Two coherent waves of intensities I₁ and I₂ pass through a region at the same time in the same direction. The sum of maximum to minimum intensities is

Step-by-step solution

The resultant intensity I of two coherent waves with intensities I₁ and I₂ is given by I = I₁ + I₂ + 2 I₁ I₂ , where is the phase difference between the waves. The maximum intensity I_ max occurs when = 1 , which gives I_ max = I₁ + I₂ + 2 I₁ I₂ = ( I₁ + I₂ )^2 . The minimum intensity I_ min occurs when = -1 , which gives I_ min = I₁ + I₂ - 2 I₁ I₂ = ( I₁ - I₂ )^2 . The sum of maximum and minimum intensities is I_ max + I_ min = (I₁ + I₂ + 2 I₁ I₂ ) + (I₁ + I₂ - 2 I₁ I₂ ) . Simplifying the expression, we get I_ max