Spherical Mirrors

Step 1: Understanding the properties of convex mirrors.
For a convex mirror, the image formed is always virtual, erect, and diminished. The magnification for a convex mirror is
given by the relation:
Here, the object size is twice the image size, so .
Step 2: Using the mirror equation.
The mirror equation is: where is the focal length, is the image distance, and is the object distance. The focal length for a convex mirror is related to the radius of curvature by:
Given that the radius of curvature is 40 cm, we find:

Step 3: Finding the image distance.
The magnification for a convex mirror is also related to the object and image distances by: Substituting , we get: Substituting this into the mirror equation, we can solve for , yielding . Thus, the correct answer is
(D) 20 cm
.