An object is placed in front of a convex mirror at a distance of 50 cm. A plane mirror is introduced covering lower half of the mirror. If the distance between the object and the plane mirror is 30 cm, 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 (in cm)?

The distance of the object from the plane mirror is 30 cm and so the distance of its image  is also 30 cm from the mirror. As images formed by both the mirrors concide,  so  distance of image for convex mirror is 10 cm .
 
    
By mirror formula     $\frac{1}{u}+\frac{1}{v}=\frac{1}{f}$    , we have
    $\frac{1}{10}+\frac{1}{-50}=\frac{1}{f}$
Which on solving gives f = 12.5 cm.
$\therefore$   Radius of curvature R= 2f =25 cm.