Curved mirror
They have convex and concave regions that produce deliberately distorted images.
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 (not inverted), though diminished (smaller), image and because they provide a wider field of view as they are curved outwards.
These mirrors are often found in the hallways of various buildings (commonly known as "hallway safety mirrors"), including hospitals, hotels, schools, stores, and apartment buildings.
They are usually mounted on a wall or ceiling where hallways intersect each other, or where they make sharp turns.
[2] 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.
Convex mirrors make everything seem smaller but cover a larger area of surveillance.
Round convex mirrors called Oeil de Sorcière (French for "sorcerer's eye") were a popular luxury item from the 15th century onwards, shown in many depictions of interiors from that time.
[3] With 15th century technology, it was easier to make a regular curved mirror (from blown glass) than a perfectly flat one.
Famous examples in art include the Arnolfini Portrait by Jan van Eyck and the left wing of the Werl Altarpiece by Robert Campin.
[4] The image on a convex mirror is always virtual (rays haven't actually passed through the image; their extensions do, like in a regular mirror), diminished (smaller), and upright (not inverted).
[5] They are also used to provide a magnified image of the face for applying make-up or shaving.
[6] In illumination applications, concave mirrors are used to gather light from a small source and direct it outward in a beam as in torches, headlamps and spotlights, or to collect light from a large area and focus it into a small spot, as in concentrated solar power.
Concave mirrors are used to form optical cavities, which are important in laser construction.
Some dental mirrors use a concave surface to provide a magnified image.
For parallel rays, such as those coming from a very distant object, a parabolic reflector can do a better job.
:[2] The sign convention used here is that the focal length is positive for concave mirrors and negative for convex ones, and
For concave mirrors, whether the image is virtual or real depends on how large the object distance is compared to the focal length.
The magnification of a mirror is defined as the height of the image divided by the height of the object: By convention, if the resulting magnification is positive, the image is upright.
The 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 mirror surface vertex (where the optical axis meets the mirror) will form an angle with the optical axis.
A second ray can be drawn from the top of the object, parallel to the optical axis.
Such a ray reflects parallel to the optical axis and also passes through the image point corresponding to the top of the object.
The ray matrix of a concave spherical mirror is shown here.
Boxes 1 and 3 feature summing the angles of a triangle and comparing to π radians (or 180°).
The derivations of the ray matrices of a convex spherical mirror and a thin lens are very similar.
