Question

Two beams of light having intensities I and $4 I$ interfere to produce a fringe pattern on a screen. The phase difference between the two beams are $\pi / 2$ and $\pi / 3$ at points $A$ and $B$ respectively. The difference between the resultant intensities at the two points is $xI$. The value of $x$ will be ____

Answer 1

$\phi_{ A }=\frac{\pi}{2} $
$ \phi_{ B }=\frac{\pi}{3} $
$I _{ A }= I +4 I +2 \sqrt{ I } \sqrt{4 I } \cos \left(\frac{\pi}{2}\right) $
$ =5 I +4 I (0)=5 I $
$ I _{ B }= I +4 I +2 \sqrt{ I } \sqrt{4 I } \cos \left(60^{\circ}\right) $
$ =5 I +4 I \times \frac{1}{2}=7 I $
$ I _{ B }- I _{ A }=7 I -5 I =2 I ,( x =2)$