Question

Find the angle of incidence at which the light ray will retrace its path after reflection from the plane mirror.

• A. ${45}^{\circ }$
• B. ${60}^{\circ }$
• C. ${30}^{\circ }$
• D. ${75}^{\circ }$

Answer 1

The correct option is A ${45}^{\circ }$

The light will retrace its path, if it falls normally at the second refracting surface (polished) of the prism.


Given, angle of prism, $A={30}^{\circ }$
$\Rightarrow ({90}^{\circ }-r)+{90}^{\circ }+{30}^{\circ }={180}^{\circ }$
$[$from geometry$]$
$\Rightarrow r={30}^{\circ }$
On applying Snell's law at first refracting surface,
${\mu }_{air}\sin i={\mu }_{glass}\sin r$
$\Rightarrow 1\times \sin i=\sqrt{2}\sin {30}^{\circ }$
$\Rightarrow \sin i=\frac{1}{\sqrt{2}}$
$\therefore i={45}^{\circ }$

Why this question? It intends to test your understanding of reversibility of light and application of Snell's law at interface.