Optics Question 869

Question: Two identical coherent sources are placed on a diameter of a circle of radius R at separation x (« R) symmetrical about the center of the circle. The sources emit identical wavelength λ each. The number of points on the circle of maximum intersity is (x=5λ)

Options:

A) 20

B) 22

C) 24

D) 26

Show Answer

Answer:

Correct Answer: A

Solution:

[a] Path difference at P is Δx=2(x2cosθ)=xcosθ

For intensity to be maximum, Δx=nλ (n=0, 1, 2, 3, ….) or xcosθ=nλ

or xcosθ=nλx1

nxλ

Subsituting x= 51, we get n5 or n= 1, 2, 3, 4, 5…….

Therefore in all four quadrants there can be 20 maxima.

There are more maxima at θ=0

and θ=180 .

But n = 5 corresponds to θ=90

and θ=270 which are coming only twice while we have multuplies it four times.

Therefore, total number of maxima are still 20, i.e., n = 1 to 4 in four quadrants (total 16) plus more at θ=0 , 90 , 180 and 270 .



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