Question

A parallel beam of light falls normally on face AB of a thin prism and under goes a deviation ${\left(\frac{5}{4}\right)}^0$ on passing through the prism. The part of the beam which is reflected internally at the face AC, on emergence from the face AB, makes an angle $6^o{30}^{\prime }$ with the incident beam. Calculate the angle of the prism and the refractive index of the material of the prism.

Answer 1

Since deviation ${\delta }_1=({\mu }_1-1)A$

$1^{\circ }{15}^{\prime }=({\mu }_1-1)A\to$ (i)

Lets find out $\mu$ from Snell's law;

$\mu \sin \left(2A\right)=\left(1\right)\sin \left(6^{\circ }{30}^{\prime }\right)-$ (2)

For small angles $\sin 2A\approx 2A$

$\Rightarrow 2A\mu =2\left(6^{\circ }{30}^{\prime }\right)-$ Equation (2)