Question

An object 1 cm tall is placed 30 cm in front of a convex mirror of focal length 20 cm. Find the size and position of the image formed by the convex mirror. 

Answer 1

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

Height of the object 'h_o' = 1 cm

Distance of the object from the mirror 'u' = -30 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/-30` 

⇒`1/30+1/20=1/v` 

⇒`2/60+3/60=1/v` 

⇒`5/60=1/v` 

⇒`v=60/5= 12 cm` 

The image will be at a distance of 12 cm behind the mirror .

Now, using the magnification formula, we get 

`m=h_i/h_o` 

`0.4=h_i/1` 

`h_i=0.4 cm `

Therefore, the height of the image is 0.4 cm.