Spark image

Waves and curved surfaces

Lenses change the curvature of the waves that fall on them.

Curvature of waves leaving the lens = curvature of waves hitting the lens + curvature added by the lens

Waves with no curvature have been converged to a point a distance f (the focal length) from the lens. This means that they have been given a curvature 1/f. The shape of the incident waves have no effect on how much the lens changes their curvature and so we can say that a lens increases the curvature of waves that pass through it by a constant amount 1/f. (Remember that 1/f will be positive for a convex lens and negative for a concave lens)

Lens equation

The curvature of the waves spreading outwards towards a lens from an object distance u from the lens have a curvature 1/u and those converging to a point image distance v on the other side of the lens have a curvature 1/v. The lens adds a constant curvature (1/f) to the wave.

Lens equation:    1/v = 1/u + 1/f
© Keith Gibbs 2011