In Young's double slit experiment, in an interference pattern, second minimum is observed exactly in front…
In Young's double slit experiment, in an interference pattern, second minimum is observed exactly in front of one slit. The distance between the two coherent sources is ' $d$ ' and the distance between the source and screen is ' $D$ '. The wave length of light $(\lambda)$ used is
$\frac{\mathrm{d}^2}{\mathrm{D}}$
$\frac{\mathrm{d}^2}{2 \mathrm{D}}$
$\frac{\mathrm{d}^2}{3 \mathrm{D}}$
$\frac{\mathrm{d}^2}{4 \mathrm{D}}$
Solution
Second minimum is exactly in front of one slit indicates, $\mathrm{y}_2=\frac{\mathrm{d}}{2}$
But $\mathrm{y}_{\mathrm{n}}^{\prime}=\frac{(2 \mathrm{n}-1) \lambda \mathrm{D}}{2 \mathrm{~d}}$
For $\mathrm{n}=2$
$\therefore \quad \frac{\mathrm{d}}{2}=\frac{(2 \times 2-1) \lambda \mathrm{D}}{2 \mathrm{~d}}$
$\therefore \quad \lambda=\frac{\mathrm{d}^2}{3 \mathrm{D}}$