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Question

There is a destructive interference between the two waves of wavelength λ coming from two different paths at a point. To get the constructive interference at that point, the path of one wave is to be increased by,

A
λ4
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B
λ2
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C
3λ4
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D
λ
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Solution

The correct option is B λ2

Let the path difference between the two wave is Δx.
So, for destructive interference
Δx=nλ2 ...(1)
Where, n=1,3,5,...

Let the path of one wave is increased by y to get constructive interference.
The constructive interference is obtained when,
Δx+y=nλ ...(2)
Where n=0,1,2,...

Subtracting equation (1) from (2),
y=nλ2
Putting n=1, we get,
y=λ2

Hence, (B) is the correct answer.

Why this Question Concept: The interference of two waves with identical wavelengths passing through a common point depends on their phase difference Δϕ. Constructive interference is obtained when Δϕ is integral multiple of 2π and fully destructive interference occurs when Δϕ is an odd multiple of π.

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