Question

A ray parallel to principle axis at height R/2 hits concave mirror and cut principle axis at point O. Length PO is

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

Answer 1

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

C is center of curvature
By $\Delta$ ABC $\Rightarrow \sin \theta =\frac{R}{2\times R}\Rightarrow \theta ={30}^{\circ }$
In $\Delta OAC,cos\theta =\frac{AC}{2\times CO}$
$\Rightarrow CO=R/\sqrt{3}\Rightarrow PO=R-R/\sqrt{3}\Rightarrow PO=(\sqrt{3}-1)R/\sqrt{3}$