Mirrors and Ray Diagrams

From the top of the object draw at least two rays. A ray parallel to the principal axis reflects through the focus F. A ray through F reflects parallel to the axis. A ray through the centre of curvature C reflects back along itself, and a ray hitting the pole reflects at an equal angle. Where the reflected rays meet (or appear to meet) is the top of the image.

1/v + 1/u = 1/f, where u is the object distance, v the image distance and f the focal length, all measured from the pole using the New Cartesian sign convention. Magnification m = −v/u = image height ÷ object height.

A concave mirror curves inward and converges light; it can form real or virtual images and is used in torches, shaving mirrors and solar furnaces. A convex mirror curves outward and diverges light; it always forms virtual, upright, diminished images and is used as rear-view mirrors and on blind corners.

Beyond C: real, inverted, diminished, between F and C. At C: real, inverted, same size, at C. Between C and F: real, inverted, magnified, beyond C. At F: image at infinity. Between F and the mirror: virtual, upright, magnified, behind the mirror.

For a spherical mirror the focal length is half the radius of curvature: f = R/2. The focus lies halfway between the pole and the centre of curvature.

In the New Cartesian sign convention, all distances are measured from the pole. Distances in the direction of the incoming light (behind the mirror) are positive and against it (in front) are negative. Heights above the principal axis are positive. So a concave mirror has a negative focal length and a convex mirror a positive one.