`M_(1)` and `M_(2)` are plane mirrors and kept parallel to each other. At point O, there will be a maxima for wavelength `lambda`. Light from a monochromatic sources S of wavelength `lambda` is not reaching directly on the screen. Then, `lambda` is

Options

A. `(3d^(2))/(D)`
B. `(3d^(2))/(2D)`
C. `(d^(2))/(D)`
D. `(2d^(2))/(D)`

Answer

B

Explanation

For reflected light waves the two virtual source (images of source in mirror) at a distance 3d
path difference at `O=S_(2)O-S_(1)O`
`sqrt(D^(2)+(2d)^(2))-sqrt(D^(2)+d^(2))=lamda`
`impliesD^(2)+4d^(2)=D^(2)+d^(2)+lamda^(2)+2sqrt(D^(2)+d^(2))lamda`
`implies3d^(2)=2Dlamdaimplieslamda=(3d^(2))/(2D)`