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