Light and Reflection Curved Mirrors

Concave Spherical Mirrors Concave spherical mirror – an inwardly curved, spherical mirrored surface that is a portion of a sphere and that converges incoming light rays Radius of curvature (R) determines size of the image –Distance from the mirror’s surface to the center of curvature Produces a real image –An image formed when rays of light actually intersect at a single point Can be projected onto a surface - hologram

Concave Spherical Mirrors Image location can be predicted using the mirror equation 1/(object distance) + 1/(image distance) = 2/(radius of curvature) 1/p + 1/q = 2/R When 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 Mirrors Focal point (F) – the point where parallel light rays converge after being reflected off of a curved mirror Focal length (f) – the distance from the mirror to the focal point; one-half the radius of curvature 1/(object distance) + 1/(image distance) = 1/(focal length) 1/p + 1/q = 1/f

Concave Spherical Mirrors

Distances in front of the mirror are positive Distances behind the mirror are negative Heights are positive when above the principal axis and negative when below –Principal axis – an imaginary axis running through the center of curvature and focal point perpendicular to the mirror

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

Concave Spherical Mirrors If the image is in front of the mirror (a real image), the image is inverted and M is negative If the image is behind the mirror (a virtual image), the image is upright and M is positive Magnification = (image height)/(object height) = - (image distance)/(object distance) M= h’/h = -q/p

Concave Spherical Mirrors You can use ray diagrams for spherical mirrors –Draw them like a flat mirror, adding center of curvature and focal point Measure distances along the principal axis

Concave Spherical Mirrors Draw three rays to verify image location They should all intersect at the same point –First ray – parallel to principal axis and reflected through the focal point –Second ray – through focal point and reflected parallel to principal axis –Third ray – through center of curvature and reflected back along itself through center of curvature

Concave Spherical Mirrors

Convex Spherical Mirrors Convex spherical mirror – an outwardly curved, mirrored surface that is a portion of a sphere and that diverges incompletely light rays –Diverging mirror Focal point and center of curvature are behind the mirror Produces a virtual image To draw the ray diagram, extend the reflected rays behind the mirror –Otherwise just like concave mirrors Usually reduce image size and distance

Convex Spherical Mirrors

Parabolic Mirrors Spherical aberration – a blurred image produced by rays reflected near the edge of the mirror that do not pass through the focal point Parabolic mirror – highly curved mirrors –Small diameters –Eliminate spherical aberration –Similar to concave spherical mirror Used in flashlights, headlights, and reflecting telescopes

Parabolic Mirrors