Question

A glass prism with a refracting angle of ${60}^0$ has a refractive index 1.52 for red and 1.6 for violet light.A parallel beam of white light is incident on one face at an angle of incidence, which gives minimum deviation for red light. Find the angle of incidence at the prism is
$\left[Use:\sin \left({50}^0\right)=0.760;\sin \left({31.6}^0\right)=0.520;\sin \left({28.4}^0\right)=0.475;\sin \left({56}^0\right)=0.832;=22/7\right]$

• A. ${30}^0$
• B. ${40}^0$
• C. ${50}^0$
• D. ${60}^0$

Answer 1

Answer: (C)

${50}^0$

For minimum deviation of red light the condition will be $r_1=r_2$

We know that

$A=r_1+r_2$

$A=2r_1$

$r_1=\frac{A}{2}=\frac{60}{2}={30}^{\circ }$

By using Snell’s law for red light,

${\mu }_1\times \sin \left(i_1\right)={\mu }_2\times \sin \left(r_1\right)$

$1\times \sin \left(i_1\right)=1.52\times \sin \left({30}^{\circ }\right)$

$\sin \left(i_1\right)=0.76$

$i_1={\sin }^{-1}\left(0.76\right)$

$i_1={50}^{\circ }$