Question

A diverging mirror of radius of curvature 40 cm forms an image which is half the height of the object. Find the object and image positions.

Answer 1

Given,
The mirror is convex.

Magnification 'm' = 12

Radius of curvature 'R' = 40 cm

Focal length of the convex mirror 'f=2 = 20 cm`

We have to find the position of the image 'v' and distance of the object from the mirror 'u'.

Using the mirror formula, we get  

`1/f=1/u+1/v`

Given, m=`1/2` 

Again, m =`-v/u` 

Therefore,V =-`-1/2u` 

By puting the value of `V` in the mirror formula, We get  

`1/f=1/u-2/u(-1)/u` 
⇒`1/20=(-1)/u` 
⇒`u=-20cm` 
⇒`v=-((-20))/2` 
⇒`v=10 cm` 

If an objet is placed at a distance of 20 cm in front of the mirror, the image will be formed 10 cm behind the mirror.