In Young’s double slit experiment, two slits S 1 and S 2 are d distance apart and the separation from slits to screen is D (as shown in figure). 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 λ = 4000 Å from S 1 and S 2 respectively. The central bright fringe spot will shift by ________ number of fringes.

Step-by-step solution

The change in path difference due to the two slabs at P is Δ x = μ 2 - μ 1 t = ( 1 . 55 - 1 . 51 ) × 0 . 1 = 0 . 04 × 10 - 4 ⇒ Δ x = 4 × 10 - 6 = 4   μm Now, the distance of central maxima from geometrical center is y = Δ x D d = 4 × 10 - 6 D d Now, fringe width, n β = 4 × 10 - 6   D d Or, n λ D d = 4 × 10 - 6   D d Number of shift, n = 4 × 10 - 6 4 × 10 - 7 = 10 .