JEE Main · 2020 · 08 Jan 2020 · Shift 2 · Wave Optics

In a double-slit experiment, at a certain point on the screen the path difference between the two interfering waves is

\frac{1}{8}

th of a wavelength. The ratio of the intensity of light at that point to that at the centre of a bright fringe is:

(A)0.672
(B)0.568
(C)0.760
(D)0.853✓ Correct

Answer: (D)

Solution

The intensity in a two-beam interference pattern is

I = I_{0} cos^{2} (\frac{Δ ϕ}{2})

, where

I_{0}

is the intensity at the centre of a bright fringe and

Δ ϕ = \frac{2 π}{λ} Δ x

is the phase difference. A path difference of

\frac{λ}{8}

gives

Δ ϕ = \frac{π}{4}

, so

\frac{I}{I _{0}} = cos^{2} (\frac{π}{8}) \approx 0.853

JEE Main · 2020 · 08 Jan 2020 · Shift 2 · Single correct option

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