Convex mirrorvirtual image, since the focus (F) and the centre of curvature (2F) are both imaginary points "inside" the mirror, which cannot be reached. Therefore images formed by these mirrors cannot be taken on screen. (As they are inside the mirror)
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.
Usescar 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. Convex mirrors are preferred in vehicles because they give an upright, though diminished, image. Also they provide a wider field of view as they are curved outwards.
Convex mirrors are used in some automated teller machines as a simple and handy security feature, allowing the users to see what is happening behind them. Similar devices are sold to be attached to ordinary computer monitors.
Some camera phones use convex mirrors to allow the user to correctly aim the camera while taking a self-portrait.
ImageThe image is always virtual (rays haven't actually passed through the image,their extensions do), diminished (smaller), and upright . These features make convex mirrors very useful: everything appears smaller in the mirror, so they cover a wider field of view than a normal plane mirror does as the image is "compressed".
|Object's position (S), |
focal point (F)
These mirrors are called "converging" because they tend to collect light that falls on them, refocusing parallel incoming rays toward a focus. This is because the light is reflected at different angles, since the normal to the surface differs with each spot on the mirror.
|Object's position (S), |
focal point (F)
|S < F |
(Object between focal point and mirror)
|S = F |
(Object at focal point)
(Note that the reflected light rays are parallel and do not meet the others. In this way, no image is formed or more properly the image is formed at infinity.)
|F < S < 2F |
(Object between focus and centre of curvature)
|S = 2F |
(Object at centre of curvature)
|S > 2F |
(Object beyond centre of curvature)
Mirror shapeMost 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.
Mirror equation and magnificationThe Gaussian mirror equation relates the object distance (do) and image distances (di) to the focal length (f):
Ray tracingThe image location and size can also be found by graphical ray tracing, as illustrated in the figures above. A ray drawn from the top of the object to the surface vertex (where the optical axis meets the mirror) will form an angle with that axis. The reflected ray has the same angle to the axis, but is below it (See Specular reflection).
A second ray can be drawn from the top of the object passing through the focal point and reflecting off the mirror at a point somewhere below the optical axis. Such a ray will be reflected from the mirror as a ray parallel to the optical axis. The point at which the two rays described above meet is the image point corresponding to the top of the object. Its distance from the axis defines the height of the image, and its location along the axis is the image location. The mirror equation and magnification equation can be derived geometrically by considering these two rays.
Ray transfer matrix of spherical mirrorsThe mathematical treatment is done under the paraxial approximation, meaning that under the 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 C element of the matrix is , where f 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.