# Use the mirror equation to show that a convex lens always produces a virtual image independent of the location of the object.

1
by christinsarah1
It is convex mirror, not lens.

2015-03-04T14:55:54+05:30

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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.