Appendix: A program to calculate the matrix of an optical system.
The program "matopt" calculates the matrix connecting the vertices of an optical system and finds the principal points, focal points, and focal lengths. To run the program, first click on the entry field and hit Enter (carriage return), then enter the requested data (the first item is the refractive index of the incident medium). A thin lens is entered as a single element, but if the surrounding medium changes, the lens must be followed by a plane interface with the new index to its right. To break out of the input loop, enter"q". The program plots the locations of the cardinal points and draws a ray diagram (if the system is not telescopic) for an upright object located at H(-). The image at H'(-) is equal to the object in size but is inverted. Try the program for two thin lenses in air with f1=15, f2=10, and separation 12 (you need 3 matrices). The program can be used to solve any of the exercises or examples in the text.