Two coherent sources with intensity ratio `alpha` interfere. Then, the ratio `(l_(max)-l_("min"))/(l_(max)+l_("min"))` is

Options

A. `2alpha`
B. `(2sqrt(alpha))/(1+alpha)`
C. `(2)/(1-alpha)`
D. `(4sqrt(alpha))/(1+alpha)`

Answer

B

Explanation

Let, `R=(l_(max)-l_("min"))/(l_(max)+l_("min"))`
`impliesR=((a_(1)+a_(2))^(2)-(a_(1)-a_(2))^(2))/((a_(1)+a_(2))^(2)+(a_(1)-a_(2))^(2))`
`=(4a_(1)a_(2))/(2(a_(1)^(2)+a_(2)^(2)))=(2a_(1)a_(2))/(a_(1)^(2)+a_(2)^(2))`
`=(2(a_(2)//a_(1)))/(1+((a_(2))/(a_(1)))^(2))`
Given, `((a_(2))/(a_(1)))^(2)=alpha`
and `(a_(2))/(a_(1))=sqrt(alpha)`
`thereforeR=(2sqrt(alpha))/(1+alpha)`