Reflections in a spherical convex mirror. The photographer is seen at top right 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. Download high resolution version (500x708, 117 KB)Spherical mirror (actually a cinema) in Millennium Square, Bristol, England. ...
Download high resolution version (500x708, 117 KB)Spherical mirror (actually a cinema) in Millennium Square, Bristol, England. ...
A mirror, reflecting a vase. ...
For other uses, see Sphere (disambiguation). ...
A parabolic reflector (also known as a parabolic dish or a parabolic mirror) is a reflective device formed in the shape of a paraboloid of revolution. ...
Convex mirror
 A convex mirror diagram showing the focus, focal Length, centre of curvature, principal axis, etc 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 centre of curvature 2F are both imaginary points "inside" the mirror, which cannot be reached. Image File history File links Convex_mirror1. ...
Image File history File links Convex_mirror1. ...
This article is about focal length related to lenses and systems of lenses. ...
Top: The formation of a virtual image using a concave lens. ...
An image that is partially in focus, but mostly out of focus in varying degrees. ...
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. A surface normal, or just normal to a flat surface is a three-dimensional vector which is perpendicular to that surface. ...
Image The image is always virtual (rays haven't actually passed though the image), 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". The passenger-side mirror on a car is typically a convex mirror. In some countries, these are labelled 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. A cameras angle of view can be measured horizontally, vertically, or diagonally. ...
A mirror, reflecting a vase. ...
This article or section does not cite its references or sources. ...
Ray diagram
 Image File history File links Convexmirror_raydiagram. ...
Concave mirrors
 A concave mirror diagram showing the focus, focal Length, centre of curviture, principal axis, etc. A concave mirror, or converging mirror, has a reflecting surface that bulges inward (away from the incident light). Unlike convex mirrors, concave mirrors show different types of image depending on the distance between the object and the mirror itself. Image File history File links Concave_mirror. ...
Image File history File links Concave_mirror. ...
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. In optics, a ray is an idealized narrow beam of light. ...
Image
This sculpture has both convex and concave reflective surfaces. Note: S here stands for distance between object and mirror. Image File history File links Metadata Size of this preview: 800 × 600 pixelsFull resolution‎ (2,592 × 1,944 pixels, file size: 1. ...
Image File history File links Metadata Size of this preview: 800 × 600 pixelsFull resolution‎ (2,592 × 1,944 pixels, file size: 1. ...
Cloud Gate, Millennium Park, Chicago, 2004 Cloud Gate is a public sculpture by Anish Kapoor in Millennium Park, Chicago. ...
- When S < F, the image is:
- Virtual
- Upright
- Magnified (larger)
 Image File history File links Concavemirror_raydiagram_F.svg‎ File historyClick on a date/time to view the file as it appeared at that time. ...
- When S = F, the image is formed at ∞ (infinity).
- 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 ∞.
 Image File history File links Concavemirror_raydiagram_FE.svg‎ File historyClick on a date/time to view the file as it appeared at that time. ...
- When F < S < 2F, the image is:
- Real
- Inverted (vertically)
- Magnified (larger)
 Image File history File links Concavemirror_raydiagram_2FE.svg‎ File historyClick on a date/time to view the file as it appeared at that time. ...
- When S = 2F, the image is:
- Real
- Inverted (vertically)
- Same size
 Image File history File links Image-Concavemirror_raydiagram_2F_F.svg‎ File historyClick on a date/time to view the file as it appeared at that time. ...
- When S > 2F, the image is:
- Real
- Inverted (vertically)
- Diminished (smaller)
 Image File history File links Concavemirror_raydiagram_2F.svg‎ File historyClick on a date/time to view the file as it appeared at that time. ...
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. Focal plane Longitudinal sections In optics, spherical aberration is an image imperfection that occurs due to the increased refraction of light rays that occurs when rays strike a lens or mirror near its edge, in comparison with those that strike nearer the center. ...
A parabolic reflector (also known as a parabolic dish or a parabolic mirror) is a reflective device formed in the shape of a paraboloid of revolution. ...
