Question

A concave mirror has a focal length of 4 cm and an object 2 cm tall is placed 9 cm away from it. Find the nature, position and size of the image formed. 

Answer 1

Distance of the object from the mirror 'u' = −9cm
Height of the object 'h_o' = 2 cm
Focal length of the mirror 'f' = −4 cm
We have to find the distance of the image 'v' and height of the image 'h_i'.
Using the mirror formula, we get  

`1/f=1/v+1/u` 

`1/-4=1/v+1/-9` 

`1/-4=1/v-1/9` 

`1/9-1/4=1/v` 

`(4-9)/36=1/v`  

`-5/36=1/v=(-1)/7.2`  

v=7.2 cm 

Therefore, distance of the image 'v' is 7.2 cm.
Now, using the magnification formula, we get 

 `m=h_i/h_o=-v/u`  

`h_i/H_o=-((-7.2))/-9` 

`h_i/2=((-7.2))/-9` 

`h_-i=(2xx(-7.2))/9` 

`h_i=-1.6 cm`   

Thus, the height of the image 'h_i' is 1.6 cm.
Again, using the magnification formula, we get 

`m=-v/u` 

`m=-(-7.2)/-9` 

m=-0.8  

Thus, the image is real, inverted and small in size.