Question

An object is placed in front of a convex mirror with a radius of curvature of magnitude 10 cm. The mirror produces an image that is 4 cm behind the mirror. How far from the mirror was the object placed?

What is the magnification?

Answer 1

u = - 20 cm

m =
`(1)/(5)`

Given:

Radius of curvature, R = 10 cm

image distance, v = 4 cm

Solution:

Focal length of the convex mirror, f:

f =
`(R)/(2) = (10)/(2) = 5 cm`

Using Lens' maker formula:

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

Substitute the given values in the above formula:

`(1)/(5) = (1)/(u) + (1)/(4)`

`(1)/(u) = (1)/(5) - (1)/(4)`

u = - 20 cm

where

u = object distance

Now, magnification is the ratio of image distance to the object distance:

magnification, m =
`(|v|)/(|u|)`

magnification, m =
`(|4|)/(|-20|)`

m =
`(4)/(20)`

m =
`(1)/(5)`