**Deviation of a Ray by a Thin Lens**

A ray incident on a lens at angle, u, relative to the lens axis, is deflected by the lens through an angle, δ, and exits the lens at angle, u’ relative to the axis:

The incident ray angle, u, and deflection angle, δ, are positive in the illustration above while the exiting ray angle u’ is negative.

The deviation angle, δ, is directly proportional to the height of the ray on the lens, y, and inversely proportional to the focal length, f:

The height of the ray, y’, on the next lens located at distance, t, from the first lens is given by

where y is the height of the ray on the first lens, and u is the angle of the ray between the first lens and the next lens. The value for u would be the value of u’ after refraction by the first lens.

An example of thin-lens ray tracing for a telescope using a spreadsheet can be accessed and used by the reader at “thin lens ray trace“.

Thanks!