In a Young’s double-slit setup (d=0.40mm, D=1.2m, λ=500nm), a transparent glass plate of thickness t=0.080mm and refractive index μ=1.50 is introduced in front of slit S1 only.
Attempt all parts.
(a) Part 1: (i) Derive an expression for the additional optical path introduced between the two waves because of the glass plate.
(b) Part 2: (ii) Hence obtain the new condition for constructive interference at the point on the screen that originally corresponded to the central maximum.
(c) Part 3: (iii) Calculate the number of fringes (complete bright–dark cycles) by which the entire interference pattern will shift on the screen due to the insertion of the glass plate.