Question

A narrow monochromatic beam of light of intensity I is incident on a glass plate as shown in figure. Another identical glass plate is kept close to the first one and parallel to it. Each glass plate reflects $25\%$ of the light incident on it and transmits the remaining. Find the ratio of minimum and maximum intensities in the interference pattern formed by two beams obtained after one reflection at each plate.

Answer 1

$I_C=\frac{1}{4}{I}_0$
$I_F=\frac{3}{4}{I}_0\times \frac{1}{4}\times \frac{3}{4}=\frac{9}{64}{I}_o$

So, $\sqrt{\frac{I_{max}}{I_{min}}}=\frac{\sqrt{I_C}+\sqrt{I_F}}{\sqrt{I_C}-\sqrt{I_F}}$
$\sqrt{\frac{I_{max}}{I_{min}}}=\frac{\frac{\sqrt{I_o}}{2}+\frac{3\sqrt{I_o}}{8}}{\frac{\sqrt{I_o}}{2}-\frac{3\sqrt{I_o}}{8}}$
$\sqrt{\frac{I_{max}}{I_{min}}}=\frac{\frac{7}{4}}{\frac{1}{4}}=\frac{7}{1}\Rightarrow 7$