The two light beams having intensities I and 9l interfere to produce a fringe pattern on a screen. The phase difference between the beams is /2 at point P and at point Q. Then the difference between the resultant intensities at P and Q will be:

For minima

$d\cos ?\theta =\left(n+\frac{1}{2}\right)\lambda$

$?\cos ?\theta =\frac{2n+1}{8}$

$?n=-4,-3,-2,-1,0,1,2,3$

$?8$ minimas

$\frac{l_{max}}{l_{min}}=\frac{{\left(\sqrt[]{\frac{l_1}{l_2}}+1\right)}^2}{{\left(\sqrt[]{\frac{l_1}{l_2}}-1\right)}^2}\Rightarrow \frac{l_{max}-l_{min}}{l_{max}+l_{min}}=\frac{2.\sqrt[]{\frac{l_1}{l_2}}}{\frac{l_1}{l_2}+1}=\frac{2\sqrt[]{2x}}{2x+1}$