question_answer

In a double slit experiment, 5th dark fringe is formed opposite to one of the slits, the wavelength of light is

A)  \[\frac{d{{e}^{2}}}{6D}\]            

B)  \[\frac{{{d}^{2}}}{9D}\]

C)  \[\frac{{{d}^{2}}}{15D}\]           

D)  \[\frac{{{d}^{2}}}{9D}\]

Correct Answer: D

Solution :

For dark fringe, \[\frac{xd}{D}=(2m-1)\frac{\lambda }{2}\] Here,  \[m=5,\] \[x=\frac{d}{2}\] \[\therefore \]  \[\frac{d}{2}.\frac{d}{D}=(2\times 5-1)\frac{\lambda }{2}\] or \[\frac{{{d}^{2}}}{D}=9\lambda \] \[\therefore \] \[\lambda =\frac{{{d}^{2}}}{9D}\]