To make the central fringe at the center`O` , mica sheet of refractive index `1.5` is introduced Choose the corect statement.

Options

A. the thickness of sheet is `2(sqrt(2)-1)d` infront of `S_(1)`
B. the thickness of sheet is `(sqrt(2)-1)d` infront of `S_(2)`
C. the thickness of sheet is `2sqrt(2)d` infront of `S_(1)`
D. the thickness of sheet is `(2sqrt(2)-1)d` infront `S_(1)`.

Answer

A

Explanation

Here the shift produced by mica sheet of thickness `t` is `(mut-t)=t(mu-1)`. It should be equal to extra path traveled by the ray `SS_(2)O` i.e., `Delta=SS_(2)-d=sqrt(2)d-d`
`implies(t)/(2)=d(sqrt(2)-1)impliest=2d(sqrt(2)-1)` infront of `S_(1)`