Question

In a Youngs 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 with the central maximum 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 $t(\mu -1)\frac{\beta }{\lambda }$

Let $d=$ distance between the slits, $\lambda =$ wavelength of light,
$D=$distance from the slits to the screen.
For a point $P$ on the screen at a distance $x$ from the centre of the screen,
Path difference $=\Delta =x\left(d/D\right)$
Path difference introduced due to film $=t(\mu -1)$
For central maximum at $P$,
$x\frac{d}{D}=t(\mu -1)$ or $x=t(\mu -1)\frac{D}{d}$
Now, $\beta =\frac{\lambda D}{d}$ or $\frac{D}{d}=\frac{\beta }{\lambda }$
$\therefore x=t(\mu -1)\frac{\beta }{\lambda }$ towards $A$.
Hence $\left(A\right)$ and $\left(C\right)$