Question

For a glass prisom $$(\mu =\sqrt{3})$$ the angle of minimum deviation is equal to the angle of the prism. Find the angle of the prism.

Answer 1

The required relation for minimum angle of deviation
$$\mu =\cfrac { \sin { \left( \cfrac { A+{ \delta }_{ m } }{ 2 } \right) } }{ \sin { \cfrac { A }{ 2 } } } \left[ \because { \delta }_{ m }=A \right] $$ (given)
$$\therefore \mu =\cfrac { \sin { A } }{ \sin { \cfrac { A }{ 2 } } } =\cfrac { 2\sin { \cfrac { A }{ 2 } } \cos { \cfrac { A }{ 2 } } }{ \sin { \cfrac { A }{ 2 } } } =2\cos { \cfrac { A }{ 2 } } $$
$$\sqrt { 3 } =2\cos { \cfrac { A }{ 2 } } \Rightarrow \cos { \cfrac { A }{ 2 } } =\cfrac { \sqrt { 3 } }{ 2 } $$

$$A/2=30^o\implies A=60^o$$