Improvements in Achromatic Dispersing Lenses.
Year: 1893

page_text: Date of Application, 19th May, 1893-Accepted, 9th Sept., 1893
Improvements in Achromatic Dispersing Lenses.
We PAUL RUDOLPH Doctor of Philosophy residing at Carl-Zeiss Strasse, Jena,
in the Grand-duchy of Saxe-Weimar German Empire and CARL ZEISS of the
same place Optician do hereby declare the nature of this invention and in what
manner the same is to be performed to be particularly described and ascertained
in and by the following statement :-
In optical systems (such for instance as the Galilean telescope and the so-called
tele-objective which has of late been used for photographic purposes) which contain
besides the achromatic objective and distinct therefrom, an achromatic dispersing
lens of a shorter focal distance than the objective, the dispersing lens has hitherto
always been achromatised in the same way as an objective consisting of single
lenses cemented to each other is achromatised in order to correct the spherical
aberration at the same time with the dispersion of colours. Analogously the main
lens (which in this case is negative) of dispersing lenses of this kind, has been
made of crown-glass of low refractive power and the correcting lens to be cemented
to it (which in this case is positive) has been made of flint-glass of considerably
greater refractive power. This difference or graduation of the refractive power
is actually as necessary and indispensable in a dispersing lens as it is in a collecting
lens, if the dispersing lens is to be not only chromatically but also spherically
corrected and consists at the same time of single lenses cemented to each other; for
it is only through the surplus or excess of refractive power of the positive
constituent or element over that of the negative constituent or element that the
inner surfaces of a dispersing lens obtain a spherical aberration contrary to and
compensating for that of the outer surfaces.
In combinations of lenses of the class described it is not advisable however as we
have found by theoretical and practical experience for obtaining a good total effect
of the combination as a whole to correct the dispersing lens by itself or separately
with regard to spherical aberration as has heretofore been done either intentionally
or otherwise.
:
If as is the case with the aforesaid combinations of lenses the focal distance of
the dispersing lens be considerably smaller than that of the objective belonging to
it and if the distance of the said dispersing lens from the objective be at least
equal to its focal distance its spherical aberration can always be easily neutralised
or prevented from injuring the total effect by intentionally leaving a small amount
of uncorrected spherical aberration on the part of the objective. In the usual
arrangement for correcting these systems the surplus of the refractive power of the
positive element of the dispersing lens invariably involves an objectionable increase
in the degree of curvature of its outer surfaces which is necessary in order to
obtain a given focal distance. Moreover this surplus of refractive power causes at
the cemented inner surfaces of the lens: (which have a comparatively great degree
of curvature) effects of aberration which render it difficult to obtain an accurate
adjustment of the total effect of the combination especially outside the axis.
These considerations have led the inventor to the discovery of means for effecting
the achromatization of such optical systems by an arrangement different from or
contrary to that heretofore employed namely an arrangement in which no
compensation or great reduction of the spherical aberration is connected with the
achromatization of the dispersing lens but this leus although perfectly achromatized
retains as regards spherical aberration the character of a simple uncorrected
dispersing lens.

page_text: This result is obtained by forming the positive part of the cemented system of
flint-glass having a refractive power equal to or only slightly greater or less than
the refractive power of the negative part but having a relative dispersion of
colours presenting a sufficient surplus over that of the negative part to admit of the
achromatization whilst retaining convenient degrees of curvature of the surfaces of
the two parts.
The chief advantages accruing from the employment of achromatic dispersing
lenses of this novel description in the optical combinations or systems hereinbefore
referred to are as follows viz. :-(1) for any required focal distance a considerably
smaller degree of curvature of the outer lens surfaces is obtained than is required
with the arrangement heretofore employed and this degree of curvature is enabled
to be even further reduced in case of need (2) the positive spherical aberration
(being of the same nature as that of a single convex lens) which takes place at the
inner cemented surfaces of the lens can be reduced or transformed into a negative
spherical aberration (which is of the same nature as that of a single dispersing
lens).
The first named advantage is made evident by the following comparison.
In all achromatic dispersing lenses heretofore employed the refractive index n D
of the crown glass is between 151 and 152 the refractive index of the flint-
glass n' D is between 1.60 and 1.63. The surplus (n¹-n) in the refractive index
of the positive element over that of the negative element is consequently between
0.08 and 0.12. Under these circumstances complete achromatization-if the most
favourable kinds of glass as regards dispersion of colours are selected-requires a
total degree of curvature K of the outer surfaces of the lens (K = algebraic sum
of the reciprocals of the radii of curvature of both surfaces) at least equal to 2.4
But if the aforesaid surplus or difference n' n is reduced to a smaller amount
say 0.03 for example at the same time retaining as great a difference as possible in
the relative dispersion of the two parts (from which follows indirectly that the
cemented lens, in the practically applicable forms retains a spherical aberration of
the same nature as that of a concave lens) complete achromatism can be obtained
with the following kinds of glass viz::-
Crown n D
=
1-574; n F-
-
nC=0.01005.
Flint D= 1.603; n¹ F
outer surfaces
-y
n¹ C = 0.01576 with a degree of curvature of the
again if n¹n be taken, (for which the kinds of glass available leave ample
margin without the complete achromatization of the lenses being affected) the
proportion of K
.
1
F
may be reduced as may be required so that the external form
of the dispersing lens may be brought near to the plano-plate or to the watch-
glass shape without the radii of curvature of the inner surfaces (if a triple cemented
lens is admissible) becoming excessively small in comparison to the focal distance.

