Two plane mirrors A and B are aligned parallel to each other, as shown in the figure. A light ray is incident at an angle 30degree at a point just inside one end of A. The plane of incidence coincides with the plane of the figure. The maximum number of times the ray undergoes reflections (including the first one) before it emerges out is

Options

A. 28
B. 30
C. 32
D. 34

Answer

B

Explanation

According to laws of reflection, `angle I = angle r`
So, `angle PQO = 30^(@)`
Given: PQ = 0.2 m
`tan 30^(@) = (OP)/(PQ)`
`rArr = (1)/(sqrt(3)) = (OP)/(0.2) rArr OP = (0.2)/(sqrt(3)) m`
OP is distance covered by the ray in one reflection. Number of times the ray undergoes reflections, before it emerges out `= (2 sqrt(3))/(OP) = (2 sqrt(3))/(0.2/sqrt(3)) = (6)/(0.2) = 30`