A parallel beam of monochromatic 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 minimum and maximum intensity in interference region of reflected light is

$$\begin{gathered} Intensity of reflected light from upper surface is I_1=I_0\times \frac{25}{100}=\frac{I_0}{4} \\ And intensity of transmitted light from upper surface is I\text{'}=I_0-\frac{I_0}{4}=\frac{3I_0}{4} \\ The intensity of reflected light from lower surface is I_2=\frac{3I_0}{4}\times \frac{50}{100}=\frac{3I_0}{8} \\ \therefore \frac{I_{\min }}{I_{\max }}=\frac{{\left(\sqrt{I_1}-\sqrt{I_2}\right)}^2}{{\left(\sqrt{I_1}+\sqrt{I_2}\right)}^2}=\frac{{\left(\sqrt{\frac{I_0}{4}}-\sqrt{\frac{3I_0}{8}}\right)}^2}{{\left(\sqrt{\frac{I_0}{4}}+\sqrt{\frac{3I_0}{8}}\right)}^2} = \frac{{\left(\frac{1}{2}-\sqrt{\frac{3}{8}}\right)}^2}{{\left(\frac{1}{2}+\sqrt{\frac{3}{8}}\right)}^2} \end{gathered}$$