Spherical Mirrors – Terms Associated with Spherical Mirrors

Spherical Mirrors

Introduction:

In this chapter, we will look at two types of spherical mirrors, concave and convex. When the light gets reflected from these mirrors, it does in a specific pattern. However, before looking at that, it is utmost necessary to learn the basic terminologies used to communicate various information about these spherical mirrors. In this section, we will be doing the same.

Explanation:

Terms Associated with Spherical Mirrors:

Pole:

The center of the reflecting surface of a spherical mirror is called its pole (P).

It lies on the reflecting surface of the mirror.

Center of Curvature:

A spherical mirror is a part of a hollow glass sphere which has a center of its own.

This center of the hollow sphere of origin of the spherical mirrors is called the center of curvature (C).

Unlike the pole, it does not lie on the reflecting surface of the mirror. Instead, it lies in front of the reflecting surface of a concave mirror and behind the reflecting surface of a convex mirror.

The Radius of Curvature:

The radius of the sphere, which the spherical mirror is a part of, is called the radius of curvature (R). This is because the distance between the pole and the center of curvature (PC) of a spherical mirror gives its radius of curvature.

Principal Axis:

An imaginary line passing through the pole and the center of curvature of a spherical mirror is called the principal axis.

The angle made by the principal axis with the mirror surface at the pole is 90 degrees. This means the principal axis acts as a normal to the reflecting surface at the pole.

Focus and Focal Length:

A parallel beam of light from the sun (parallel to the principal axis), when it hits the surface of a concave mirror after reflection, converges to a point on the principal axis in front of the mirror.

This point where the light rays converge is called the principal focus (F) of the concave mirror. The distance between the pole and the focus of the concave mirror is called its focal length (f).

A parallel beam of light from the sun (parallel to the principal axis), when it hits the surface of a convex mirror after reflection, appears to diverge to a point on the principal axis behind the mirror.

This point from where the light rays appear to diverge is called the principal focus (F) of the convex mirror. The distance between the pole and the focus of the convex mirror is called its focal length (f).

The focal length is measured in the units of length, i.e., meter, centimeter, etc.; its SI unit is “meter.”

Aperture:

The diameter of the reflecting surface of the spherical mirror is called its aperture.

In the adjacent picture, the length MM’ represents the aperture of the mirrors. In this chapter, we are considering the spherical mirrors with apertures much smaller than their radius of curvature.

Relation Between the Radius of Curvature and the Focal Length:

For spherical mirrors of small apertures, the radius of curvature is twice its focal length. That is,

R = 2f