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 principles axis suffers reflection more than one is

• A. 30${}^o$
• B. 45${}^o$
• C. 60${}^o$
• D. 75${}^o$
• E. Answer required

Answer 1

Answer: (B)

45${}^o$

An incident ray that is parallel to the principal axis will suffer multiple reflections from the mirror only when it is incident on 1 part of the mirror, reflects perpendicularly and goes on to intersect the other part. Thus, this is only possible when angle of incidence is ${45}^0$
Thus, ${45}^0$ $+\theta +\frac{\pi }{2}=\pi$

Thus, $\theta ={45}^0$