Question

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 $\text{d}$ and the distance between source and screen is $\text{D}$ . The wavelength of the light source used is

• A. $\frac{{\text{d}}^2}{\text{D}}$
• B. $\frac{{\text{d}}^2}{2\text{D}}$
• C. $\frac{{\text{d}}^2}{3\text{D}}$
• D. $\frac{{\text{d}}^2}{4\text{D}}$

Answer 1

Answer: (C)

Distance of second minima from central point is $y=\frac{d}{2}$ .
We know that minima is given by,
$dsin\theta =\left(n-\frac{1}{2}\right)\lambda \frac{dy}{D}=\left(2-\frac{1}{2}\right)\lambda$
$\frac{d^{}}{2}=\frac{D}{d}\left(\frac{2\times 2-1}{2}\right)\lambda$
$\therefore \frac{d}{2}=\frac{D}{d}\times \frac{3}{2}\lambda$
$\therefore \lambda =\frac{{\text{d}}^2}{3\text{D}}$