An object 8.0 cm high forms a virtual image 3.5 cm high located 4.0 cm behind a mirror. (a) F

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An object 8.0 cm high forms a virtual image 3.5 cm high...

An object $8.0 \mathrm{~cm}$ high forms a virtual image $3.5 \mathrm{~cm}$ high located $4.0 \mathrm{~cm}$ behind a mirror. (a) Find the object distance. (b) Describe the mirror: is it plane, convex, or concave? (c) What are its focal length and radius of curvature?

Key Concepts

Mirror Equation

The mirror equation, given by 1/f = 1/d_o + 1/d_i, is a fundamental relation in geometrical optics that relates the focal length (f), object distance (d_o), and image distance (d_i) of a mirror. This equation is used to analyze image formation by mirrors, accounting for sign conventions that indicate whether distances are real or virtual.

Virtual Image

A virtual image is formed when the light rays appear to diverge from a point behind the mirror rather than actually converging at that point. In mirror problems, a virtual image is indicated by a negative image distance according to the sign convention, and the image cannot be projected onto a screen because it does not result from actual light convergence.

Magnification

Magnification in mirror optics is defined as the ratio of the image height to the object height, and also relates to the image distance and object distance by the relation m = -d_i/d_o. This concept helps determine the relative size and orientation of the image compared to the object.

Types of Mirrors

The type of mirror—whether concave, convex, or plane—is determined by the shape of its reflecting surface. Concave mirrors (curved inward) can produce real or virtual images depending on the object position, while convex mirrors (curved outward) always form virtual, diminished images. Plane mirrors always produce virtual images that are of the same size as the object.

Focal Length and Radius of Curvature Relationship

The focal length of a spherical mirror is directly related to its radius of curvature by the formula f = R/2. Understanding this relationship allows one to connect the geometrical shape of the mirror (its radius of curvature) with its optical properties (its ability to converge or diverge light).

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