Question

In Young's double-slit experiment, let $A$ and $B$ be the two slits. A thin film of thickness $t$ and refractive index $\mu$ is placed in front of $A$. Let $\beta =$fringe width. Then the central maxima will shift

• A. toward $A$
• B. toward $B$
• C. By $t(\mu -1)\frac{\beta }{\lambda }$
• D. by $\mu t\frac{\beta }{\lambda }$

Answer 1

Answer: (A), (C)

The correct options are
A toward $A$
C By $t(\mu -1)\frac{\beta }{\lambda }$

The insertion of thin film increases the path traveled by light from slit A by $t(\mu -1)$.

Thus the ray from slit B needs to travel an extra path by amount equal to $t(\mu -1)$

Thus the shift is toward A.

Path difference at some point y on the screen=$\frac{yd}{D}$

Thus $\frac{y_{central}d}{D}=t(\mu -1)$

Hence $y_{central}=\frac{Dt}{d}(\mu -1)=\frac{t\beta }{\lambda }(\mu -1)$