Question

Use the mirror equation to show that a convex lens always produces a virtual and diminished image .

Answer 1

Hi..

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, 1/v always positive. So v, the image distance is always positive or the image is always virtual.


Hope this helps u!!

Answer 2

For a convex  mirror,
 focal length(f) is always positive
 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.
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