Question

show that the image formed by a convex mirror of an object is always virtual​

Answer 1

For a convex  mirror, focal length(f) is always positive  and object distance (u) is always negative according to the convention.

We have to show that the image formed is virtual. A virtual image means image is formed behind the mirror or image distance(v) is always positive.

Mirror formula is given as

Thus we can write

here,  is positive(since f is positive) and  is also positive(as u is negative). Since  is sum of two positive quantities, always positive. So v, the image distance is always positive or the image is always virtual.

Answer 2

Convex mirror have the property of diverging rays of light.

This is because the reflected ray of light always diverge from a convex mirror surface.

Hence the divergent ray appears to come from behind he convex surface.

Therefore it always forms virtual image.

hope it helps you.