Question

Find the focal length of a convex mirror whose radius of curvature is 32cm.

Answer 1

Hint: We know that the radius of curvature of a mirror is twice that of focus. The sign convention is also very important, as in the case of convex mirrors, the focal point is situated to the right of the horizontal axis.

Complete step by step solution:
In the given question, we are supplied with the following data:
There is a spherical mirror, which is a type of convex.
The radius of curvature of the mirror is given as \[32\,{\text{cm}}\].
We are asked to find out the focal length of the convex mirror.
To begin with, we must know the terms which are used here. The radius of curvature and the focal length or we say the length of focal point are two different things. The radius of
the curvature of a mirror is the radius of the sphere of which the mirror is a part. Focus is a point which is of great significance. The light rays which come from far away seem to be parallel to the optical axis in case of the spherical mirror. These rays after reflection tend to bend in or bend away through a point which is called focus.We know, in general the focal length is half the radius of curvature.Again, we have to give special importance to the sign of the radius of curvature and the focal length.The sign of the radius of curvature or the focal length in case of convex mirrors is always positive, as according to the sign convention the focal point is situated to the right of the horizontal axis.Hence, the radius of curvature of the convex mirror is \[ + 32\,{\text{cm}}\].
So, the focal length of the convex mirror is:
\[f = \dfrac{R}{2}\] …… (1)
Where,
\[f\] indicates the focal length of the mirror.
\[R\] indicates the radius of curvature of the mirror.
Now, we substitute the required value in the equation (1) we get:
$f = \dfrac{R}{2} \\
\Rightarrow f = \dfrac{{ + 32}}{2} \\
\therefore f = + 16\,{\text{cm}} \\$

Hence, the focal length of the convex mirror is \[ + 16\,{\text{cm}}\].

Note: It should be remembered that the focal length of a convex mirror is positive while that of the concave mirror is negative. In case of the convex mirror the focal length is measured towards the positive part of the horizontal axis while in case of concave mirror the focal length is measured towards the negative part of the horizontal axis.