question_answer

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)            \[18\,cm\]

Correct Answer: B

Solution :

                   Since there is no parallex, 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 \[\frac{1}{f}=\frac{1}{v}+\frac{1}{u}\]     \[\Rightarrow \,\,\,\frac{1}{f}=\frac{1}{+10}+\frac{1}{-50}=\frac{4}{50}\] \[\Rightarrow \]   \[f=\frac{25}{2}cm\]           \[\Rightarrow \,\,\,R=2f=25cm.\]