question_answer

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 focused is Q such that PQ is

A) \[\frac{R}{2}\]

B) \[\frac{R}{\sqrt{3}}\]

C) \[\frac{2\sqrt{R}-\sqrt{R}}{\sqrt{2}}\]

D) \[R\left( 1-\frac{1}{\sqrt{3}} \right)\]

Correct Answer: D

Solution :

[d] 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 \[PQ=PC-QC=R-\frac{R}{\sqrt{3}}=R\left( 1-\frac{1}{\sqrt{3}} \right)\]