Question

2. Two identical coherent sources placed on a diameter
of a circle of radius R at separation x (< < R)
symmetrically about the centre of the circle. The
sources emit identical wavelength 2 each. The
number of points on the circle with maximum
intensity is (x = 52).
(a) 24
(b) 20
(c) 22
(d) 26

Answer 1

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Physics

Wave Optics

Young's Double Slit Experiment

Two identical coherent sour...

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Asked on October 15, 2019 by

Mona Bhandari

Two identical coherent sources placed on a diameter of a circle of radius R at separation x(≪R) symmetrically about the centre of the circle. The sources emit identical wavelength λ each. The number of points on the circle with maximum intensity is (x=5λ)

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ANSWER

Path difference at P is

Δx=2(

2

x

cosθ)=xcosθ

For intensity to be maximum

Δx=nλ (n=0,1,…)

⇒xcosθ=nλ

cosθ=

x

nλ

or cosθ≯1

∴

x

nλ

≯1

∴n≯

λ

x

Substituting x=5λ

n≯5 or n=1,2,3,4,5,…

Therefore, in all four quadrants, there can be 2 maximas. There are more maximas at θ=0

o

and θ=180

o

.

But n=5 corresponds to θ=90

o

and θ=270

o

which are coming only twice. While we have multiplied it four times. Therefore, total number of maximas still 20.

solution