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Question

Physics Question on Dual nature of matter

In the ideal double-slit experiment, when a glass-plate (refractive index 1.5) of thickness t is introduced in the path of one of the interfering beams (wavelength λ\lambda), the intensity at the position where the central maximum occurred previously remains unchanged. The minimum thickness of the glass-plate is

A

2λ\lambda

B

2λ3\frac{2 \lambda}{3}

C

λ3\frac{\lambda}{3}

D

λ\lambda

Answer

2λ\lambda

Explanation

Solution

Path difference due to slab should be integral multiple of λ\lambda or
\hspace10mm ? x=n \lambda \, or \, (\mu-1)t=n \lambda n = 1,2,3,..
or \hspace20mm t=\frac{n \lambda}{\mu-1}
For minimum value of t, n = 1
\therefore \hspace20mm t=\frac{\lambda}{\mu-1}=\frac{\lambda}{1.5-1}=2 \lambda