page_text: while the radius of the inner cemented surfaces of a symmetrical triple lens of
these kinds of glass with the flint-glass situated inside is
r = 0·094 f.
As regards the second advantage mentioned namely the reduction of the
spherical aberration at the inner cemented surfaces of the dispersing lenses or the
transformation or conversion of the character of this aberration, it is evident that
in the same degree as the indices of refraction n' and approach conformity the
effect of refraction of the inner cemented surface or surfaces, and in connection
therewith the spherical aberration ceases more and more that is to say, greater
degrees of curvature of these surfaces can be selected without causing irregularities
in the correction. If n¹ = n be taken the cemented achromatic dispersing lens
considered apart from the achromatism acts as a simple dispersing-lens. Of special
practical importance however is the power of employing (in dispersing-lenses of the
kind in question) a positive element (flint glass) whose refractive index is smaller
than the refractive index of the negative element (crown glass) and thereby
obtaining in addition to the aforesaid great reduction of the degree of the outer
curvature, a conversion of the character of the spherical aberration of the inner
surfaces being a different effect to that obtained with the constructions heretofore
employed for achromatic dispersing lenses. This conversion is extremely
advantageous in the lens-combinations now under consideration (Galilean
telescopes tele-objectives and the like) for obtaining correcting effects outside
the axis through the dispersing lens which cannot be obtained with the ordinary
composition of the latter.
According to the special requirements of the purpose for which it is to be
employed the new dispersing lens is composed of two or three single lenses cemented
together the said lenses being composed of two, or in some cases three, different
kinds of glass and may be constructed either as a symmetrical or as an
unsymmetrical lens.
The selection of the several separate elements of the combination must (if the best
effect possible is to be obtained) be governed by the construction of the objective
with which they are to be combined taking especially into consideration its
aperture and its spherical correction.
In order to more clearly explain the practical effects of the invention we will
now proceed to describe by way of example several types of lenses suitable for
different constructions of objectives and for various purposes of application the said
lenses being represented in section in Figures 1 to 6 of the annexed drawing. The
signs or letters of reference in the formulæ hereinafter given correspond with those
marked on the figures, and the kinds of glass are determined by the indices of
refraction n D n C and n F for the Fraunhofer lines D. C and F.
All the figures given refer to an undetermined focal length which is regarded as
the unit of length. The radii thickness and diameter which are required for a lens
of a given or determined focal length f are then obtained in inches or millimetres
by multiplying the figures given in the formula by the number ƒ expressed in
incheses or millimetres.
(1) Unsymmetrical double achromatic dispersing lens for Galilean telescopes
with achromatic objectives of ordinary construction represented by Figure 1 for
the focal distance of 50 mm. The part L, is composed of flint glass and the
part L, of crown glass.

page_text: The following formulæ correspond with a focal distance of 1.0 referred to a focal
distance of + 1 of the objective lens this factor
formulæ.
10, being omitted from the
2. Symmetrical triple achromatic dispersing lenses for Galilean telescopes with
objectives of relatively large aperture. Focal distance of 10:
-
(a) Flint glass L, Figure 2 between two crown glass lenses L, and L, for the
focal distance of 50 mm.

page_text: 3. Double negative lenses of various focal distances for a photographic
combination and which may be employed with any photographic objective but
are especially adapted for use with an achromatic objective of three cemented
lenses of which the elements of construction are for the focal distance of 1-0 : as
calculated for the focal length of the positive lens employed.
Radii.
1=&
1201128
130-2655
Crown: L₁
Flint L
n D
= 1-57420
= 1.60310
Thickness of Lenses.
di
= 0.022
dz = 0.044
Kinds of Glass.
Diameter of Lenses.
0.20
n C
1.57124
n F
1.58129
1-59858
1.61434
Degree of the Unter Curvature.
I
K
= 1.9 × 1/
x
6) Dispersing lens of a focal distance
=
1/3, and composed of one crown
30 glass L and one flint glass L₁ represented in Figure 5 for the focal distance of
50mm.

page_text: c) Dispersing lens of a focal distance
=
-
1/4 composed of one crown glass L₁
and one fint glass L, as represented in Figure 6 for the focal distance of 37.5 mm.
711
Having now particularly described and ascertained the nature of our inven-
tion and in what manner the same is to be performed we declare that what we
claim is.―
In cemented achromatic dispersing lenses employed in combination with a
collecting lens of longer focal distance than the dispersing lens obtaining the
achromatization by constructing the said dispersing lens with a positive constituent
having a refractive power equal to or but slightly greater or less than the
refractive power of the negative constituent substantially as hereinbefore described.
Dated this 18th day of May 1893.
J. H. JOHNSON & Co.,
47, Lincoln's Inn Fields, Agents.