Question

A ray parallel to principal axis is incident at ${30}^{\circ }$ from normal on concave mirror having radius of curvature $R$. The point on principal axis where rays are focussed is $Q$ such that $PQ$ is

• A. $\frac{R}{2}$
• B. $\frac{R}{\sqrt{3}}$
• C. $\frac{2\sqrt{R}-R}{\sqrt{2}}$
• D. $R(1-\frac{1}{\sqrt{3}})$

Answer 1

The correct option is D $R(1-\frac{1}{\sqrt{3}})$

From similar triangles,
$\frac{QC}{\sin {30}^{\circ }}=\frac{R}{\sin {120}^{\circ }}$
or $QC=R\times \frac{\sin {30}^{\circ }}{\sin {120}^{\circ }}=\frac{R}{\sqrt{3}}$
Thus $PQ=PC-QC=R-\frac{R}{\sqrt{3}}=R(1-\frac{1}{\sqrt{3}})$.