Question

Use the mirror equation to deduce that the virtual image produced by a convex mirror is always diminished in size and is located between the focus and the pole.

Answer 1

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

∴ f > 0

When the object is placed on the left side of the mirror, the object distance (u) is negative,

∴ u < 0

For image distance v, we have the mirror formula:

`1/"v" + 1/"u" = 1/"f"`

`1/"v" = 1/"f" - 1/"u"`

But we have u < 0

∴ `1/"v" > 1/"f"`

v < f

Hence, the image formed is diminished and is located between the focus (f) and the pole.