Question

A small plane mirror is placed at the centre of a spherical screen of radius$R$ and a beam of light is falling on the mirror. If the mirror makes n revolutions per second, then the speed of light on the screen after reflection from the mirror will be
A. $4\pi {\text{nR}}$
B. $2\pi {\text{nR}}$
C. $\dfrac{{{\text{nR}}}}{{2\pi }}$
D. $\dfrac{{{\text{nR}}}}{{4\pi }}$

Answer 1

Hint:The smooth surface on which the process of reflection takes place is called a mirror. There are two common types of mirrors. They are concave and convex. If the concave side of a sphere acts as a reflector, that is if the concave surface of the spherical mirror helps in reflection of light then it is called a concave mirror. If the convex side of a sphere acts as a reflector, that is if the convex surface of the spherical mirror helps in reflection of light then it is called convex mirror.

Complete step by step answer:
If the incident light ray is fixed and if the mirror is rotated by an angle $\theta $(about an axis which lies in the plane of mirror and is perpendicular to the plane of incidence) then reflected turns through an angle $2\theta $. So, the spot on the screen will make $2n$ revolution per second.
\[w' = 2w \\
\Rightarrow w' = 2 \times 2\pi n \\
\Rightarrow w' = 4\pi n\]
$\Rightarrow v = w'R \\
\therefore v= 4\pi nR$

Hence, the correct answer is option A.

Note:Remember that for a fixed beam of light, the reflection angle is double the angle by which the reflector rotated. The images which are formed by plane mirrors are virtual and they show left-right inversion. In the case of plane mirrors, the distance from object to the mirror is equal to the distance of the image inside the mirror and also the size of the image is equal to the size of the object.