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Paraxial Optics and Calculations 47
Figure 3.7 The location of the focal points and principal
points for several shapes of converging and diverging
elements.
two effective focal lengths and the back focal length can be calculated
from
n (n n ) (n n ) (n n ) (n n ) t
n 1 3 2 1 2 3 2 3 2 1
(3.23)
f f′ R R n R R
1 2 2 1 2
f ′t (n n )
2
1
bf l f′ (3.24)
n R
2 1
Note that if n 1 and n 3 are equal to 1.0 (i.e., the index of air), these
expressions reduce to Eqs. 3.21 and 3.22.
3.5 The “Thin Lens”
If the thickness of a lens element is small enough so that its effect on
the accuracy of the calculation may be neglected, the element is called
a thin lens. The “thin lens” concept is an extremely useful one for the
purposes of quick preliminary calculations and analysis and as a
design tool.
