Question

In Young's double slit experiment the distance between the slits is $1mm$ . Find the width of each slit of YDSE setup so that $10^{th}$ maxima of the double slit pattern is within the central maximum of the single slit pattern?

• A. $0.9mm$
• B. $0.8mm$
• C. $0.2mm$
• D. $0.6mm$

Answer 1

Answer: (C)

The angular separation between $n$ bright fringes, ${\theta }_n=\frac{x_n}{D}=\frac{n\lambda }{d}$
Fringes, ${\theta }_n=\frac{x_n}{D}=\frac{n\lambda }{d}$
For 10 bright fringes, ${\theta }_{10}=\frac{10\lambda }{d}$
The angular width of the central maximum in the diffraction pattern due to slit of width $a$ is
$2{\theta }_1=\frac{2\lambda }{a}$
Now $\frac{10\lambda }{d}\le \frac{2\lambda }{a}$ or $a\le \frac{d}{5}=\frac{1}{5}mn=0.2mn$