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. $R\left(1-\frac{1}{\sqrt{2}}\right)$

Answer 1

The Correct Option is D

From similar triangles,
$\frac{Q C}{\sin 30^{\circ}}=\frac{R}{\sin 120^{\circ}}$
or $Q C=R \times \frac{\sin 30^{\circ}}{\sin 120^{\circ}}=\frac{R}{\sqrt{3}}$
Thus $P Q=P C-Q C=R-\frac{R}{\sqrt{3}}$
$=R\left(1-\frac{1}{\sqrt{3}}\right)$