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

Correct Answer: D

Solution :

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     \[PQ=PC-QC\]

\[=R-\frac{R}{\sqrt{3}}\]

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