Q147 / 150 · MHT CET 2017 · Physics

In Young's double-slit experiment, in an interference pattern, the second minimum is observed exactly in front of one slit. The distance between the slits is $d$ and the distance between source and screen is $D$ . The wavelength of the light source used is

Solution

Distance of second minima from central point is $y = \frac{d}{2}$ .

We know that minima is given by,

$dsinθ = (n - \frac{1}{2}) λ \frac{dy}{D} = (2 - \frac{1}{2}) λ$

$\frac{d^{}}{2} = \frac{D}{d} (\frac{2 \times 2 - 1}{2}) λ$
$∴ \frac{d}{2} = \frac{D}{d} \times \frac{3}{2} λ$
$∴ λ = \frac{d^{2}}{3 D}$

Hence, the correct answer is option: 'C'.