Question

An isosceles prism of angle $A={30}^o$ has one of its surfaces silvered. Light rays falling at an angle of incidence ${60}^o$ on the other surface retrace their path after reflection from the silvered surface. The refractive index of prism material is

• A. $1.414$
• B. $1.5$
• C. $1.732$
• D. $1.866$

Answer 1

The correct option is C $1.732$

Given that $i={60}^o$

In $\Delta APQ:-$

${90}^o-r+{30}^o={90}^o$ using exterior angle property

$⟹r={30}^o$

$\mu =\frac{\sin i}{\sin r}$

$⟹\mu =\frac{\sin {60}^o}{\sin {30}^o}$

$⟹\mu =\sqrt{3}$

$⟹\mu =1.732$

Answer-(C)