The distance between a real object and its image in a convex mirror of focal length 12cm is 32cm. Find the size of image if the object size if 1cm.

Explanation

Let x and y be the magnitudes of object and image distances.
We have `A A^' =32 cm`
`rArr AO+A^'O=32cm`
`rArr (x+y) =32` (i)
And also, u =-x,v=+y
`1/(-x)+1/y=1/(+12)` (ii)
Solving (i) and (ii) simultaneously, we can get u and v.
The relevant answers are u=-24 cm, v =+8cm
Using `I=-1((+8)/(-24))=+1/3`
So, the image size is `1//3 `cm.