question_answer

\[{{M}_{1}}\text{ }and\text{ }{{M}_{2}}\] are plane mirrors and kept parallel to each other. At point O there will be maxima for wavelength. Light from monochromatic source S of wavelength \[\lambda \] is not reaching directly on the screen. The \[\lambda \] is \[-\,[D>>d,d>>\lambda ]\]

A) \[\frac{3{{d}^{2}}}{D}\]                                 

B) \[\frac{3{{d}^{2}}}{2D}\]

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

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

Correct Answer: B

Solution :

[B]

The situation can be taken as if there are two sources Si and & as shown in figure. Due to these \[{{S}_{1}}\] and \[{{S}_{2}},\] the central maxima will be at P at a distance d/2 from O.

Path difference \[=\frac{3d.d}{2D}=n\lambda \]

\[\Rightarrow \lambda =\frac{3{{d}^{2}}}{2nD}\]

i e. \[\lambda =\frac{3{{d}^{2}}}{2D},\frac{3{{d}^{2}}}{4D}\]