Improvements in Lenses.
Year: 1896

page_text: PROVISIONAL SPECIFICATION.
Improvements in Lenses.
I, PAUL RUDOLPH, Doctor of Philosophy, residing at Jena in the Grand-
Duchy of Saxe-Weimar, German Empire, do hereby declare the nature of said
invention to be as follows:-
The object of this invention is to facilitate the chromatic and spherical
correction of lens systems (object glasses) which are to be composed of single
lenses cemented together.
In all object glasses consisting of two lenses both chromatic and spherical
aberration may be simultaneously corrected by making the negative constituent
of the double lens of fint glass possessing not only a greater dispersive power but
also a higher refractive index than the crown glass of which the positive
constituent is formed, so that the inner or cemented surface of the compound
lens produces a negative spherical aberration, which by suitably selecting the
curvatures is made equal to the positive spherical aberration of the two outer
surfaces of the compound lens so as to compensate for the last mentioned
aberration.
In the case of achromatic lenses which--like the object glasses of ordinary
telescopes-are only used with a relative aperture of 1 to 1, a degree of
spherico-chromatic correction, sufficient to meet most requirements of practice,
may by the above method be secured with any pair of flint and crown glass,
where the refractive index of the flint does not too closely approach that of the
crown.
For considerably larger relative apertures, however, the correction of such
lenses is somewhat seriously interfered with by the circumstance that, amongst
the available kinds of optical glass, there cannot be found such pairs of flint and
crown with which achromatism is attainable without a material enlargement of the
total cuter curvature (ie. of the-algebraic difference between the reciprocal radii
of the outer surfaces) of the compound lens over and above that total outer
curvature which would be required for a non-composite (non-achromatic) lens of
the same focal length.
i
In order to avoid the necessity of thus augmenting in the case in consideration
the total outer curvature of the compound lens and to obviate the objectionable
increase of the spherical aberration of its outer surfaces that would result
therefrom, pairs of flint and crown would be necessary, wherein the dispersive
power of the flint glass is far more considerable than that of the crown glass,
while its refractive power exceeds that of the crown glass only to an extent
sufficient to produce the desired corrective effects upon the inner surface. Among
the existing kinds of glass, however, a great value of the ratio d nn: d ner of
the dispersive powers of the flint and the crown is always associated with a
comparatively great difference n-ner between their refractive indices, the
consequence being, that in the case of a comparatively large relative aperture no
chromatic combinations can be formed by cementing together a flint glass lens
and a crown glass lens unless the total outer curvature of the object glass is
made so large that a sufficient correction of the spherical aberration becomes
minossible

page_text: This drawback, which has so far hindered cemented lens systems to be adopted
for certain purposes-namely, the lack of flint glass possessing a great dispersive
power but a comparatively small refractive power-may, however, be entirely
obviated by producing indirectly (whilst employing the kinds of glass now
available) the same effect as would be obtained directly with flint glass of a
comparatively low refractive index, but the dispersive power of which might be
increased at will. This result is attained by constructing the negative component
of the double lens also as a compound lens consisting of two components, viz. a
negative lens-the radii r2, p of which present an increased total curvature in
comparison with a non-composite negative component of the double lens-and a
positive lens, of the radii p, r, cemented to the said negative one, and made of
glass of the same refractive index, but of a less dispersive power, so that the total
outer curvatures of the compound lens-that is to say the difference
constitutes a lens of negative character.
-
1
Та
-still
A compound negative lens made up as just described has the following
characteristic properties:-
1. With regard to effects independent of colour, i.e. refraction-or variation of
the divergence of the pencils of rays traversing the lens-and spherical aberration,
such leus (owing to the fact that on the intermediate surface the radius of which
is p the light is refracted but to an imperceptible extent, or not at all) will behave.
exactly like a single lens of homogeneous material, having the same outer]
curvatures.
2. With regard to the chromatic dispersion attending the said variation of
divergence, the lens in question will be equivalent to a single (homogeneous)
negative lens of the same total outer curvature and supposed to be made of glass
of greater dispersive power than the maximum dispersive power actually existing
in the constituent parts of the compound negative lens.
Owing to the latter effect such a hyperchromatic lens presents therefore, with
regard to chromatic dispersion, an analogous phenomenon as is known to exist
in the combined layers of the eye lens of vertebrate animals with regard to
refraction where the resultant average refractive power of the combined lens is
greater than the maximum value actually occurring in its interior.
Mathematically the resultant dispersive power A n of a negative compound
lens constructed in the manner described above, may be determined by means of
the following formula, which may be readily deduced:
An expresses the (higher) dispersive power of the negative constituent,
Athe (lesser) dispersive power of the positive constituent, the absolute
value of the total outer curvature of the compound lens (or in other words
the value of the difference
curvature
lens.
1 1
1
12 T3
irrespective of the sign) and K the total
(-7) of the positive constituent contained in the compound negative
According to this formula the resulting average dispersive power of the
compound negative lens will surpass the dispersive power An of the glass of the
negative component, owing to the additional effect of the positive compouent
although of less dispersive power Av, firstly in proportion to the excess of An
over Av, and secondly according to the ratio K: k.
Thus a negative lens made of flint glass of a given dispersive power An may
by inserting in it a positive lens of another kind of glass of less dispersive
power Av-without varying its total outer curvature -be provided, as it were,
2.

