Physics - Wave Optics Question with Solution | TestHub

Given, wavelength of light $\lambda =5500\text{ A˚}=5500\times 10^{-10}\text{ m}=5.5\times 10^{-7}\text{ m}$

Distance of the screen from the slits $D=1\text{ m}$

Separation of $5$ bright fringes is given as $1\text{ cm}$. This corresponds to $5$ fringe widths.

$5\beta =1\text{ cm}=10^{-2}\text{ m}$

$\beta =\frac{10^{-2}}{5}=2\times 10^{-3}\text{ m}$

The formula for fringe width is $\beta =\frac{\lambda D}{d}$, where $d$ is the distance between the two slits.

Rearranging for $d$:

$d=\frac{\lambda D}{\beta }$

$d=\frac{5.5\times 10^{-7}\times 1}{2\times 10^{-3}}$

$d=2.75\times 10^{-4}\text{ m}$