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Light and ReflectionCurved Mirrors

Concave Spherical MirrorsConcave spherical mirror an inwardly curved, spherical mirrored surface that is a portion of a sphere and that converges incoming light raysRadius of curvature (R) determines size of the imageDistance from the mirrors surface to the center of curvatureProduces a real imageAn image formed when rays of light actually intersect at a single pointCan be projected onto a surface - hologram

Concave Spherical MirrorsImage location can be predicted using the mirror equation1/(object distance) + 1/(image distance) = 2/(radius of curvature)1/p + 1/q = 2/RWhen light rays originate from a large distance (p approaches infinity, so 1/p approaches 0), the light rays converge on a single point and the image forms halfway between the mirror and the radius of curvature

Concave Spherical MirrorsFocal point (F) the point where parallel light rays converge after being reflected off of a curved mirrorFocal length (f) the distance from the mirror to the focal point; one-half the radius of curvature1/(object distance) + 1/(image distance) = 1/(focal length)1/p + 1/q = 1/f

Concave Spherical Mirrors

Concave Spherical Mirrors

Concave Spherical MirrorsDistances in front of the mirror are positiveDistances behind the mirror are negativeHeights are positive when above the principal axis and negative when belowPrincipal axis an imaginary axis running through the center of curvature and focal point perpendicular to the mirror

Concave Spherical MirrorsMagnification (M) the measure of the size of the image with respect to the size of the original objectIf you know image location, image size can be determinedFor images smaller than the object, magnification is less than 1For images larger than the object, magnification is greater than 1Magnification has no unit

Concave Spherical MirrorsIf the image is in front of the mirror (a real image), the image is inverted and M is negativeIf the image is behind the mirror (a virtual image), the image is upright and M is positiveMagnification = (image height)/(object height) = -(image distance)/(object distance)M= h/h = -q/p

Concave Spherical MirrorsYou can use ray diagrams for spherical mirrorsDraw them like a flat mirror, adding center of curvature and focal pointMeasure distances along the principal axis

Concave Spherical MirrorsDraw three rays to verify image locationThey should all intersect at the same pointFirst ray parallel to principal axis and reflected through the focal pointSecond ray through focal point and reflected parallel to principal axisThird ray through center of curvature and reflected back along itself through center of curvature

Concave Spherical Mirrors

Convex Spherical MirrorsConvex spherical mirror an outwardly curved, mirrored surface that is a portion of a sphere and that diverges incompletely light raysDiverging mirrorFocal point and center of curvature are behind the mirrorProduces a virtual imageTo draw the ray diagram, extend the reflected rays behind the mirrorOtherwise just like concave mirrorsUsually reduce image size and distance

Convex Spherical Mirrors

Convex Spherical Mirrors

Parabolic MirrorsSpherical aberration a blurred image produced by rays reflected near the edge of the mirror that do not pass through the focal pointParabolic mirror highly curved mirrorsSmall diametersEliminate spherical aberrationSimilar to concave spherical mirrorUsed in flashlights, headlights, and reflecting telescopes

Parabolic Mirrors

Parabolic Mirrors