mirror: Convex and Concave Mirrors

Convex and concave mirrors are known collectively as spherical mirrors, since their curved reflecting surfaces are usually part of the surface of a sphere. The concave type is one in which the midpoint or vertex of the reflecting surface is farther away from the object than are the edges. The center of the imaginary sphere of which it is a part is called the center of curvature and each point of the mirror surface is, therefore, equidistant from this point. A line extending through the center of curvature and the vertex of the mirror is the principal axis, and rays parallel to it are all reflected in such a way that they meet at a point on it lying halfway between the center of curvature and the vertex. This point is called the principal focus.

The size, nature, and position of an image formed by a concave spherical mirror depend on the position of the object in relation to the principal focus and the center of curvature. If the object is at a point farther from the mirror than the center of curvature, the image is real (i.e., it is formed directly by the reflected rays), inverted, and smaller than the object. If the object is at the center of curvature, the image is the same size as the object and is real and inverted. If the object is between the center of curvature and the principal focus, the image is larger, real, and inverted. If the object is inside the principal focus, the image is virtual, erect (right side up), and larger than the object. The position of the object can be found from the equation relating the focal length f of the mirror (the distance from the mirror to the principal focus), the distance d_o of the object from the mirror, and the distance d_i of the image from the mirror: 1/f=1/d_o+1/d_i. In the case of the virtual image, this equation yields a negative image distance, indicating that the image is behind the mirror. In the case of both the real and the virtual image, the size of the image is to the size of the object as the distance of the image from the mirror is to the distance of the object from the mirror.

In a convex spherical mirror the vertex of the mirror is nearer to the object than the edges—the mirror bulges toward the object. The image formed by it is always smaller than the object and always erect. It is never real because the reflected rays diverge outward from the face of the mirror and are not brought to a focus, and the image, therefore, is determined by their prolongation behind the mirror as in the case of the plane mirror.

Sections in this article:

• Introduction
• History and Development
• Convex and Concave Mirrors
• The Plane Mirror

The Columbia Electronic Encyclopedia, 6th ed. Copyright © 2024, Columbia University Press. All rights reserved.

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