Melles Griot Optics Guide - Sign Conventions

Imaging Properties of a Lens System

Sign Conventions

The validity of the paraxial formulae is dependent on adherence to the following sign conventions
For lenses: (see figure below) s is positive for object to left of H (the first principal point) s is negative for object to right of H s" is positive for image to right of H" (the second principal point) s" is negative for image to left of H" m is positive for an inverted image m is negative for an upright image	For Mirrors: f is positive for convex (diverging) mirrors f is negative for concave (converging) mirrors s is positive for object to left of H s is negative for object to right of H s" is positive for image to right of H" s" is positive for image to right of H" m is positive for an inverted image m is negative for an upright image
When using the thin-lens approximation, simply refer to the left and right of the lens

Note location of object and image relative to front and rear focal points
f q h h" m	= = = = =	lens diameter arcsin (f/2s) object height image height s"/s = h"/h = magnification or conjugate ratio, said to be infinite if either s" or s is infinite	s	=	object distance, positive for object (whether real or virtual) to the left of principal point H
			s"	=	image distance (s and s" are collectively called conjugate distances, with object and image in conjugate planes), positive for image (whether real or virtual) to the right of the principal point H"
			f	=	effective focal length (EFL), which may be positive (as shown) or negative. f represents both FH and H"F", assuming lens to be surrounded by medium of index 1.0

Previous Next