Discuss the pattern of interference fringes obtained on the screen away from the two point sources.

Explanation

For two waves, ratio of their intensities, `(I_(1))/(I_(2))=alpha` (given)
But we know that `IpropA^(2)`, where A is an amplitude.
`:.(I_(1))/(I_(2))=(A_(1)^(2))/(A_(2)^(2))=alpha`
`:.(A_(1))/(A_(2))=(sqrt(alpha))/(l)`
Taking componendo and dividendo,
`:.(A_(1)+A_(2))/(A_(1)-A_(2))=(A_(max))/(A_(min))=(sqrtalpha+1)/(sqrtalpha-1)`
`:.(I_(max))/(I_(min))=(A_(max)^(2))/(A_(min))=(sqrtalpha+1)^(2)/((sqrtalpha-1)^(2))=(alpha+2sqrtalpha+1)/(alpha-2sqrt+1)`
`(I_(max)+I_(min))/(I_(max)-I_(min))=((alpha+2sqrtalpha+1)+(alpha-2sqrtalpha+1))/((alpha+2sqrtalpha+1)-(alpha-2sqrtalpha+1))`
`=(alpha+1)/(2sqrtalpha)`
Note : Reciprocal of the above term, i.e. `(I_(max)-I_(min))/(I_(max)+I_(min))` is known as visibility of fringes.