In young’s Double Slit Experiment, the distance between the slits and the screen is 1.2 m and the distance between the two slits is 2.4 mm. If a thin transparent mica sheet of thickness 1 μ m and R.I. 1.5 is introduced between one of the interfering beams, the shift in the position of central bright fringe is

Question

In young’s Double Slit Experiment, the distance between the slits and the screen is 1.2 m and the distance between the two slits is 2.4 mm. If a thin transparent mica sheet of thickness 1 μ m and R.I. 1.5 is introduced between one of the interfering beams, the shift in the position of central bright fringe is (A) 2 mm (B) 0.5 mm (C) 0.125 mm (D) 0.25 mm

Tardigrade Admin · Accepted Answer

Path difference due to insertion of mica sheet

Δ x = (μ - 1) t

Let the shift in the fringe pattern be

^{'} y^{'}

Also, path difference

Δ x = y \times d / D

,
so comparing both

(μ - 1) t = y \times (d / D)

y = (μ - 1) t \times (D / d)

,
where

μ = 1.5, D = 2.4

and

d = 1.2

putting the values, we get

y = 0.25 mm

.

2 mm

0.5 mm

0.125 mm

0.25 mm

Path difference due to insertion of mica sheet Δx=(μ−1)t Let the shift in the fringe pattern be ′y′ Also, path difference Δx=y×d/D, so comparing both (μ−1)t=y×(d/D) y=(μ−1)t×(D/d), where μ=1.5,D=2.4 and d=1.2 putting the values, we get y=0.25mm.