Q. An object is placed infront of a convex mirror at a distance of $50\ cm$. A plane mirror is introduced covering the lower half of the convex mirror. If the distance between the object and plane mirror is $30\ cm$, it is found that there is no parallax between the images formed by two mirrors. Radius of curvature of mirror will be
A) 12.5 $cm$
B) 25 $cm$
C) $\frac{50}{3}cm$
D) 18 $cm$
Explanation
(b) Since there is no parallax, it means that both images (By plane mirror and convex mirror) coinciding each other
According to property of plane mirror it will form image at a distance of $30\ cm$ behind it. Hence for convex mirror $u = - 50\ cm,\ v = + 10\ cm$
By using $\frac{1}{f} = \frac{1}{v} + \frac{1}{u} \Rightarrow \frac{1}{f} = \frac{1}{+ 10} + \frac{1}{- 50} = \frac{4}{50}$
$\Rightarrow f = \frac{25}{2}cm \Rightarrow R = 2f = 25cm$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.