In Young’s double slit experiment a mica plate of thickness t and refractive index μ is introduced in one of the interfering beams. Then the central fringe will be displaced through (d = distance between the slits; D = distance between the slits and the screen) 

Explanation:

Step 1: Optical Path Difference

The optical path difference (Δx) introduced by the mica plate is given by:

Δx = (μ − 1) × t

Step 2: Relation with Fringe Shift

In Young's double-slit experiment, the path difference (Δx) is related to the fringe shift (y) on the screen by:

Δx = (y × d) / D

Step 3: Equating the Two Expressions

Equating the expressions for Δx:

(μ − 1) × t = (y × d) / D

Step 4: Solve for Fringe Shift

Solving for y (fringe shift):

y = ((μ − 1) × t × D) / d

The central fringe will be displaced by:

y = ((μ − 1) × t × D) / d

Final Answer

The correct option is: B: (μ − 1)tDd