Interference Light Waves Youngs Experiment

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

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

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

$=10l-6l$  

              $l_P-I_Q=10l-4l=6l$  

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