Two slits in Youngs experiment have widths in the ratio 1 : 25. The ratio of intensity at the maxima and minima in the interference pattern, $\frac{I_{\max }}{I_{\min }}\text{ is }$

As we know, slit width is directly proportional to intensity,
$\begin{array}{l}d\propto l\\ \frac{d_1}{d_2}=\frac{l_1}{I_2}=\frac{1}{25}\\ \frac{a_1^2}{a_2^2}=\frac{l_1}{I_2}=\frac{1}{25}\end{array}$
(a₁ and a₂ are amplitudes)
$\begin{array}{l}\frac{a_1}{a_2}=\frac{1}{5}\\ \frac{I_{max}}{I_{min}}=\frac{{\left(a_1+a_2\right)}^2}{{\left(a_1-a_2\right)}^2}=\frac{(5+1{)}^2}{(5-1{)}^2}=\frac{36}{16}=\frac{9}{4}\end{array}$