The radius of curvature of a spherical mirror is 20 cm. What is its focal length?

By BYJU'S Exam Prep

Updated on: September 25th, 2023

If the radius of curvature of a spherical mirror is 20 cm, the focal length of the mirror would be 10 cm. The focal length, an essential parameter in optics, plays a significant role in determining the extent to which light rays converge or diverge upon interacting with a spherical mirror. By comprehending the relation between the radius of curvature and the focal length, one can understand the behavior of light. The focal length denotes the distance between the mirror’s focal point and its center and is intrinsically linked to the mirror’s curvature. Understanding this relationship helps us comprehend how light propagates through mirrors.

Table of content

1. Focal Length
2. Steps to Calculate Focal Length
3. The radius of curvature of a spherical mirror is 20 cm. What is its focal length?

Focal Length

Focal length is a fundamental concept in optics that refers to the distance between the focal point and the optical center of a lens or a curved mirror. It is a crucial parameter that determines the degree of convergence or divergence of light rays when they pass through or reflect off the lens or mirror.

A shorter focal length indicates a stronger convergence or divergence, while a longer focal length implies a weaker effect. Focal length plays a crucial role in determining the image formation, magnification, and overall optical behavior of lenses and mirrors in various optical systems.

Focal Length Formula

The focal length formula is expressed as f = R/2, where f represents the focal length and R denotes the radius of curvature. This formula states that the focal length of a lens or mirror is equal to half of its radius of curvature. It provides a direct relationship between these two parameters in optical systems.

Steps to Calculate Focal Length

As we have explained above, the focal length (f) is directly proportional to half of the radius of curvature (R). Mathematically, it can be expressed as:

f = R/2

So, if the radius of curvature of a spherical mirror, R = 20 cm

f = 20/2 = 10 cm

Hence, the focal length of the mirror will be 10 cm.

Summary: