Question

An arrow 2.5 cm high is placed at a distance of 25 cm from a diverging mirror of focal length 20 cm. Find the nature, position and size of the image formed. 

Answer 1

Given,
The mirror is a diverging mirror, i.e. convex mirror.

Height of the object 'h_o' = 2.5 cm

Distance of the object from the mirror 'u' = -25 cm

Focal length of the convex mirror 'f' = 20 cm

We have to find the position of the image 'v', height of the image 'h_i' and its magnification 'm'.

Using the mirror formula, we get   

`1/f=1/v+1/u` 

`1/20=1/v+1/-25` 

`1/20+1/25=1/v` 

`5/100+4/100=1/v` 

`1/v=9/100` 

`v=100/9=11.1 cm ` 

Thus, the distance of the image 'v' is 11.1 cm behind the mirror.
Now, using the magnification formula, we get  

`m=-v/u=(-11.1)/-25` 

`m=0.44

 Therefore, the image is virtual, erect and smaller in size.
Again, 

`m=h_i/h_0` 

0.4=h_1/2.5 

`h_i=0.44xx2.5=1.1 cm` 

Therefore, the height of the image is 1.1cm.