Question

The circular boundary of the concave mirror subtends a cone of half angle $\theta$ at its centre of curvature. The minimum value of $\theta$ for which ray incident on this mirror parallel to the principal axis suffers reflection more than once is

• A. ${30}^{\circ }$
• B. ${45}^{\circ }$
• C. ${60}^{\circ }$
• D. ${75}^{\circ }$

Answer 1

The correct option is B ${45}^{\circ }$

For minimum $\theta$ at with reflection happens twice can be considered as shown below,


As incident ray is parallel to principal axis, we can say that
$i=r=\theta$
From triangle $ABC,$
$90+2\theta ={180}^{\circ }$
$2\theta ={90}^{\circ }$
$\theta ={45}^{\circ }$