Chapter 17, Problem 50A

To determine

To discuss: The relationship between the radius of curvature and the focal length of a concave mirror.

Answer to Problem 50A

The focal length of a concave mirror is the half of the radius of curvature of the mirror.

Explanation of Solution

Introduction:

The point at which all rays coming from infinity converge after getting reflected from a mirror is termed as focus of a concave mirror. And, the distance between the mirror and the focus is called the focal length of the mirror.

Now, if $R$ is the radius of curvature of the mirror, then the focal length $\left(f\right)$ of the mirror can be written in terms of $R$ as,

  $f=\frac{R}{2}$

Conclusion:

Hence, the radius of curvature of a concave mirror is twice the focal length of the mirror.