,

$2\beta =\frac{2\lambda D}{a}$
$=\frac{2\times 600\times {10}^{-9}\times 2}{{10}^{-3}}=2.4\text{mm}$

Hence, $\left(D\right)$ is the correct answer.

Why this question? To understand the layout of diffraction pattern and to know/find out the distance between maxima/minima of different order.