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288:(not inverted). As the object gets closer to the mirror, the image gets larger, until approximately the size of the object, when it touches the mirror. As the object moves away, the image diminishes in size and gets gradually closer to the focus, until it is reduced to a point in the focus when the object is at an infinite distance. These features make convex mirrors very useful: since everything appears smaller in the mirror, they cover a wider
1760:
412:
88:
232:(French for "sorcerer's eye") were a popular luxury item from the 15th century onwards, shown in many depictions of interiors from that time. With 15th century technology, it was easier to make a regular curved mirror (from blown glass) than a perfectly flat one. They were also known as "bankers' eyes" due to the fact that their wide field of vision was useful for security. Famous examples in art include the
261:
1730:
1393:
image location. The mirror equation and magnification equation can be derived geometrically by considering these two rays. A ray that goes from the top of the object through the focal point can be considered instead. Such a ray reflects parallel to the optical axis and also passes through the image point corresponding to the top of the object.
1791:
1392:
to the optical axis. This ray is reflected by the mirror and passes through its focal point. The point at which these two rays meet is the image point corresponding to the top of the object. Its distance from the optical axis defines the height of the image, and its location along the axis is the
431:, has a reflecting surface that is recessed inward (away from the incident light). Concave mirrors reflect light inward to one focal point. They are used to focus light. Unlike convex mirrors, concave mirrors show different image types depending on the distance between the object and the mirror.
1494:
1677:
171:", 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.
123:) are both imaginary points "inside" the mirror, that cannot be reached. As a result, images formed by these mirrors cannot be projected on a screen, since the image is inside the mirror. The image is smaller than the object, but gets larger as the object approaches the mirror.
1349:
202:. They are usually mounted on a wall or ceiling where hallways intersect each other, or where they make sharp turns. They are useful for people to look at any obstruction they will face on the next hallway or after the next turn. They are also used on
998:
78:
are used for entertainment. They have convex and concave regions that produce deliberately distorted images. They also provide highly magnified or highly diminished (smaller) images when the object is placed at certain distances.
1619:
1566:
107:
is a curved mirror in which the reflective surface bulges towards the light source. Convex mirrors reflect light outwards, therefore they are not used to focus light. Such mirrors always form a
1143:, then the result is always a negative number, meaning that the image distance is negative—the image is virtual, located "behind" the mirror. This is consistent with the behavior described
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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
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toward a focus. This is because the light is reflected at different angles at different spots on the mirror as the normal to the mirror surface differs at each spot.
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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
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By convention, if the resulting magnification is positive, the image is upright. If the magnification is negative, the image is inverted (upside down).
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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
823:—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
1775:
618:, and the image can be either real or virtual and either upright or inverted depending on whether S approaches F from its left or right side.
168:
1150:
For concave mirrors, whether the image is virtual or real depends on how large the object distance is compared to the focal length. If the
1252:
is positive and the image is real. Otherwise, the term is negative and the image is virtual. Again, this validates the behavior described
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are positive when the object and image are in front of the mirror, respectively. (They are positive when the object or image is real.)
1819:
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The mirrors are called "converging mirrors" because they tend to collect light that falls on them, refocusing parallel incoming
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can do a better job. Such a mirror can focus incoming parallel rays to a much smaller spot than a spherical mirror can. A
1785:
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1724:
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1344:{\displaystyle m\equiv {\frac {h_{\mathrm {i} }}{h_{\mathrm {o} }}}=-{\frac {d_{\mathrm {i} }}{d_{\mathrm {o} }}}}
483:
454:
applications, concave mirrors are used to gather light from a small source and direct it outward in a beam as in
17:
296:, so useful for looking at cars behind a driver's car on a road, watching a wider area for surveillance, etc.
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is a form of parabolic reflector which has a different focal distance depending on the angle of the mirror.
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with the optical axis. The reflected ray has the same angle to the axis, but on the opposite side (See
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to provide safety for road users where there is a lack of visibility, especially at curves and turns.
