Question

A thin prism has different medium on its either side. A light ray is incident almost normally on the first face. What is the angle of deviation if all the angles are very small

• A. $I\left(1-\frac{\mu_1}{\mu_2}\right)-A\left(1-\frac{\mu}{\mu_2}\right)$
• B. $I\left(1-\frac{\mu_1}{\mu_2}\right)+A\left(1-\frac{\mu}{\mu_2}\right)$
• C. $I\left(1+\frac{\mu_1}{\mu_2}\right)-A\left(1-\frac{\mu}{\mu_2}\right)$
• D. none of these

Answer 1

Answer: (A)

From Snell's law at first refraction,
$\mu _{1}I=\mu r_{1}$
$r_{1}=I\frac{\mu _{1}}{\mu }$ ...(1)
From Snell's law at second refraction,
$ \mu\left(A-r_1\right)=\mu_2 e $
$\therefore$ From (1),
$\mu\left(A-I \frac{\mu_1}{\mu}\right)=\mu_2 e $
$e=\frac{\mu}{\mu_2}\left(A-I \frac{\mu_1}{\mu}\right) . $
Overall deviation, $ \delta=I+e-A $ $ \delta=I+\frac{\mu}{\mu_2}\left(A-I \frac{\mu_1}{\mu}\right)-A $ $ \delta=I\left(1-\frac{\mu_1}{\mu_2}\right)-A\left(1-\frac{\mu}{\mu_2}\right) $