For the setup shown in figure, the distance between slits much smaller as compared to the distance of slits from the screen. The total number of minimas on the screen are (where $d=4\lambda )$

 

Given, l₁ = 1

  l₂ = 9l

case 1  $\theta =\frac{\pi }{2}$  

$l_P=l_1+l_2+2\sqrt[]{l_1{l}_2}cos\theta$  

= 10 l

case 2 q = p

$l_Q=l_1+l_2+2\sqrt[]{l_1{l}_2}cos\theta$  

$=10l-6l$  

              $l_P-I_Q=10l-4l=6l$  

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