In Young's double slit experiment, the ratio of maximum and minimum intensities in the fringe
system is 9 : 1. The ratio of amplitudes of coherent sources is [UK PMT 2014]

$\frac{I_{\max }}{I_{\min }}={\left(\frac{a_{\max }}{a_{\min }}\right)}^2={\left(\frac{a_1+a_2}{a_1-a_2}\right)}^2$

According to given question,  $\frac{I_{\max }}{I_{\min }}=\frac{9}{1}$

$\Rightarrow$     $9={\left(\frac{a_1/a_2+1}{a_1/a_2-1}\right)}^2\Rightarrow (3{)}^2={\left(\frac{a_1/a_2+1}{a_1/a_2-1}\right)}^2$

$\Rightarrow$  $3=\frac{a_1/a_2+1}{a_1/a_2-1}\Rightarrow 3\left(\frac{a_1}{a_2}\right)-3=\frac{a_1}{a_2}+1$

$\Rightarrow$  $2\left(\frac{a_1}{a_2}\right)=4\Rightarrow \frac{a_1}{a_2}=\frac{4}{2}=\frac{2}{1}\Rightarrow a_1:a_2=2:1$