A point object O is kept at a distance of 30cm from a convex lenx of power `+4` D towards its left. It is observed that when a convex mirror is kept on the right side at a distance of 50cm from the convex lens, theimage of the object O formed by the lens-mirror combination coincides with the object itself. Calculate the focal length of the convex mirror.

Explanation

Focal length of the convex lens `= ( 1)/( P) m`
`f = ( 1)/( 4) m = 25 cm`
Let v be the position of the imae, I, of the object formed by the convex lens alone . We then have
`(1)/( v) - ( 1)/( ( -u)) = ( 1)/( f)`
`rArr (1)/(v) = ( 1)/( 25) - ( 1)/( 30) = ( 6-5)/( 150) = ( 1)/( 150)`
`rArr v = 150 cm`
Hence the distance of the image (formed by the convex lens alone ) from the convex mirror would be ( 150-150) cm, i.e., 100cm. This distance is equal to the radius of the curvature of the convex mirror.
Hence focal length of the convex mirror equals `100 //2`. i.e., 50 cm.
`:.` Radius of the curvature of the convex mirror,
`R = LI - LM `