Two coherent light beams of intensity I and 4 I are superposed. If the maximum and minimum possible intensities in the resulting beam are I max and I min , then I max − I min = nI . Find the value of n .

Step-by-step solution

As I ∝ a 2 or a ∝ I , where a is the amplitude of the wave. ∴ a 1 a 2 = I ⁡ 4 I ⁡ ⇒ a 1 a 2 = 1 2 I ⁡ max I ⁡ min = a 1 + a 2 a 1 - a 2 2 = 1 + 2 1 - 2 2 = 9 1 ∴ I ⁡ max = 9 I ⁡ , I ⁡ min = I ⁡ Now, I max − I min = 8 I ⇒ n = 8