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The Translation matrix
A lot of the optical systems instruments have two or even more lenses. From the last section, we used graphical method to find out the transfer point. Here we are using calculation method to calculate where the transfer point. This calculation method is called linear approximation. The top figure is the transfer matrix for a thin lens. The varaible n is the index of refraction, r is the radii of the lens surface and d is the distance between the two lens surface but in thin lens system d=0.
The bottom figure is for a two thin lens system which is the system of compound microscope. We assume the variable f1 is the focal length of the objective lens and f2 is the focal length of the eyepiece and d is the distance between the two lens.