Question

A beam of light of wavelength $400nm$ from a distant source falls on a single slit $1mm$ wide and the resulting diffraction pattern is observed on a screen $1m$ away. What is the distance between the first dark fringes on either side of central bright fringe?

• A. $0.2mm$
• B. $0.6mm$
• C. $0.8mm$
• D. $1.2mm$

Answer 1

The correct option is C $0.8mm$

Given, $\lambda =400nm,a=1mm,D=1m$
Distance of first dark fringe from centre,
$y_1=\frac{\lambda D}{a}$
Distance between the first dark fringes on either side of the central bright fringe,
$2y_1=\frac{2D\lambda }{a}=\frac{2\times 1\times 400\times {10}^{-9}}{{10}^{-3}}=800\times {10}^{-6}=0.8mm$