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<p>Expressions are derived for the deflection and transverse translation of a ray as it traverses an arbitrary optical system.  The system may be astigmatic and have relatively decentred refracting elements.  The expressions are in terms of the fundamental properties of the system.  Because nodal rays are rays that undergo no deflection the results lead immediately to expressions that define nodal rays through the system.  An optical axis of an optical system is a nodal ray that is a straight line through the system.  This allows one to write an expression that determines the optical axis of an arbitrary optical  system.</p

Deflection and translation of a ray traversing an optical system, nodal rays and the optical axis