Question

An object is placed between the pole and the focus of a concave mirror. Using mirror formula, prove mathematically that it produces a virtual and an enlarged image.

Answer 1

Apply mirror's focal length formula.

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

for concave mirror, f < 0 & u < 0

⇒ `1/v = 1/f - 1/u`; Since, u < f < 0

⇒ `1/f - 1/u > 0`

or `1/v > 0`

⇒ v > 0

This shows that the image is on the right side of a concave mirror.

Now, `m = (-v)/u`

∵ v > 0 & u < 0

⇒ m > 0

Therefore, a virtual and enlarged image is obtained.