In the Young's double slit experiment , a mica slip of thickness t and refractive index `mu` is introduced in the ray from first source `S_(1)` . By how much distance fringes pattern will be displaced ? (d = distance between the slits and D is the distance between slits and screen)

Options

A. `(d)/(D)(mu-1)t`
B. `(D)/(d)(mu-1)t`
C. `(d)/((mu-1)D)`
D. `(D)/(d)(mu-1)`

Answer

B

Explanation

Mica sheet of thickness 't'
refractive index `mu`
`DeltaX_(P)=S_(2)P-[(S_(1)P-t)_(air)+t_("sheet")]`
`=(S_(2)P-S_(1)P)-(mut-t)`
Additional path difference position of `n^(th)` maxima
`nlamda=(dy_(n))/(D)-(mu-1)timpliesy_(n)=(nDlamda)/(d)+(D)/(d)(mu-1)t`
Shift of interference pattern `=(D)/(d)(mu-1)t`