Two coherent sources of intensity ratio `alpha` interfere in interference pattern `(I_(max)-I_(min))/(I_(max)+I_(min))` is equal to

Options

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

Answer

B

Explanation

`(I_("max")-I_("min"))/(I_("max")+I_("min"))=((a_(1)+a_(2))^(2))/((a_(1)+a_(2))^(2))`
`[because I_("max")=(a_(1)+a_(2))^(2), I_("min")=(a_(1)-a_(2))^(2), "where a = amplitude"]`
`=(4a_(1)a_(2))/(2(a_(1)^(2)+a_(2)^(2)))=(2a_(1)a_(2))/(a_(1)^(2)+a_(2)^(2))`
Now, dividing the numerator and denominator by `a_(1)a_(2)`, we get
`(I_("max")-I_("min"))/(I_("max")+I_("min"))=(2)/([(a_(1))/(a_(2))+(a_(2))/(a_(1))])`
`=(2)/([sqrt(alpha)+(1)/(sqrt(alpha))])=(2sqrt(alpha))/((alpha+1))`