Question

If an object of 10 cm height is placed at a distance of 36 cm from a concave mirror of focal length 12 cm, find the position, nature and height of the image. 

 

Answer 1

Distance of the object from the mirror 'u' = −36 cm
Height of the object 'h_o'​ = 10 cm
Focal length of the mirror 'f' = −12 cm
We have to find the distance of the image 'v'.
Height of the image  h_i = ?
Using the mirror formula, we get  

`1/f=1/v+1/u` 

`1/-12=1/v+1/(-36)` 

`1/v=1/36-1/12` 

`1/v=(1-3)/36=-2/36` 

v=-18cm  

Distance of the image 'v' = −18 cm
Using the magnification formula, we get  

`m=h_i/h_o=-v/u` 

`h_i/10=(-(-18))/-36=-1/2` 

`h_i=-1/2` 

`h_i=-1/2` 

`h_i=-5cm` 

Height of the image 'h_i'​ = −5 cm
Again using the magnification formula, we get​ 

`m=-v/v=(-(-18))/36` 

m=-1/2  

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