Question

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.

Answer 1

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`