Three plane mirrors form an equilateral triangle with each side of length . There is a small hole at a distance from one of the corners as shown in the figure. A ray of light is passed through the hole at an angle and can only come out through the same hole. The cross section of the mirror configuration and the ray of light lie on the same plane.
Which of the following statement(s) is(are) correct?
- A
The ray of light will come out for , for .
- B
There is an angle for at which the ray of light will come out after two reflections.
- C
The ray of light will NEVER come out for , and .
- D
The ray of light will come out for , and after six reflections.
(A) At , the ray strikes the opposite (slanted) mirror at normal incidence (since the interior angle of the equilateral triangle is and the geometry forces a perpendicular incidence). The ray then retraces its path back through the hole, regardless of . Correct.
(B) For , the hole is at the midpoint of the side. By symmetry, a ray launched along the perpendicular bisector path bounces off the top vertex region symmetrically and returns after two reflections. Correct.
(C) At and , tracing the geometry shows the ray reflects off internal mirrors and ultimately reaches the hole side again. It does come out. Wrong.
(D) Same geometry as (C); the total number of reflections before re-emerging through the hole is 5, not 6. Wrong.
