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 image is formed on the screen, if is real. Real object and real image implies concave mirror.
Applying `m=(f)/(f-u)` or `-2= (f)/(f-u)` (i)
After shifting, `-3= (f)/(f-(u+5))` (ii)
Here, care should be taken that distance of the object becomes `u+5` not `u-5`: In a concave mirror the size of real image will increase only when the real object is brought closer to the mirror. In doing so, its x-coordinate will increase.
From (i) and (ii), we get
`f=-30 cm` or `R=60 cm`