Question

A narrow slit of width 1 mm is illuminated by monochromatic light of wavelength 600 nm. The distance between the first minima on either side of a screen at a distance of 2m is

• A. 1.2 cm
• B. 1.2 mm
• C. 2.4 cm
• D. 2.4 mm

Answer 1

Answer: (D)

For first dark fringe on either side,
$\begin{array}{l}d\sin \theta =\lambda \\ \Rightarrow \frac{dy}{D}=\lambda [\sin \theta \simeq \tan \theta ]\\ \therefore y=\frac{\lambda D}{d}\end{array}$
There fore, dis $\tan$ ce between two dark fringes on either side $=2y=\frac{2\lambda D}{d}$
Substituting the values, we have dis $\tan ce=\frac{2\left(600\times 10^{-6}mm\right)\left(2\times 10^{3}mm\right)}{(1.0mm)}=2.4mm$