Question

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

Answer 1

u = -50 cm
The image is formed at a distance of 30 + 30 cm from the object.
So v = 60-50 = 10 cm

1/f = 1/u +1/v
= -1/50 + 1/10 = 2/25

f = 12.5 cm
Radius of curvature = 12.5* 2 = 25 cm

Answer 2

we know plane mirror form image equal distance and opposite side so,
image distance in opposite side = 30 cm
  A/C to question,
object is placed 50 cm from convex mirror and 30 cm from plane mirror , also it is found that there is no parallax so, image concide of both mirror ,
hence

      v = +10 cm
and u = -50cm
   f= ?
    use mirror formula,
 1/v + 1/u = 1/f 
1/10 + 1/-50 = 1/f 
4/50 = 1/f 
 f = 50/4 so, R = 2F = 2 * (50/4 ) = 25 cm