A parallel beam of light of intensity \(I_0\) is incident on a glass plate, \(25 \%\) of light is reflected by upper surface and \(50 \%\) of light is reflected from lower surface. The ratio of maximum to minimum intensity in interference region of reflected rays is

Given that, \(25 \%\) of total intensity of incident light is reflected from upper surface. This implies, if intensity of incident light is \(\mathrm{I}_0\), the intensity of light reaching the lower surface of plate will be \(\frac{3}{4} \mathrm{I}_0\).
As \(50 \%\) of this intensity is reflected, the final intensity of light emerging from glass plate will be \(\frac{3}{8} \mathrm{I}_0\).
\(\begin{aligned}
\therefore \quad I_1 & =\frac{I_0}{4} \\
& I_2=\frac{3}{8} I_0
\end{aligned}\)
Now, \(\frac{I_{\max }}{I_{\min }}=\frac{\left(\sqrt{I_1}+\sqrt{I_2}\right)^2}{\left(\sqrt{I_1}-\sqrt{I_2}\right)^2}=\left(\frac{\frac{1}{2}+\sqrt{\frac{3}{8}}}{\frac{1}{2}-\sqrt{\frac{3}{8}}}\right)^2\)

Given that, \(25 \%\) of total intensity of incident light is reflected from upper surface. This implies, if intensity of incident light is \(\mathrm{I}_0\), the intensity of light reaching the lower surface of plate will be \(\frac{3}{4} \mathrm{I}_0\).
As \(50 \%\) of this intensity is reflected, the final intensity of light emerging from glass plate will be \(\frac{3}{8} \mathrm{I}_0\).
\(\begin{aligned}
\therefore \quad I_1 & =\frac{I_0}{4} \\
& I_2=\frac{3}{8} I_0
\end{aligned}\)
Now, \(\frac{I_{\max }}{I_{\min }}=\frac{\left(\sqrt{I_1}+\sqrt{I_2}\right)^2}{\left(\sqrt{I_1}-\sqrt{I_2}\right)^2}=\left(\frac{\frac{1}{2}+\sqrt{\frac{3}{8}}}{\frac{1}{2}-\sqrt{\frac{3}{8}}}\right)^2\)