Two coherent sources of light of intensity ratio `beta` produce interference pattern. Prove that in the interferencepattern
`(I_(max) - I_(min))/(I_(max) + (I_(min))) = (2 sqrt beta)/(1 + beta)`
where `I_(max)` and `I_(min)` are maximum and mininum intensities in the resultant wave.

Explanation

`(I_(max)-I_(min))/(I_(max)+I_(min))=((sqrt(I_(1))+sqrt(I_(2)))^(2)-(sqrt(I_(1))-sqrt(I_(2)))^(2))/((sqrt(I_(1))+sqrt(I_(2)))^(2)+(sqrt(I_(1))-sqrt(I_(2)))^(2))`
`=(4sqrt(I_(1)I_(2)))/(2(I_(1)+I_(2)))`
`=(2sqrt(I_(1)I_(2)))/(I_(1)(1+I_(2)//I_(1)))`
`=(2sqrt(I_(2)//I_(1)))/((1+I_(2)//I_(1)))=(2sqrt(beta))/(1+beta)`