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

As shwon in Fig., `M` is a convex mirror and `M'` is a plane mirror. `O` is point object

`OP = 50 cm and OM' = 30 cm`. `I` is the image of `O` in plane mirror, where
`M'I = OM' = 30 cm`.
As there is no parallax between the two images in the two mirrors, therefore, images of `O` in convex mirror is also at `I`.
Now, for convex mirror, `u = - 50 cm`
`v = PI = M'I - MP = 30 - 20 = 10 cm`
`(1)/(f) = (1)/(v) + (1)/(u) = (1)/(10) - (1)/(50) = (5 - 1)/(50) = (4)/(50)`
`f = (50)/(4) cm`
`R = 2f = 2 xx (50)/(4)cm = 25 cm`