Use the mirror equation to deduce that:
an object placed between the pole and focus of a concave mirror produces a virtual and enlarged image.
[Note: This exercise helps you deduce algebraically properties of images that one obtains from explicit ray diagrams.]

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Solution

From the mirror formula, for a concave mirror, f < 0 and for an object located between the pole and focus of a concave mirror,

f < u < 0

∴

\frac{1}{f} > \frac{1}{u}

\Rightarrow

\frac{1}{f} - \frac{1}{u} > 0

\Rightarrow

\frac{1}{v} > 0 or v > 0

(∵ \frac{1}{v} = \frac{1}{f} - \frac{1}{u})

i.e., a virtual image is formed on the right.

Also,

\frac{1}{v} < \frac{1}{|u|} or v > |u|

∴

|m| = \frac{v}{|u|} > 1 .

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