Question

A prism having refractive index $1.414$ and refracting angle ${30}^o$ has one of the refracting surfaces silvered. A beam of light incident on the other refracting surface will retrace its path, if the angle of incidence is

• A. $45$
  
• B. $60$
  
• C. $30$
  
• D. $0$
  

Answer 1

The correct option is A $45$

Given that_

$A={30}^o$ and $\mu =1.414=\sqrt{2}$

From figure, the refracted ray at from surface AB must incident normally on surface AC so that it can retrace its path.

From figure in $\Delta APQ:-$

${90}^0=A+{90}^o-r$ using external angle property

$⟹r=A={30}^o$

Now at surface AB:-

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

$⟹\sin i=\mu \sin r=\sqrt{2}\sin {30}^o$

$⟹\sin i=\frac{\sqrt{2}}{2}=\frac{1}{\sqrt{2}}$

$⟹i={45}^0$

Answer-(A)