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?

Explanation

It is clear that virtual image in plane mirror is 30 cm behind and there is no parallax so image formed by two mirror will coincide and u = 50 cm
the distance of image formed by plane mirror from convex mirror
`V= PI = MI - MP = MO - MP = 30 -20 =10 cm [MI = MO]`
Since this image coincides will image formed by convex mirror

so for convex mirror `m= - [(V)/(u)] = - [(-30)/( -15)] =-2`
`rArr f = (50)/( 4) = 12.5 cm ` so R = 2f = 25 cm
The image formed by convex mirror is erect virtual and diminished
magnfication `m = - [(V)/(u )] =- [(+10)/( -50)] = + [(1)/(5)]`