page_text: with a higher dispersive power An¹ the degree of which may be optionally
increased by diminishing the radius p of the intermediate surface of the combination.
Moreover it will be observed that the compound negative lens-provided the
condition of an equal refractive power in both its constituent parts be fulfilled-will,
as regards variation of divergence and spherical as well as chromatic aberration, be
exactly equivalent to a single homogeneous lens with the same outer curvatures,
made of glass which is supposed to combine with the same refractive index as that
of the compound lens the increased dispersive power An'.
Only in respect of the variation of spherical aberration relative to rays of
different colours does the compound negative lens under consideration not behave
exactly as would a single lens of glass of the supposed high dispersive power.
This variation of spherical aberration depending from the colour of the rays--or in
other words, the chromatic difference of spherical aberration-is, in the case of
the compound negative lens, less than it would be under like circumstances in the
case of an equivalent single lens with equal outer curvatures, could the supposed
high dispersive power really be inherent in its substance. For on the two outer
surfaces of the compound lens, on which mainly originate both the spherical
aberration itself and also, consequently, the differences thereof relative to the
various colours, only the comparatively small actual values dn, dv of dispersive
power produce chromatic effect, whereas in a corresponding single lens, the supposed
greater value would come into operation on both surfaces.
This reduced chromatic difference of the negative spherical aberration amounts
to a further advantage, arising from the achromatism provided for by constructing
a compound negative lens in the manner described, viz.: the surplus of the
spherical correction of the blue rays over that of the red rays is thereby reduced;
which over-correction in an achromatic lens system consisting of components
cemented together is unavoidable, and must prove all the more injurious to the
general effect of the system, the greater the extent to which it is allowed to
subsist.
Owing to these two advantages, namely the last mentioned reduction of the
chromatic difference in spherical correction and the reduction of the total outer
curvature, previously referred to, the achromatizing method herein described, by
means of a compound negative lens, instead of by a single dispersing lens as usual
in the ordinary cemented double object pieces, realizes an essential improvement in
the production of spherically and chromatically corrected lens systems made up of
cemented single lenses, this method affording the possibility of attaining with a
considerably large relative aperture a degree of perfection, as regards spherico-
chromatic correction, which by the prior achromatizing method can only be reached
with comparatively small relative apertures.
The inconvenience which consists in the addition of one more component to each
lens system is practically counterbalanced by various favourable circumstances.
Thus, in as much as only a scarcely perceptible amount of refraction, or indeed no
refraction at all, takes place upon the intermediate surface having the radius p, the
general effect will be found to be very insensitive to anything occurring on that
intermediate surface. The curvature of the same, and the angles of incidence
occurring thereon, may therefore, without disadvantage, be augmented almost to
any extent, and possible imperfections in the two lens-surfaces brought into contact
(such as defective polishing, or errors of shape) will remain almost entirely harmless,
provided the two surfaces are cemented with a substance, the refractive index of
which approximately equals the refractive index common to both lenses. Suitable
cementing materials having refractive indices as here required are readily
procurable.
As to the pairs of flint and crown glass, which are required for negative lenses
constructed according to the present invention, suitable pairs may be readily
obtained, at least such having a refractive index n = 154 to n = 1.61.
The table hereinafter given indicates (by way of example) the dispersive
powers An', which will be obtained in the hyperchromatic negative lenses when

page_text: K
the ratio
k
is increased step by step and the components of the lens are supposed
to be constructed of three different pairs of glass successively.

