Question

In Young's double slit experiment the distance between the slits is $1 \, mm$ . Find the width of each slit of YDSE setup so that $10^{t h}$ maxima of the double slit pattern is within the central maximum of the single slit pattern?

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

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 $\frac{10 \lambda }{d}\leq \frac{2 \lambda }{a}$ or $a\leq \frac{d}{5}=\frac{1}{5}mn=0.2mn$