Question

At what distance from a concave mirror focal length 10 cm should an object 2 cm long be placed in order to get an erect image 6 cm tall?   

 

Answer 1

Height of the object 'h_o' = 2 cm

Focal length of the mirror 'f' = −10 cm
Height of the image 'h_i' = 6 cm
We have to find the distance of the object from the mirror 'u'.
Using the magnification formula, we get 

`m= h_i/h_o=-v/u` 

`m=6/2=-v/u` 

`m=3=-v/u` 

thus v=-3u 

Now, using the mirror formula, we get

 `1/f=1/v+1/u` 

`1/-10=1/(-3u)+1/u` 

`1/10=1/(3u)-3/(3u) =(-2)/(3u)` 

`u=(-2xx10)/3` 

u=-6.67 cm  

Thus, the distance of the object from the mirror 'u' is −6.67 cm.