Column I shows four situations of standard Young's double slit arrangement with the screen placed far away…
Column I shows four situations of standard Young's double slit arrangement with the screen placed far away from the slits $S_1$ and $S_2$. In each of these cases $S_1 P_0=S_2 P_0$, $S_1 P_1-S_2 P_1=\frac{\lambda}{4}$ and $S_1 P_2-S_2 P_2=\frac{\lambda}{3}$, where $\lambda$ is the wavelength of the light used. In the cases $\mathrm{B}, \mathrm{C}$ and $\mathrm{D}$, a transparent sheet of refractive index $\mu$ and thickness $t$ is pasted on slit $S_2$. The thickness of the sheets are different in different cases. The phase difference between the light waves reaching a point $P$ on the screen from the two slits is denoted by $\delta(P)$ and the intensity by $I(P)$. Match each situation given in Column-I with the statement(s) in Column-II valid for that situation.
(A) q,t, (B) q, (C) t, (D) r,s,t
(A) q,r,s, (B) r, (C) q,r, (D) q,s,t
(A) p,s, (B) r, (C) q,t, (D) r,s
(A) p,s, (B) q, (C) t, (D) r,s,t
Solution
(A) $\rightarrow(\mathrm{p}, \mathrm{s}) \rightarrow$ Intensity at $P_0$ is maximum. It will continuously decrease from $P_0$ towards $P_2$.
$(B) \rightarrow(q) \rightarrow$ Path difference due to slap will be compensated by geometrical path difference. Hence, $\delta\left(P_1\right)=0$.
$(\mathrm{C}) \rightarrow(\mathrm{t}) \rightarrow \delta\left(P_0\right)=\frac{\lambda}{2}, \delta\left(P_1\right)=\frac{\lambda}{2}-\frac{\lambda}{4}=\frac{\lambda}{4}$ and $\delta\left(P_2\right)=\frac{\lambda}{2}-\frac{\lambda}{3}=\frac{\lambda}{6}$. When path difference increases from 0 to $\frac{\lambda}{2}$, intensity will decrease from maximum to zero. Hence, in this case,
$
I\left(P_2\right)>I\left(P_1\right)>I\left(P_0\right)
$
$(\mathrm{D}) \rightarrow(\mathrm{r}, \mathrm{s}, \mathrm{t})$
$
\delta\left(P_0\right)=\frac{3 \lambda}{4}, \delta\left(P_1\right)=\frac{3 \lambda}{4}-\frac{\lambda}{4}=\frac{\lambda}{2}
$
and $\delta\left(P_2\right)=\frac{3 \lambda}{4}-\frac{\lambda}{3}=\frac{5 \lambda}{12}$
In this case $I\left(P_1\right)=0$
