Curved Mirrors

Curved MirrorsTerminology

center of curvature - C; the center of the original sphere

radius of curvature - r;distance from center of curvature to the mirror

vertex - V; the center of the mirror

principal axis - a line through C and V

principal focus - F; the point on the principal axis where light rays parallel and close to the principal axis

converge; or from where they appear to diverge

focal length - f; distance from V to F

Ray DiagramsConcave(Converging) Mirrors

C F

1. rays parallel to the principal axis reflect through the focus2. rays passing through the focus reflect parallel to the principal axis

Convex (Diverging) Mirrors1. rays parallel and close to the principal axis reflect away from the focus2. rays heading toward the principal focus reflect parallel to the principal axis

F C

Click here to view these three rays that are important in the formation of images in concave (converging) and convex (diverging) mirrors.

Also view reflectionfrom curved mirrorshere, here,and here.

Diverging rays must be extended as dotted linesbehind the mirror in order to locate some images.

Mirror Equation

1/f = 1/do + 1/di

Magnification

di/do = hi/ho

f = focal length; positive for converging mirrors, negative for diverging mirrors

do = object distance; usually positivedi = image distance; can be positive or negative

ho = object heighthi = image height

Images formed by concave (converging) mirrors may be:

1. real, virtual, or non-existent2. upright or inverted

3. reduced, enlarged, or same size4. in front or behind the mirror

The image properties depend on theobject’s location with respect to themirror, focus, and center of curvature.

Learn more about concave mirror images here.

Learn more about characteristicsof convex mirror images here.

Images formed by convex (diverging) mirrors are always:

1. virtual2. upright3. reduced4. located behind the mirror between the vertex and focus

General Image Trends• •

Real Images Inverted Front of mirror positive image

distance

• Virtual images • always upright behind the

mirror• negative image

distance