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used here is that the focal length is positive for concave mirrors and negative for convex ones, and
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In the limit where S approaches infinity, the image size approaches zero as the image approaches F
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450:. They are also used to provide a magnified image of the face for applying make-up or shaving. In
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130:(parallel) beam of light diverges (spreads out) after reflection from a convex mirror, since the
58:, but other shapes are sometimes used in optical devices. The most common non-spherical type are
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is typically a convex mirror. In some countries, these are labeled with the safety warning "
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haven't actually passed through the image; their extensions do, like in a regular mirror),
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63:
993:{\displaystyle {\frac {1}{d_{\mathrm {o} }}}+{\frac {1}{d_{\mathrm {i} }}}={\frac {1}{f}}}
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150:
8:
1412:
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1382:
1153:
848:
mirror equation, also known as the mirror and lens equation, relates the object distance
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59:
225:. Convex mirrors make everything seem smaller but cover a larger area of surveillance.
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of a mirror is defined as the height of the image divided by the height of the object:
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up to order 1. The derivations of the ray matrices of a convex spherical mirror and a
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54:(recessed inward). Most curved mirrors have surfaces that are shaped like part of a
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that need to image distant objects, since spherical mirror systems, like spherical
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Reflections in a convex mirror. The photographer is seen reflected at top right
1595:- a method of solar power generation using curved mirrors or arrays of mirrors
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Effect on image of object's position relative to mirror focal point (concave)
466:, or to collect light from a large area and focus it into a small spot, as in
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Effect on image of object's position relative to mirror focal point (convex)
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Venice
Botteghe: Antiques, Bijouterie, Coffee, Cakes, Carpet, Glass
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Reflected rays are parallel and never meet, so no image is formed.
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with a curved reflecting surface. The surface may be either
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Lorne
Campbell, National Gallery Catalogues (new series):
1507:
feature summing the angles of a triangle and comparing to
164:
482:
use a concave surface to provide a magnified image. The
182:(commonly known as "hallway safety mirrors"), including
1508:
1809:
Java applets to explore ray tracing for curved mirrors
1624:. New Delhi: Tata McGraw-Hill Education. p. 6.4.
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A second ray can be drawn from the top of the object,
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1561:{\displaystyle \arccos \left(-{\frac {r}{R}}\right)}
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term to the right side of the equation to solve for
614:
where S approaches F, the image distance approaches
792:As the distance of the object increases, the image
134:to the surface differs at each spot on the mirror.
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1816:, Molecular Expressions Optical Microscopy Primer
1419:of a concave spherical mirror is shown here. The
146:Convex mirror lets motorists see around a corner.
1836:
1654:(2nd ed.). Addison Wesley. pp. 160–1.
840:Mirror equation, magnification, and focal length
667:(Object between focus and centre of curvature)
1694:The Fifteenth Century Netherlandish Paintings
1407:The mathematical treatment is done under the
169:Objects in mirror are closer than they appear
1617:
415:A concave mirror diagram showing the focus,
419:, centre of curvature, principal axis, etc.
95:, centre of curvature, principal axis, etc.
91:A convex mirror diagram showing the focus,
1777:Light and Optics: Principles and Practices
1645:
1643:
1641:
1489:is the focal point of the optical device.
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137:
1618:Nayak, Sanjay K.; Bhuvana, K.P. (2012).
1599:List of telescope parts and construction
1397:Ray transfer matrix of spherical mirrors
551:(Object between focal point and mirror)
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259:
149:
141:
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29:
1638:
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272:The image on a convex mirror is always
27:Mirror with a curved reflecting surface
14:
1837:
255:
1826:"Grinding the World's Largest Mirror"
1649:
1069:For convex mirrors, if one moves the
374:{\displaystyle S>F,\ S=F,\ S<F}
174:These mirrors are often found in the
1584:(reflection from a spherical mirror)
1253:
778:(Object beyond centre of curvature)
1144:
735:Image formed at centre of curvature
470:. Concave mirrors are used to form
154:Detail of the convex mirror in the
62:, found in optical devices such as
24:
1333:
1321:
1299:
1287:
1245:{\displaystyle 1/d_{\mathrm {i} }}
1236:
1208:{\displaystyle 1/d_{\mathrm {o} }}
1199:
1136:{\displaystyle 1/d_{\mathrm {i} }}
1127:
1099:{\displaystyle 1/d_{\mathrm {o} }}
1090:
1050:
1021:
969:
947:
890:
861:
406:
25:
1856:
1802:
1712:
82:
1794:from the original on 2018-01-18.
