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 $AB$ and $A^{\prime }{B}^{\prime }$ undergo interference. The ratio $I_{\max }/I_{\min }$ is_______

Answer 1

Answer: 81

According to the given condition in question, Intensity of ray
$AB,I_1=\frac{I_0}{5}$, and Intensity of ray $A^{\prime }{B}^{\prime }$ is given
corresponding to $20\%$ reflection at each surface as
$I_2=\frac{16I_0}{125}$

For light rays $AS$ 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
$I_{\min }={\left(\sqrt{I_1}-\sqrt{I_2}\right)}^2=\frac{I_0}{125}$
$\Rightarrow \frac{I_{\max }}{I_{\min }}=81$