Calculating the deflection of an arbitrary beam of light from a thin lens

Question

Suppose we have a lens with known focal length and are using the thin lens approximation. Is it possible to determine how an arbitrary beam of light will be deflected by it? Or, is it the case that there are multiple kinds of thin lenses, and so more information is required. I'm asking this question just so I can solve first year university optics problems.

Answer 1

The subject you are looking for is called "the ABCD matrix method," "Matrix Paraxial Optics," "Matrix Ray Tracing," or some variation of that.

A thin lens is represented by a 2x2 matrix and the incident ray is a 2 element vector. Computing the height and angle of the outbound ray is a simple matrix multiplication.

Answer 2

Okay, I've got an idea. I would have liked to draw a diagram, but my graphics software is playing up at the moment. First find where the light ray, R, crosses the axis of symmetry of the lens - call this X. Using the paraxial ray approximation: 1\s+1\s'=1/f where s is the object distance, s' the image distance and f is the focal length. Note that s, s' are signed variables. Anyway, find where the image, I, of point X is by using the formula. All light rays from X passing through the lens arrive at I, so we now have the coordinates of two points the light ray must pass through after the lens and hence the angle.