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, $\delta =I+e-A$ $\delta =I+\frac{\mu }{{\mu }_2}\left(A-I\frac{{\mu }_1}{\mu }\right)-A$ $\delta =I\left(1-\frac{{\mu }_1}{{\mu }_2}\right)-A\left(1-\frac{\mu }{{\mu }_2}\right)$