Lenses and Waves

TS = 7 BG, where BG is the thickness
6
of the lens. 68 When the lens is reversed
and rays are incident on the plane
side, the aberration becomes
TS = 9
2 BG.69 The aberration is
therefore considerably smaller –
almost four times – when the convex
side faces the incident rays. This time
Huygens went further than the mere
observation that the orientation of a
lens affects the amount of aberration.
The faces of a lens are surfaces with
different radii – infinite in the case of
a plane face. The proportion between
these radii apparently determines how
large the aberration is. Consequently,
an ideal lens can be found by
determining the optimal proportion
of both radii.
To do so, Huygens derived an
expression for the aberration of a
parallel ray HC incident on the
extreme end of a lens IMCB (Figure
27). AB = a and NM = n are the radii
of the anterior and posterior side and
BG = b is the thickness of the anterior
half of the lens. The thickness of the
entire lens BM = q can be expressed as
q =
ba
b . The anterior face refracts
n
an extreme ray HC towards P, a little
off its focus R. The posterior face, in
its turn, refracts the extension CF of
ray CP towards D, a little off the focus
E of the lens. Huygens then expressed
the spherical aberration DE of the
extreme ray in terms of the radii of
the faces and the thickness of half the
2 2
7nq6anq27aq lens: DE = 2 “…
6(
an) 68 OC13, 357.
69 OC13, 359.
1655-1672 - DE ABERRATIONE 69
Figure 27 Aberration of a bi-convex lens