Question

A light ray $1$ is incident on a plane mirror $M$. The mirror is rotated in the direction as shown in the figure by an arrow at frequency $\frac{9}{\pi }rev/s$. The light reflected by the mirror is received on the wall $W$ at a distance $10m$ from the axis of rotation. When the angle of incidence becomes ${37}^o$ the speed of the spot (a point) on the wall is:

• A. $10m/s$
• B. $1000m/s$
• C. $360m/s$
• D. None of these

Answer 1

Answer: (B)

$1000m/s$

Rotational speed of reflected light is given by,

${\omega }^{\prime }=2\times \frac{9}{\pi }\times 2\pi =18rad/s$

Now, $v^{\prime }=R{\omega }^{\prime }$

The velocity of spot on wall is given as,

$v\cos ({90}^o-{37}^o)=R{\omega }^{\prime }$

$v\cos {53}^o=R{\omega }^{\prime }$

$v=\frac{10}{\cos {53}^o}\times \frac{36}{\cos {53}^o}$

$=\frac{36\times 25}{9}=1000rad/s$