1763:from the original on 2018-01-18.
1733:from the original on 2018-01-18.
1492:
1059:{\displaystyle d_{\mathrm {i} }}
1030:{\displaystyle d_{\mathrm {o} }}
899:{\displaystyle d_{\mathrm {i} }}
870:{\displaystyle d_{\mathrm {o} }}
804:
740:
721:(Object at centre of curvature)
683:
623:
567:
396:
217:Convex mirrors are used in some
1774:Al-Azzawi, Abdul (2006-12-26).
1746:Sura's Year Book 2006 (English)
1650:Hecht, Eugene (1987). "5.4.3".
1462:{\displaystyle -{\frac {1}{f}}}
1377:meets the mirror) will form an
814:
163:The passenger-side mirror on a
119:) and the centre of curvature (
1767:
1737:
1706:
1696:, pp. 178-179, 188-189, 1998,
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1668:
1611:
1358:
13:
1:
1814:Concave mirrors — real images
1604:
1403:Ray transfer matrix analysis
789:Reduced (diminished/smaller)
659:{\displaystyle F<S<2F}
490:also uses a concave mirror.
446:Concave mirrors are used in
391:Reduced (diminished/smaller)
228:Round convex mirrors called
7:
1575:
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503:
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10:
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796:approaches the focal point
1716:Living Science Physics 10
1439:element of the matrix is
474:, which are important in
242:and the left wing of the
219:automated teller machines
1593:Concentrated solar power
1178:term is larger than the
602:(Object at focal point)
468:concentrated solar power
770:{\displaystyle S>2F}
442:Uses of concave mirrors
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1409:paraxial approximation
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543:{\displaystyle S<F}
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138:Uses of convex mirrors
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1401:Further information:
1365:Ray tracing (physics)
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786:Inverted (vertically)
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729:Inverted (vertically)
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675:Inverted (vertically)
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448:reflecting telescopes
414:
376:
264:A virtual image in a
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64:reflecting telescopes
50:(bulging outward) or
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1822:, online physics lab
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713:{\displaystyle S=2F}
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494:Concave mirror image
329:
72:spherical aberration
60:parabolic reflectors
1621:Engineering Physics
1413:parabolic reflector
1383:Specular reflection
1171:{\displaystyle 1/f}
877:and image distance
825:parabolic reflector
594:{\displaystyle S=F}
504:Object's position (
500:
305:Object's position (
301:
256:Convex mirror image
200:apartment buildings
1680:2017-03-06 at the
1572:are very similar.
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562:Magnified (larger)
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484:mirror landing aid
476:laser construction
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235:Arnolfini Portrait
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157:Arnolfini Portrait
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76:Distorting mirrors
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1820:Spherical mirrors
1713:Joshi, Dhiren M.
1582:Alhazen's problem
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1482:{\displaystyle f}
1457:
1432:{\displaystyle C}
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919:{\displaystyle f}
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488:aircraft carriers
486:system of modern
429:converging mirror
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223:computer monitors
16:(Redirected from
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266:Christmas bauble
230:Oeil de Sorcière
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1719:. Ratna Sagar.
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1803:External links
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1749:. Sura Books.
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178:of various
113:focal point
1605:References
1518:shows the
1417:ray matrix
783:Real image
726:Real image
672:Real image
464:spotlights
282:diminished
128:collimated
1570:thin lens
1541:−
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1277:≡
732:Same size
460:headlamps
208:driveways
184:hospitals
180:buildings
1839:Category
1792:Archived
1761:Archived
1731:Archived
1678:Archived
1576:See also
1469:, where
1390:parallel
846:Gaussian
835:Analysis
616:infinity
520:Diagram
321:Diagram
176:hallways
1845:Mirrors
1512:radians
610:In the
559:Upright
556:Virtual
478:. Some
456:torches
388:Upright
385:Virtual
286:upright
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192:schools
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198:, and
196:stores
188:hotels
132:normal
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44:mirror
1379:angle
1254:above
1145:above
612:limit
427:, or
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