page_text: Each of these pairs of glasses may serve for the construction of negative
compound lenses which, on being combined with a crown glass collecting lens-
the refractive index of which is less by from 0-03 to 0-10 than that of the
compound dispersing lens-will form an achromatic lens system, the total outer
curvature of which is only a little larger than that of a corresponding single crown
glass lens of the same focal length.
It will be understood that the hyperchromatic negative lenses hereinabove
described are applicable to any lens system that may require to be achromatized.
In the case of those lens systems however, in which all the constituent parts are
cemented together, and which therefore represent compound lenses with only two
surfaces in contact with the air, the said hyperchromatic negative lenses overcome,
by diminishing the total outer curvature of the lens system and the chromatic
difference of the spherical aberration of the negative lens, constructional difficulties
which cannot be removed by other means. Moreover in such lens systems it makes
no material difference in the specific advantages, which affords the hyperchromatic
negative lens, whether this lens be connected with only one collecting lens, or
with two such lenses; or in other words, whether the complete lens system consists
of three or of four constituent single lenses.
Besides, the employment of such a compound negative lens together with two
other lenses admits of the same variations in the order of succession of the latter
lenses, as those which are feasible in a treble lens with a non-composite negative
component.
Dated this 4th day of June 1896
JOHNSONS & WILLCOX,
47 Lincoln's Inn Fields, London, W.C., Agents.
Improvements in Lenses.
I, PAUL RUDOLPH, Doctor of Philosophy, residing at Jena in the Grand-
Duchy of Saxe-Weimar, German Empire, 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 :-
The object of this invention is to facilitate the chromatic and spherical
correction of lens systems (object glasses) which are to be composed of single
lenses cemented together.
In all object glasses consisting of two lenses both chromatic and spherical
aberration may be simultaneously corrected by making the negative constituent of
the double lens of flint, glass possessing not only a greater dispersive power but
also a higher refractive index than the crown glass of which the positive
constituent is formed, so that the inner or cemented surface of the compound lens
produces a negative spherical aberration, which by suitably selecting the curvatures
is made equal to the positive spherical aberration of the two outer surfaces of the
compound lens so as to compensate for the last mentioned aberration.
In the case of achromatic lenses which-like the object glasses of ordinary
telescopes are only used with a relative aperture of 1 to 1, a degree of spherico-
chromatic correction, sufficient to meet most requirements of practice, may by the
above method be secured with any pair of Hint and crown glass, where the
refractive index of the flint does not too closely approach that of the crown.
For considerably larger relative apertures, however, the correction of such
lenses is somewhat seriously interfered with by the circumstances that, amongst
the available kinds of optical glass, there cannot be found such pairs of flint and
crown with which achromatism is attainable without a material enlargement of the

