Ratio of the amplitudes of two waves emitted from a pair of coherent sources is 2:1. If the two waves superpose, what will be the ratio of maximum and minimum intensities? What would have been the intensity at different points on screen if the sources were not coherent?

Explanation

Let the amplitudes of the waves be `A_(1)` and `A_(2)` respectively.
By hypothesis,
`A_(1)/A_(2)=(2)/(1) " ""or" (A_(1)+A_(2))/(A_(1)-A_(2))=(2+1)/(2-1)=(3)/(1) " "or (A_("max"))/A_("min")=(3)/(1)`
`:. I_("max")/I_("min")=(A_("max")^(2))/A_("min")^(2)=(9)/(1)`
`:.` Ratio of intensities = 9:1
For incoherent sources at any point on the screen intensitity would be the sum of intensities of two waves.
If amplitudes are 2A and A repectively then intensities
`I_(1)=4 A^(2) "and" I_(2) = A^(2)`
`:.` Resultant intensity at any point on screen = `4 A^(2) + A^(2)= 5 A^(2)`