Question

If a concave mirror has a focal length of 10 cm, find the two positions where an object can be placed to give, in each case, an image twice the height of the object.

Answer 1

Given,
Focal length (f) of the concave mirror = -10 cm
Case-1 
The image is real, and its magnification (m) is -2.
Using the magnification formula, we get  
`1-10=12u+1u`

`m=(-v)/u` 

`-2=(-v)/u` 

v=2u 

Now, using the mirror formula, we get 

`1/f=1/v+1/u` 

`1/-10=1/2u+1/u` 

`1/-10=1/(2u)+2/(2u)=3/2u` 

`u=(3xx(-10))/2=-15 cm 

The object should be placed at a distance of 15cm from the concave mirror.

Case-2
The image is virtual and has a magnification 'm' of 2.
Using the magnification formula, we get 

`m=-v/u` 

`2=-v/u` 

 v=-2u
Now, using the mirror formula, we get 

`1/f=1/v+1/u` 

`1/-10=1/(-2u)+1/u` 

`1/-10=-1/(2u)+2/(2u)=1/(2u)` 

`u=(-10)/2=-5 cm ` 

Thus, the object should be placed at a distance of 5 cm in front of the concave mirror.