- See also: Toroidal reflector
A toroidal mirror is a form of parabolic reflector which has a different focal distance depending on the angle of the mirror. ...
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 C element of the matrix is  , where f is the focal point of the optical device. In geometric optics, the paraxial approximation is an approximation used in ray tracing of light through an optical system (such as a lens). ...
A parabolic reflector (also known as a parabolic dish or a parabolic mirror) is a reflective device formed in the shape of a paraboloid of revolution. ...
Ray transfer matrix analysis (also known as ABCD matrix analysis) is a type of ray tracing technique used in the design of some optical systems, particularly lasers. ...
 Image File history File links Size of this preview: 800 × 557 pixelsFull resolution‎ (979 × 682 pixels, file size: 35 KB, MIME type: image/png) Derivation of the ray matrix of a spherical (concave) mirror. ...
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. Lower-case pi The mathematical constant Ï€ is a real number which may be defined as the ratio of a circles circumference (Greek πεÏιφÎÏεια, periphery) to its diameter in Euclidean geometry, and which is in common use in mathematics, physics, and engineering. ...
In mathematics and physics, the radian is a unit of angle measure. ...
As the degree of the taylor series rises, it approaches the correct function. ...
A lens can be considered a thin lens if d << f. ...
Mirror equation and magnification The mirror equation relates the object distance (do) and image distances (di) to the focal length (f). A mirror, reflecting a vase. ...
The magnification of a mirror is defined as the height of the image divided by the height of the object. Magnification is the process of enlarging something only in appearance, not physical size. ...
A mirror, reflecting a vase. ...
The negative sign in front of this fraction is used as a convention. Simply put, using the formula above, if the magnification is positive, the image is upright. If the magnification is negative, the image is inverted (upside down).
Consider a concave mirror, with a radius of curvature of 30.0 cm. A 10.0 cm tall object is placed 18.0 cm in front of the mirror. A ray drawn from the top of the object (10.0 cm above the principal axis) to the surface vertex (where the principal axis meets the mirror, or the center of the mirror) will form an angle with the principal axis. The ray will be reflected by the mirror below the principal axis at an angle equal to the angle of the incident ray. Remember the angle of incidence equals the angle of reflection. This article is about an authentication, authorization, and accounting protocol. ...
In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. ...
A mirror, reflecting a vase. ...
In optics, a ray is an idealized narrow beam of light. ...
In mathematics, particularly linear algebra and functional analysis, the spectral theorem is a collection of results about linear operators or about matrices. ...
The cardinal points and the associated cardinal planes are a set of special points and planes in an optical system, which help in the analysis of its paraxial properties. ...
In mathematics, particularly linear algebra and functional analysis, the spectral theorem is a collection of results about linear operators or about matrices. ...
This article is about angles in geometry. ...
This article is about angles in geometry. ...
A second ray can be drawn from the top of the object passing through the focal point and relecting off the mirror at a point somewhere below the principal axis. As a rule, any incident ray passing through the focal point will be reflected from the mirror as a ray parallel to the principal axis. The point at which these two reflected rays meet is the image point (the location of the image). Parallel may refer to: Parallel (geometry) Parallel (latitude), an imaginary east-west line circling a globe Parallelism (grammar), a balance of two or more similar words, phrases, or clauses Parallel (manga), a shÅnen manga by Toshihiko Kobayashi Parallel (video), a video album by R.E.M. The Parallel, an...
The height of the image hi and the height of the object ho are different in magnitude, but can be considered similar due to the two right triangles formed when drawing the two rays previously mentioned. As such, the distance to the object do and the distance to the image di are also similar. The magnitude of a mathematical object is its size: a property by which it can be larger or smaller than other objects of the same kind; in technical terms, an ordering of the class of objects to which it belongs. ...
This equation can be re-written as you refer to the drawing:
Divide both sides by do and rearrange to obtain the mirror equation:
External links |
Feeds |
Contact