In Young's double slit experiment, two slits S₁ and S₂ are 'd' distance apart and the separation from slits to screen is D . Now if two transparent slabs of equal thickness 0.1 mm but refractive index 1.51 and 1.55 are introduced in the path of beam ( = 4000 Å) from S₁ and S₂ respectively. The central bright fringe spot will shift by ___ number of fringes.

Step-by-step solution

The net path difference introduced at the center of the screen due to the two transparent slabs is given by: x = ( ₂ - 1)t - ( ₁ - 1)t = ( ₂ - ₁)t The number of fringes by which the central bright fringe shifts is: n = x = ( ₂ - ₁)t Substituting the given values, ₁ = 1.51 , ₂ = 1.55 , t = 0.1 10⁻³ m, and = 4000 10⁻¹⁰ m: n = (1.55 - 1.51) 10⁻⁴ 4 10⁻⁷ n = 0.04 10⁻⁴ 4 10⁻⁷ n = 4 10⁻⁶ 4 10⁻⁷ = 10