question_answer

In Youngs 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)  \[\frac{{{d}^{2}}}{D}\]

Correct Answer: D

Solution :

                 We have the Youngs 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 \[n=1.\]