Question

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

• A. 10 m/s
• B. 1000 m/s
• C. 500 m/s
• D. None of these

Answer 1

The correct option is B 1000 m/s

When the mirror is rotated by angle $\theta$,


Total angle of incidence $i$ = Total angle of reflection $r=\alpha +\theta$

In $\Delta AOB$,

$tan[\frac{\pi }{2}-(\alpha +2\theta \left)\right]=\frac{h}{10}$
i.e $cot[\alpha +2\theta ]=\frac{h}{10}$

Differentiating both sides,

$-2cose{c}^2(\alpha +2\theta )\omega =\frac{v}{10}$

Substituting $\alpha +2\theta ={37}^o,\omega =2\pi \times \frac{9}{\pi }$,

$v=-1000m/s$