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
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
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