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Physics Question on Youngs double slit experiment

In Young's double slit experiment performed using a monochromatic light of wavelength λ, when a glass plate (μ = 1.5) of thickness xλ is introduced in the path of the one of the interfering beams, the intensity at the position where the central maximum occurred previously remains unchanged. The value of x will be:

A

3

B

2

C

1.5

D

0.5

Answer

2

Explanation

Solution

The correct answer is (B) : 2

Path difference at O = (μ-1)t
If the intensity at O remains (maximum) unchanged, path difference must be n 2.
⇒ (μ-1)t = nλ
(1.51) x 2 = nλ
⇒ x = 2n x = 2n
For n = 1, x = 2