Paraxial Analysis
An initial analysis of an optical design is often performed using the paraxial approximation, which is valid at the small angles of incidence common for rays propagating near the optical axis. Using the series expansion of the sine function given by:
sin Ø= Ø- Ø3/3! + Ø5/5! (Ø measured in radians), paraxial (first-order) theory retains only the first term.
In the following calculation, assume:
sin Ø = tan Ø = Ø and cos Ø =1.
Snell’s Law then can be written as:
n1Ø1 = n2Ø2
Focal Length
Rays that pass through either focal point are parallel to the optical axis on the other side of the lens. The focal length is related to the object and image locations by the “lens formula”:
1/f = 1/S +1/S' where S = object distance and
S' = image distance.
Magnification
The magnification, M, is defined as the ratio of the image height, y',
to the object height, y:
M = y'/y; also, M = S'/S
