Question

A ray of light of intensity $I$ is incident on a parallel glass-slab at a point as shown in the figure. It undergoes partial reflection and refraction. At each reflection $20 \%$ of incident energy is reflected. The rays $A B$ and $A^{\prime} B^{\prime}$ undergo interference. The ratio $I_{\max } / I_{\min }$ is_______

Answer 1

According to the given condition in question, Intensity of ray
$A B, I_{1}=\frac{I_{0}}{5}$, and Intensity of ray $A^{\prime} B^{\prime}$ is given
corresponding to $20 \%$ reflection at each surface as
$I_{2}=\frac{16 I_{0}}{125}$

For light rays $A S$ and $A^{\prime} B^{\prime}$, after interference maximum and minimum intensities are given as
$I_{\max }=\left(\sqrt{I_{1}}+\sqrt{I_{2}}\right)^{2}=\frac{81}{125} I_{0}$
and
$I_{\min }=\left(\sqrt{I_{1}}-\sqrt{I_{2}}\right)^{2}=\frac{I_{0}}{125}$
$ \Rightarrow \frac{I_{\max }}{I_{\min }}=81$