question_answer

Inner surface of a cone is coated with a reflecting layer forms a conical mirror. A small point source S is placed over the axis of this cone. Minimum angle a of the cone for which rays emitted by source S will be reflected from conical surface only once is

A) \[\alpha =45{}^\circ \]

B) \[\alpha =90{}^\circ \]

C) \[\alpha =120{}^\circ \]

D) \[\alpha =135{}^\circ \]

Correct Answer: C

Solution :

Cone with angle a and source S is as shown below.

Now, we draw reflected rays as shown below.

From above construction, image of S is S'.

Now, for rays to reflect only once point S' must be below line OB and OCC'.

So, \[\angle S'OB+\angle SOB+\angle AOC=\frac{3\alpha }{2}\ge 180{}^\circ \]

or \[\alpha \ge \frac{2\times 180}{3}\]\[\Rightarrow \]\[\alpha \ge 120{}^\circ \]