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Question:

In a double slit experiment, when a thin film of thickness t having refractive index μ is introduced in front of one of the slits, the maximum at the centre of the fringe pattern shifts by one fringe width. The value of t is (λ is the wavelength of the light used)

λ2(μ-1)

λ(2μ-1)

2λ(μ-1)

λ(μ-1)

Solution:

Correct option is D. λ(μ-1)
Shift = ΔX
Width of one fringe = λ
ΔX = (μ-1)t = 1λ
For one maximum shift :
t = λ/(μ-1)