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 $9/\pi$ rev/sec. The light reflected the mirror is received on the wall $W$ at a distance $10m$ from the axis of rotation. When the angle of incidence becomes ${37}^0$ fine the speed of the spot ( point) on the wall?

• A. $960m/s$
• B. $840m/s$
• C. $500m/s$
• D. $900m/s$

Answer 1

Answer: (C)

$500m/s$

$y=10\cot \theta$

$(-\frac{dy}{dt})=\left(10{\csc }^2\theta \right)\left(\frac{d\theta }{dt}\right)$

$v_p=\left(10{\csc }^2\theta \right)w$

$=\left(2\pi f\right)\left(10{\csc }^2{37}^{\circ }\right)$

$=\left(2\right)\left(\pi \right)\left(\frac{9}{\pi }\right)\left(10\right)\left(\frac{25}{9}\right)$

$=500m/s$