Question

Use the mirror equation to show that an object placed between f and 2f of a concave mirror produces a real image beyond 2f.

Answer 1

We know for a concave mirror, f < 0 [negative] and u < 0 [negative]

2f < u < f

∴ `1/(2"f") > 1/"u" > 1/"f"`

or `(-1)/(2"f") < (-1)/"u" < (-1)/"f"`

or `1/"f" - 1/(2"f") < 1/"f" - 1/"u" < 1/"f" - 1/"f"`

or `1/(2"f") < 1/"v" < 0  ...[∵ 1/"f" - 1/"u" = 1/"v"]`

This implies that v < 0 forms an image on the left.

Also, 2f > v .....[∵ 2f and v are negative]

|2f| < |v|

So, the real image is formed beyond 2f.