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

Answer:

u = - 20 cm

m =$\frac{1}{5}$

Given:

Radius of curvature, R = 10 cm

image distance, v = 4 cm

Solution:

Focal length of the convex mirror, f:

f = $\frac{R}{2} = \frac{10}{2} = 5 cm$

Using Lens' maker formula:

$\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$

Substitute the given values in the above formula:

$\frac{1}{5} = \frac{1}{u} + \frac{1}{4}$

$\frac{1}{u} = \frac{1}{5} - \frac{1}{4}$

u = - 20 cm

where

u = object distance

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

magnification, m =$\frac{|v|}{|u|}$

magnification, m =$\frac{|4|}{|-20|}$

m =$\frac{4}{20}$

m =$\frac{1}{5}$