Question

An object is placed (a) 20 cm, (b) 4 cm, in front of a concave mirror of focal length 12 cm. Find the nature and position of the image formed in each case.

Answer 1

 Case (a)

Distance of the object from the mirror (u) = -20 cm
The focal length of the concave mirror (f) = -12 cm
We have to find the distance of the image (v).
Using the magnification formula, we get  

`1/f=1/v+1/u` 

so 

`or 1/-12=1/v+1/-20` 

`1/-12=1/v-1/20` 

`or 1/20-1/12=1/v` 

`or(3-5)/60=1/v` 

`or -2/60=1/v` 

`or v= 60/-2` 

`v=-30` cm 

The image will be at a distace of 30 cm in front of mirror.Again, 

Magnification `(m)=(-v)/u ` 

     `m=-(-30)/-20=-1.5`  

 Therefore, the image will be real, inverted and enlarged. 

Thus the image is real, inverted and enlarged. 

Case B 

 Distance of the object from the mirror (u) = -4 cm
The focal length of the concave mirror (f) = -12 cm
We have to find the distance of the image (v).
Using the mirror formula, we get 

`1/f=1/v+1/u` 

`1/-12=1/v+1/-4` 

`or 1/4-1/12=1/v` 

`or(3-1)/12=1/v` 

`or 2/12=1/v` 

Therefore, distance of image (v) is 6 cm.Now, using the magnification formula, we get 

`m=-v/u` 

`m=-6/-4=1.5` 

Thus, the image is virtual and erect.