page_text: total outer curvature (ie. of the algebraic difference between the reciprocal radii
of the outer surfaces) of the compound lens over and above that total outer
curvature which would be required for a non-composite (non-achromátic) lens of
the same focal length.
In order to avoid the necessity of thus augmenting in the case in consideration
the total outer curvature of the compound lens and to obviate the objectionable
increase of the spherical aberration of its outer surfaces that would result
therefrom, pairs of flint and crown would be necessary, wherein the dispersive
power of the flint glass is far more considerable than that of the crown glass, while
its refractive power exceeds that of the crown glass only to an extent sufficient to
produce the desired corrective effects upon the inner surface. Among the existing
kinds of glass, however, a great value of the ratio d n d ner of the dispersive
powers of the flint and the crown is always associated with a comparatively great
difference nner between their refractive indices, the consequence being, that in
the case of a comparatively large relative aperture no achromatic combinations can
be formed by cementing together a flint glass lens and a crown glass lens unless
the total outer curvature of the object glass is made so large that a sufficient
correction of the spherical aberration becomes impossible.
This drawback, which has so far hindered cemented lens systems to be adopted
for certain purposes-namely, the lack of flint glass possessing a great dispersive
power but a comparatively small refractive power-may, however, be entirely
obviated by producing indirectly (whilst employing the kinds of glass now available)
the same effect as would be obtained directly with fiint glass of a comparatively low
refractive index, but the dispersive power of which might be increased at will.
This result is attained by constructing the negative component of the double lens
also as a compound lens consisting of two components, viz. a negative lens-the
radii, of which present an increased total curvature in comparison with a non-
composite negative component of the double lens-and a positive lens, of the
radii p,, cemented to the said negative one, and made of glass of the same
refractive index, but of a less dispersive power, so that the total outer curvature
of the compound lens-that is to say the difference -still constitutes a lens
of negative character.
1 1
T2 13
A compound negative lens made up as just described has the following
characteristic properties:-
1. With regard to effects independent of colour, i.e. refraction-or variation of
the divergence of the pencils of rays traversing the lens-and spherical aberration,
such lens (owing to the fact that on the intermediate surface the radius of which
is p the light is refracted but to an imperceptible extent, or not at all) will
behave exactly like a single lens of homogeneous material, having the same outer
curvatures.
2. With regard to the chromatic dispersion attending the said variation of
divergence, the lens in question will be equivalent to a single (homogeneous)
negative lens of the same total outer curvature and supposed to be made of glass
of greater dispersive power than the maximum dispersive power actually existing
in the constituent parts of the compound negative lens.
Owing to the latter effect such a byperchromatic lens presents therefore, with
regard to chromatic dispersion, an analogous phenomenon as is known to exist in
the combined layers of the eye lens of vertebrate animals with regard to refraction
where the resultant average refractive power of the combined lens is greater than
the maximum value actually occurring in its interior.
Mathematically the resultant dispersive power An¹ of a negative compound lens
constructed in the manner described above, may be determined by means of the
following formula, which may be readily deduced:

page_text: An expresses the (higher) dispersive power of the negative constituent,
A the (lesser) dispersive power of the positive constituent, the absolute
value of the total outer curvature of the compound lens (or in other words
irrespective of the sign) and K the total
the value of the difference
(6)
curvatures
negative lens.
1.1
T2 13
of the positive constituent contained in the compound
According to this formula the resulting average dispersive power of the
compound negative lens will surpass the dispersive power An of the glass of the
negative component, owing to the additional effect of the positive component.
although of less dispersive power Av, firstly in proportion to the excess of An
over Av, and secondly according to the ratio K: .
Thus a negative lens made of flint glass of a given dispersive power An may by
inserting in it a positive lens of another kind of glass of less dispersive power A-
without varying its total outer curvature -be provided, as it were, with a higher.
dispersive power An' the degree of which may be optionally increase by
diminishing the radius p of the intermediate surface of the combination. Moreover
it will be observed that the compound negative lens-provided the condition of an
equal refractive power in both its constituent parts be fulfilled-will, as regards.
variation of divergence and spherical as well as chromatic aberration, be exactly
equivalent to a single homogeneous lens with the same outer curvatures, made of
glass which is supposed to combine with the same refractive index as that of the
compound lens the increased dispersive power An.
Only in respect of the variation of spherical aberration relative to rays of
different colours does the compound negative lens under consideration not behave
exactly as would a single lens of glass of the supposed high dispersive power. This
variation of spherical aberration depending from the colour of the rays-or in other
words, the chromatic difference of spherical aberration-is, in the case of the
compound negative lens, less than it would be under like circumstances in the case
of an equivalent single lens with equal outer curvatures, could the supposed high
dispersive power really be inherent in its substance. For on the two outer
surfaces of the compound lens, on which mainly originate both the spherical
aberration itself and also, consequently, the. differences thereof relative to the
various colours, only the comparatively small actual values d n, dv of dispersive
power produce chromatic effect, whereas in a corresponding single lens, the
supposed greater value would come into operation on both surfaces.
This reduced chromatic difference of the negative spherical aberration amounts
to a further advantage, arising from the achromatism provided for by constructing
a compound negative lens in the manner described, viz. the surplus -of-the.
spherical correction of the blue rays over that of the red rays is thereby reduced;
which over-correction in an achromatic lens system consisting of components
cemented together is unavoidable, and must prove all the more injurious to the
general effect of the system, the greater the extent to which it is allowed to
subsist...
Owing to these two advantages, namely the last mentioned reduction of the
chromatic difference in spherical correction and the reduction of the total outer
curvature, previously referred to, the achromatizing method herein described, by
means of a compound negative lens, instead of by a single dispersing lenis as usual
in the ordinary cemented double object pieces, realizes an essential improvement in
the production of spherically and chromatically corrected lens systems made up of
cemented single lenses, this method affording-the possibility of attaining with a
considerably large relative aperture a degree of perfection, as regards spherico-
chromatic correction, which by the prior achromatizing method can only be reached
with comparatively small relative apertures.
The inconvenience which consists in the addition of one more component to each

