Four monochromatic and coherent sources of light emitting waves in phase at placed on y axis at y = 0 , a , 2 a and 3 a . If the intensity of wave reaching at point P far away on y axis from each of t

Question

Four monochromatic and coherent sources of light emitting waves in phase at placed on $y$ axis at $y = 0, a, 2 a$ and $3 a .$ If the intensity of wave reaching at point P far away on $y$ axis from each of the source is almost the same and equal to $I_{0}$ , then the resultant intensity at P for $a = \frac{λ}{8}$ is $n I_{0}$ . The value of [n] is.
Here $[]$ is greatest integer function.

TestHub · Accepted Answer

Δ x = λ 8 ϕ between 1 and 3 = 2 π λ × λ 4 = π 2 ϕ between 2 and 4 = π 2 Intensity because of 1 and 3, 2 and 4 = I 1 + I 2 + 2 I 1 I 2 cos ϕ = 2 I 0 Now phase difference between resultant of 1 and 3, 2 and 4 is π 4 ∴ I = I 1 + I 2 + 2 I 1 I 2 cos ⁡ d = 2 I 0 + 2 I 0 + 2 2 × 2 I 0 × 1 2 4 I 0 + 2 2 I 0 4 I 0 + 2 2 I 0 = 6.8 I 0 ∴ n = 6

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