A convex mirror has a focal length of 20 cm. If an object is placed 20 cm in front of the mirror, find the distance between the object and its image.

The object is placed in front of a convex mirror.
Object distance, $u = 20$ cm. According to the Cartesian sign convention, for a real object, $u$ is negative.
So, $u = -20$ cm.
Focal length, $f = 20$ cm. For a convex mirror, the focal length $f$ is positive.
So, $f = +20$ cm.
We need to determine the distance between the object and its image.

The mirror formula is:

Substitute the known values:

To solve for $\frac{1}{v}$, rearrange the equation:

The positive value of $v$ indicates that the image is virtual and formed 10 cm behind the mirror.

The object is located 20 cm in front of the mirror ($u = -20$ cm).
The image is located 10 cm behind the mirror ($v = +10$ cm).
Since the object and image are on opposite sides of the mirror, the distance between them is the sum of their absolute distances from the mirror.
Distance between object and image $= |u| + |v|$
Distance between object and image $= |-20 \text{ cm}| + |10 \text{ cm}|$
Distance between object and image $= 20 \text{ cm} + 10 \text{ cm}$
Distance between object and image $= 30 \text{ cm}$

The distance between the object and its image is $\text{30 cm}$.