An image of a candle on a screen is found to be double its size. When the candle is shifted by a distance of 5cm, then the image becomes triple its size. Find the nature and radius of curvature of the mirror.

Explanation

Since the images formed on screen it is real. Real object and real image implies concave mirror.
Applying `m = (f)/(f-u)` or `-2 = (f)/(f-(u))..........(1)`
After shifting `-3 = (f)/(f-(u+5)).....(2)`
[Why `u + 5` why not `u-5` in a concave mirror, teh size of real image will increases only when the real object is brought closer to the mirror. In doing so, its `x` coordinate will increases]
From `(1) & (2)` we get,
`f = -30cm`, or `R = -60cm` (concave) adn `R.O.C = 60cm`