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A curved mirror is a mirror with a curved reflective surface, which may be either convex (bulging outward) or concave (bulging inward). Most curved mirrors have surfaces that are shaped like part of a sphere, but other shapes are sometimes used in optical devices. The most common non-spherical type are parabolic reflectors.
Convex mirror A convex mirror, or diverging mirror, is a curved mirror in which the reflective surface bulges toward the light source. Such mirrors always form a virtual image, since the focus F and the center of curvature 2F are both imaginary points "inside" the mirror, which cannot be reached. A collimated (parallel) beam of light diverges (spreads out) after reflection from a convex mirror, since the normal to the surface differs with each spot on the mirror. Image The image is always virtual, smaller, and upright. These features make convex mirrors very useful: since they make everything appear smaller, they can cover a wider field of view than a normal flat mirror would, since the image is "compressed". The passenger-side mirror on a car is typically a convex mirror. In some countries, these are labeled with the safety warning "Objects in mirror are closer than they appear", to warn the driver of the convex mirror's distorting effects on distance perception. Concave mirrors
Image Note: S here stands for distance between object and mirror. Mirror shape Most curved mirrors have a spherical profile. These are the simplest to make, and it is the best shape for general-purpose use. Spherical mirrors, however, suffer from spherical aberration. Parallel rays reflected from such mirrors do not focus to a single point. For parallel rays, such as those coming from a very distant object, a parabolic reflector can do a better job. Such a mirror can focus incoming parallel rays to a much smaller spot than a spherical mirror can. Mathematical treatment of spherical mirrors The mathematical treatment is done under the paraxial approximation, meaning that the under first approximation a spherical mirror is a parabolic reflector. The ray matrix of a spherical mirror is shown here for the concave reflecting surface of a spherical mirror. The element of the matrix is , where is the focal point of the optical device. Boxes 1 and 3 feature summing the angles of a triangle and comparing to π radians (or 180°). Box 2 shows the Maclaurin series of up to order 1. The derivations of the ray matrices of a convex spherical mirror and a thin lens are very similar. | ||||||||||
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