Question

A ray of light of intensity $I$ is incident on a parallel glass-slab at the point $A$ and it undergoes partial reflection and refraction as shown in the figure. At each reflection, $25\%$ of the incident energy is reflected and the rest is transmitted. If the rays $AB$ and $A\prime B\prime$ undergo interference, then the ratio $\frac{I_{max}}{I_{min}}$ is

• A. $4:1$
• B. $8:1$
• C. $7:1$
• D. $49:1$

Answer 1

Answer: (D)

From figure $I_1=\frac{I}{4}$ and $I_2=\frac{9I}{64}$
$\Rightarrow \frac{I_2}{I_1}=\frac{9}{16}$


By using $\frac{I_{max}}{I_{min}}={\left(\frac{\sqrt{\frac{{\left(I\right)}_2}{{\left(I\right)}_1}}+1}{\sqrt{\frac{{\left(I\right)}_2}{{\left(I\right)}_1}}-1}\right)}^2={\left(\frac{\sqrt{\frac{9}{16}}+1}{\sqrt{\frac{9}{16}}-1}\right)}^2=\frac{49}{1}$