An object is placed in front of a convex mirror at a distance of 50cm. A plane mirror is introduced covering the lower half of the convex mirror. If the distance between the object and the plane mirror is 30cm, it is found that there is no parallax between the images formed by the two mirrors. What is the radius of curvature of the convex mirror?

Options

A. 12.5 cm
B. 25 cm
C. `(50)/(3)m`
D. 18cm

Answer

B

Explanation

No parallax i.e., images by both mirrors are formed at the same place.
Image of O is formed at A by plane mirror. Image by convex mirror:
`(1)/(f)=(1)/(10)+(1)/(-50)=(5-1)/(50)=(4)/(5)impliesf=(50)/(4)`cm
Radius of curvature `R=2f=(50)/(2)cm=25cm`