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.

Advertisement Remove all ads

#### Solution

Given,

The mirror is convex.

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`

⇒`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.

#### Notes

`1/f=1/u-2/u(-1)/u`

⇒`1/20=(-1)/u`

⇒`u=-20cm`

⇒`v=-((-20))/2`

⇒`v=10 cm`

Is there an error in this question or solution?

Advertisement Remove all ads

#### APPEARS IN

Advertisement Remove all ads

Advertisement Remove all ads