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

The correct option is A $25\text{cm}$

If you cover half of the convex mirror, there is no change in the position or size of the image. Only the intensity/brightness of the image is reduced.

The image formed by the plane mirror is $10cm$ to the right of the convex mirror. Therefore according to the question, the image formed by the convex mirror is also at $10cm$ to the right of it.

So, $u=-50cm,v=+10cm$ and we have to find $f$.

Using mirror formula,

$f=\frac{uv}{u+v}=12.5cm$
$R=2f=25cm$