Answer :

(a)

The image formation distance is 30cm and the object distance is 15cm.

Given

The mirror radius of curvature is 20 cm; the real image magnification is 2

Formula Used

Using the mirror formula, which states the relationship between the object and image distance along with the focal length of the object. The formula states that

where

f is the focal length, u is the distance of the object, v is the distance of the image.

To find the focal length we divide the radius of curvature in half with which we get:

Radius of Curvature,

The focal length,

The magnification (m) of the image = 2

Hence, the relation between the object and the image is

To find the distance of the image formed is

Therefore, the image formation distance is 30cm and the object distance is 15cm.

(b)

Using the mirror formula, the nature of convex image has the focal length always greater than zero meaning if the objects focal length is greater than zero than the position of the object is less than zero. So by using these contexts we can assume that

Making the value of image greater than zero, proving that the image is virtual in nature

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