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 $
$\therefore \lambda =\frac{\text{d}^{2}}{3 \text{D}}$