JEE Main · 2019 · 12 Apr 2019 · Shift 1 · Wave Optics

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) :

(A) $\frac{λ}{2 ( μ - 1 )}$
(B) $\frac{λ}{( μ - 1 )}$ ✓ Correct
(C) $\frac{λ}{( 2 μ - 1 )}$
(D) $\frac{2 λ}{( μ - 1 )}$

Answer: (B)

Solution

Inserting a film of thickness

t

and index

μ

in front of one slit adds an extra optical path of

(μ - 1) t

for that beam. A shift of the central maximum by exactly one fringe width corresponds to introducing one extra wavelength of path, so

(μ - 1) t = λ

. Solving,

t = \frac{λ}{μ - 1}

JEE Main · 2019 · 12 Apr 2019 · Shift 1 · Single correct option

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