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 plane mirror is 30cm, it is found that the images formed by two mirrors are along same line. Radius of curvature of mirror will be

25 cm

According to property of plane mirror it will form an image at a distance of 30 cm behind it. Hence, for convex mirror u = –50cm, v = +10cm

By using $\frac{1}{f}=\frac{1}{v}+\frac{1}{u} \Rightarrow \frac{1}{f}=\frac{1}{+10}+\frac{1}{-50}=\frac{4}{50}$

⇒ f = $\frac{25}{2}$ cm   ⇒  R = 2f = 25 cm