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Paraxial Formulas<br />

SIGN CONVENTIONS<br />

The validity of the paraxial lens formulas is dependent on adherence to the following sign conventions:<br />

For lenses: (refer to figure 1.1)<br />

s is 1 for object to left of H<br />

(the first principal point)<br />

s is 5 for object to right of H<br />

s″ is 1 for image to right of H″<br />

(the second principal point)<br />

s″ is 5 for image to left of H″<br />

m is 1 for an inverted image<br />

m is 5 for an upright image<br />

For mirrors:<br />

When using the thin-lens approximation, simply refer to the left and right of the lens.<br />

Figure 1.1<br />

h<br />

front focal point<br />

f object v<br />

H H″<br />

F<br />

s<br />

f<br />

principal points<br />

f<br />

f is 1 for convex (diverging) mirrors<br />

f is 5 for concave (converging) mirrors<br />

s is 1 for object to left of H<br />

s is 5 for object to right of H<br />

s″ is 5 for image to right of H″<br />

s″ is 1 for image to left of H″<br />

m is 1 for an inverted image<br />

m is 5 for an upright image<br />

rear focal point<br />

Note location of object and image relative to front and rear focal points.<br />

f = lens diameter<br />

m =<br />

s″/s = h″/h = magnification or<br />

conjugate ratio, said to be infinite if<br />

either s″ or s is infinite<br />

v = arcsin (f/2s)<br />

h = object height<br />

h″ = image height<br />

Sign conventions<br />

F″<br />

s″<br />

image<br />

s = object distance, positive for object (whether real<br />

or virtual) to the left of principal point H<br />

s″ = image distance (s and s″ are collectively called<br />

conjugate distances, with object and image in<br />

conjugate planes), positive for image (whether real<br />

or virtual) to the right of the principal point H″<br />

f = effective focal length (EFL) which may be positive<br />

(as shown) or negative. f represents both FH and<br />

H″F″, assuming lens to be surrounded by medium<br />

of index 1.0<br />

h″<br />

Fundamental Optics Gaussian Beam Optics <strong>Optical</strong> Specifications Material Properties <strong>Optical</strong> <strong>Coatings</strong><br />

Visit Us Online! www.mellesgriot.com 1 1.3

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