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 fringe on either side of the central maxima is :

• A. $1.2cm$
• B. $1.2mm$
• C. $2.4mm$
• D. $4.8mm$

Answer 1

The correct option is C $2.4mm$

Condition for obtaining $m^{th}$ order minima is
$asin\theta =m\lambda$

Thus for obtaining first diffraction minima,

$asin\theta =\lambda$

$⟹sin\theta =\frac{600\times {10}^{-9}m}{{10}^{-3}m}\approx tan\theta =\frac{y}{D}$

$⟹y=1.2mm$

Thus distance between fringes on either side=$2\times y=2.4mm$