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

Explanation

MM' is a convex mirror and A is a plane mirror. PQ is the object and P'Q' is the image formed at the same place by the two mirrors [Fig.1.43].
`"Here" " " OR=50 cm, AR = 30 cm`
`therefore` Image distance from the plane mirror = O ' A = 30 cm

According to the figure,
OA=OR-AR=50-30=20 cm
`therefore` Image distacne from the convex mirror,
O'O = O'A - OA = 30 - 20 = 10 cm
`"We know", (1)/(v)+(1)/(u)=(1)/(f)`
`"Here" " " v=+10 cm , u=-50 cm`
`therefore " " (1)/(10)+(1)/(-50)=(1)/(f)`
`or, " " (4)/(50)=(1)/(f)`
`or, " " f=+(25)/(2)`
` therefore` Radius of curvature,
`r=2f=2xx(25)/(2)=25 cm`
`therefore` Radius of curvature of the convex mirror = 25 cm