\[{{M}_{1}}\] 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. \[\lambda =\frac{3{{d}^{2}}}{2D},\]\[\frac{3{{d}^{2}}}{4D}\] |
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