Physics - Wave Optics Question with Solution | TestHub

The angular width of the central maximum in a single slit diffraction pattern is given by ${\theta }_0=\frac{2\lambda }{a}$, where $a$ is the width of the slit.

The angular separation between two consecutive maxima (fringe width) in a double slit interference pattern is given by $\theta =\frac{\lambda }{d}$, where $d$ is the distance between the two slits.

The number of interference maxima $N$ that can be accommodated within the central diffraction maximum is the ratio of their angular widths:

$N=\frac{{\theta }_0}{\theta }=\frac{\frac{2\lambda }{a}}{\frac{\lambda }{d}}=\frac{2d}{a}$

Given that $N=10$ and $d=1$ mm, substituting these values we get:

$10=\frac{2\times 1}{a}$

$a=\frac{2}{10}=0.2$ mm

The width of each slit is $0.2$ mm.

Answer: $0.2$ mm