Ray Optics and Optical Instruments Part 2

It is given that image coincides with the object. In the arrangement given, the image will only coincide with the object when the ray on mirror falls directly perpendicular on the surface of it. The light will converge at centre of curvature of mirror and due to that after removing the mirror the light will converge at same position.
The focal length of mirror, f = 15 cm. So, radius of curvature of mirror, 2f = 30 cm
The image distance from the object after convex mirror is removed will be calculated as, 12 cm + 8 cm + 30 cm = 50 cm.
Thus, the image will formed at a distance of 50 cm from object.