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
$(2n-1)\frac{D\lambda }{2d}=\frac{d}{2}$
Hence, we get $\lambda =\frac{d^2}{(2n-1)D}$
$=\frac{d^2}{D}$ for $n=1$.