YDSE: Film, Medium & Two Wavelengths question from MHT CET 2024 (15 May, Shift 2)

Answer: (b)

1. The plate adds optical path $(\mu-1)t$ to the ray through it.
2. Zero path difference now occurs where the geometric path from that slit is shorter, i.e. on the side of the plate.
3. Fringe width $\beta = \frac{\lambda D}{d}$ is unchanged; the whole pattern just shifts.
4. So the answer is (b) the central maximum shifts towards this side.