question_answer

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

The situation can be taken as if there are two soureces \[{{S}_{1}}\] and \[{{S}_{2}}\] 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.

For 'O' to be a maxima:

Path difference\[=\frac{3d.d}{2D}=n\lambda \]    \[\Rightarrow \]\[\lambda =\frac{3{{d}^{2}}}{2nD}\] ie. \[\lambda =\frac{3{{d}^{2}}}{2D},\]\[\frac{3{{d}^{2}}}{4D}\]