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

Step-by-step solution

Resultant intensity of two periodic waves is given by I=I₁+I₂+2 I₁ I₂ where is the phase difference between the waves. For maximum intensity, =2 n ; n=0,1,2 etc. Therefore, for zero order maxima, =1I_ max =I₁+I₂+2 I₁ I₂ = ( I₁ + I₂ )^2 For minimum intensity, =(2 n-1) ; n=1,2 etc Therefore, for Ist order minima, =-1 aligned I_ & =I₁+I₂-2 I₁ I₂ & = ( I₁ - I₂ )^2 aligned Therefore, aligned I_ +I_ & = ( I₁ + I₂ )^2+ ( I₁ - I₂ )^2 & =2 (I₁+I₂ ) aligned