Question

In a double-slit experiment, the distance between the two slits is $1mm$ and the screen is placed $1m$ away. What should be the width of each slit to obtain $20$ maxima of double slit pattern within the central maximum of the single slit pattern?

• A. $0.05cm$
• B. $0.02cm$
• C. $0.01cm$
• D. $0.08cm$

Answer 1

The correct option is C $0.01cm$

Given,

$d=1mm$

$D=1m$

$n=20$

Lets consider, $a=$ width of each slit

Width of the central maxima, ${\beta }^{\prime }=\frac{2\lambda D}{a}$

Fringe width, $\beta =\frac{\lambda D}{d}$

According to the question,

$20\beta ={\beta }^{\prime }$

$20.\frac{\lambda D}{d}=\frac{2\lambda D}{a}$

$10.a=d$

$a=\frac{d}{10}=\frac{1mm}{10}$

$a=0.1mm=0.01cm$

The correct option is C.