Question

A beam of light of $\lambda =600nm$ from a distant source falls on a single slit $1mm$ wide and the resulting diffraction pattern is observed on a screen $2m$ away. The distance between first dark fringes on either side of the central bright fringe is

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

Answer 1

The correct option is B $2.4cm$

Putting $n=1$ for condition for first minimum,

$\sin \frac{\lambda }{d}⟶1$

If $x$ is the distance between the dark fringes

$\sin \theta =\frac{x}{2D}x=\frac{2D\lambda }{d}=\frac{2\times 2\times 600\times {10}^{-4}}{{10}^{-3}}=2.4cm$