Question

How far should an object be placed from the pole of a converging mirror of focal length 20cm to form a real image of the size exactly `1/4`th the size of the object?

Answer 1

Given,
Focal length of the concave mirror (f) = 20 cm
Magnification (m) = -1/4
Using the magnification formula, we get  

`m=-v/u` 

`-1/4=(-v)/u` 

`v=u/4`  

Using the mirror formula, we get 

`1/f=1/v+1/u` 

`1/-20=4/u+1/u` 

`-1/20=5/u` 

u=−100 cmThus, the object should be placed in front of the concave mirror at a distance of 100 cm.