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 $(\mu -1)t$
Path difference at $P$
$\Delta x_P=(S_{1}P+(\mu -1)t)-S_{2}P$
$=\left(S_{1}P-S_{2}P\right)+(\mu -1)t$
Hence, it increases by $(\mu -1)t$