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 \[D=180{}^\circ \] |
\[\therefore \theta +105+30=180\,\,or\,\,\theta =45{}^\circ \] |
\[\frac{R}{\sin 45{}^\circ }=\frac{\ell }{\sin 30{}^\circ };\] |
\[\frac{R}{\ell }=\frac{\sin 45{}^\circ }{\sin 30{}^\circ }=\sqrt{2}\] |
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