Question

A small plane mirror kept at the centre of a sphere of a diameter of $3m$ , makes $12$ revolution per second. A thin light beam is made on the mirror. The linear speed of the light spot on the surface, formed after reflection from the surface of the mirror is:

Answer 1

In order to solve this question, we will use the concept that whenever a plane mirror rotates to an angle say $\theta$ then the light ray which is reflected from the plane mirror will rotate through an angle of $2\theta$ and hence will make double rotations as compared with rotations of plane mirror.

Complete answer:
As, it’s given that the plane mirror rotates with the number of revolutions in one second is $12$ .
So, the number of revolutions made by reflected rays from the plane mirror will be twice of twelve which is $24$ .
Also, this number of revolutions per second is also called the frequency of the body so, $f = 24$
Speed of the reflected light can be calculated by:
$v = 2\pi R \times f$
Where, $R = 1.5m$ which is the radius of the sphere.
So,
$v = 2\pi \times 1.5 \times 24$
$v = 72\pi m{\sec ^{ - 1}}$
Hence, the speed of the light spot on the surface is given by $v = 72\pi m{\sec ^{ - 1}}$ .

Note: It must be remembered that, whenever a plane mirror is rotated with some angle say $\theta$ then the reflected ray of light will always rotate with an angle of $2\theta$ and the revolutions per second is the frequency of a body in $radians{\sec ^{ - 1}}$ , which also have a unit denoted as $Hertz$ written as $Hz$.