Question

A mica sheet of thickness, $t$ and refractive index, $\mu $ is placed in front of the slit $S_{1}$ in a YDSE setup given below then the path difference $\left(S_{1} P - S_{2} P\right)$ .

• A. Decreases by $\left(\mu - 1\right)t$ .
• B. Increases by $\left(\mu - 1\right)t$ .
• C. Does not change.
• D. Increases by $\mu t$ .

Answer 1

Answer: (B)

As shown in the diagram, path difference would be due to:
i) Difference in path covered by two sources at $P$ , $S_{1}P-S_{2}P$ .
ii) Pressence of glass slab which shift the light emerging from $S_{1}$ by $\left(\right.\mu -1\left.\right)t$
Path difference at $P$
$\Delta x_{P}=\left(\right.S_{1}P+\left(\right.\mu -1\left.\right)t\left.\right)-S_{2}P$
$=\left(S_{1} P - S_{2} P\right)+\left(\right.\mu -1\left.\right)t$
Hence, it increases by $\left(\right.\mu -1\left.\right)t$