Question

If we have two coherent sources S₁ and S₂ vibrating in phase with same amplitude, then for an arbitrary point P with path difference corresponding to ϕ, the resultant intensity if the intensity due to each is I₀ would be ______.

Options

• `4"I"_0cos^2(phi//2)`

• `"I"_0cos^2(phi)`

• `"I"_0cos^2(phi//2)`

• `4"I"_0cos^2(phi)`

Answer 1

If we have two coherent sources S₁ and S₂ vibrating in phase with same amplitude, then for an arbitrary point P with path difference corresponding to ϕ, the resultant intensity if the intensity due to each is I₀ would be `underline(4"I"_0cos^2(phi//2))`.

Explanation:

I = `"I"_1 + "I"_2 + 2sqrt"I"_1 sqrt"I"_2 cos phi`

`"I"_1 = "I"_2 = "I"_0`

I = `"I"_0 = "I"_0 + "I"_0 cos phi`

I = `2"I"_0(1 + cos phi)`

I = `4"I"_0cos^2 phi//2`