Question

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 of ${30^ \circ }$ at a point just inside one end of A. The plane of incidence coincides with the plane of the figure. What is the maximum number of times the ray undergoes reflection (including the first one) before it emerges out?

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

Answer 1

Hint: The total distance that the ray will cover before emerging out will be equivalent to the length of the plane mirrors. To solve the above question, first calculate the distance that the ray will cover in one reflection and then proceed further to calculate the maximum number of reflections.



Complete answer:
The length of the mirrors is the distance that the ray should cover in order to emerge out.
Separation between the mirrors, $d = 0.2{\text{ m}}$
Let us calculate the distance that the ray covers in the first reflection.
For plane mirrors, the angle of incidence is equivalent to the angle of reflection.
Hence, angle of reflection $ = {30^ \circ }$ .

In the above triangle,
$\tan {30^ \circ } = \dfrac{a}{d}$
Substituting the values,
$\dfrac{1}{{\sqrt 3 }} = \dfrac{a}{{0.2}}$
This gives $a = \dfrac{{0.2}}{{\sqrt 3 }}$
First reflection onwards, the distance covered by each ray would be $\dfrac{{0.2}}{{\sqrt 3 }}$ .
Let the total number of times the ray was reflected including the first one be $n$ , then
$n\left( {\dfrac{{0.2}}{{\sqrt 3 }}} \right) = 2\sqrt 3 $
On simplifying, we get $n = 30$ .
Hence, the maximum number of times the ray undergoes reflection before it emerges is 30.
Thus, the correct option is B.

Note:Angle of incidence is the angle that the incident ray makes with the normal of the mirror and angle of reflection is the angle that the reflected ray makes with the normal of the mirror. In the case of plane mirrors, the angle of incidence is equivalent to the angle of reflection. Use this property of plane mirrors and trigonometric relations to solve the given question.