question_answer

The mirror of length \[2\ell \] makes 10 revolutions per minute about the axis crossing  its  midpoint \[O\] and perpendicular to the plane of the figure There is a light source in point A and an observer at point B of the circle of radius R drawn around centre \[O\,\,(\angle AOB=90{}^\circ )\] What is the proportion \[\frac{R}{\ell }\] if the observer B sees the light source first time when the angle of mirror \[\psi =15{}^\circ ?\]

A) \[\sqrt{2}\]

B) \[\frac{1}{\sqrt{2}}\]

C) \[2\sqrt{2}\]

D) \[\frac{1}{2\sqrt{2}}\]

Correct Answer: A

Solution :

\[{{A}_{1}}\] is the image of A which is seen by b

\[\angle OCB=\theta \] sum of angle of \[D=180{}^\circ \]

\[\therefore \theta +105+30=180\,\,or\,\,\theta =45{}^\circ \]

\[\frac{R}{\sin 45{}^\circ }=\frac{\ell }{\sin 30{}^\circ };\]

\[\frac{R}{\ell }=\frac{\sin 45{}^\circ }{\sin 30{}^\circ }=\sqrt{2}\]