Question

In Young’s double slit experiment the two slits are d distance apart. Interference pattern is observed on a screen at a distance $D$ from the slits. A dark fringe is observed on the screen directly opposite to one of the slits. The wavelength of light is

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

Answer 1

Answer: (D)

We have the Young’s double slit experiment given by

From the question, we see that the distance between the slits is equal to d and the distance between the slit and screen is equal to $D$. Hence for the nth dark fringe, we have
$(2 n-1) \frac{D \lambda}{2 d}=\frac{d}{2}$
Hence, we get $\lambda=\frac{d^{2}}{(2 n-1) D}$
$=\frac{d^{2}}{D}$ for $n=1$.