Question

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

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

Answer 1

Answer: (D)

$2.4mm$

$\text{Given}:$ $\lambda =600nm$, d = 1.00 mm, D = 2 m

$\text{Solution}:$

For the diffraction at a single slit, the position of minima is given by

$dsin\theta =n\lambda$

For small value of $\theta$,

$sin\theta \approx \theta =\frac{y}{D}$

$\therefore \frac{dy}{d}=\lambda$ or

$y=\frac{D}{d}\lambda$

Substituting the values ,we have

$y=\frac{2\times 6\times {10}^{-7}}{1\times {10}^{-3}}=1.2\times {10}^{-3}m=1.2mm$

$\therefore$ Distance between first minima on either side of central side of central maxima=2y=2.4mm.

$\text{Hence D is the correct option}$