page_text: lens system is practically counterbalanced by various favourable circumstances.
Thus, in as much as only a scarcely perceptible amount of refraction, or indeed no
refraction at all, takes place upon the intermediate surface having the radius p,
general effect will be found to be very insensitive to anything occurring on that
intermediate surface. The curvature of the same, and the angles of incidence
occurring thereon, may therefore, without disadvantage, be augmented almost to
any extent, and possible imperfections in the two-lens surfaces brought into contact
(such as defective polishing, or errors of shape) will remain almost entirely
harmless, provided the two surfaces are cemented with a substance, the refractive
index of which approximately equals the refractive index common to both lenses.
Suitable cementing materials having refractive indices as here required are readily
procurable.
As to the pairs of flint and crown glass, which are required for negative lenses
constructed according to the present invention, suitable pairs may be readily
obtained, at least such having a refractive index n = 1.54 to n = 1.61.
The table hereinafter given indicates (by way of example) the dispersive
powers An, which will be obtained in the hyperchromatic negative lenses when
K
the ratio
ki
is increased step by step and the components of the lens are supposed
to be constructed of three different pairs of glass successively:

page_text: Each of these pairs of glasses may serve for the construction of negative com-
pound lenses which, on being combined with a crown glass collecting lens-the
refractive index of which is less by from 003 to 0.10 than that of the compound
dispersing lens-will form an achromatic lens system, the total outer curvature of
which is only a little larger than that of a corresponding single crown glass lens'
of the same focal length.
It will be understood that the hyperchromatic negative lenses hereinabove
described are applicable to any lens system that may require to be achromatised.
In the case of those lens systems however, in which all the constituent parts are
cemented together, and which therefore represent compound lenses with only two
surfaces in contact with the air, the said hyperchromatic negative lenses overcome,
by diminishing the total outer curvature of the lens system and the chromatic
difference of the spherical aberration of the negative lens, constructional difficulties
which cannot be removed by other means. Moreover in such lens systems it makes
no material difference in the specific advantages, which affords the hyperchromatic
negative lens, whether this lens be connected with only one collecting lens, or with
two such lenses; or in other words, whether the complete lens system consists of
three or of four constituent single lenses.
Besides, the employment of such a compound negative lens together with two
other lenses admits of the same variations in the order of succession of the latter
senses-as those which are feasible in a treble lens with a non-compositive negative
component.
In the annexed sheet of drawings:
Fig. 1 represents the fundamental form of the usual achromatic lens combined of
two components cemented together. From this biconvex compound lens the other
characteristic forms may be derived by mnere "bending" that is to say by altering
the three radii of curvature 71, 72, 73 whilst retaining a constant value of the total
curvature (ie. of the algebraic difference between both curvatures measured by
the reciprocal radii) of either lens.
Fig. 2 represents a biconvex compound lens as shown in Fig. 1 but in which the
negative component is itself a compound lens constructed according to the present
invention. The inner surface (having the radius p) of the compound negative lens
has been shown in dotted lines so as to indicate the equal refractive index of both
components.
Figs. 3 and 4 represent two cemented lens systems forming examples of the
invention, the numeral data of the compound lenses being given hereinafter. The,

page_text: letters 1, 2, 3, 4, denote the radii of the spherical lens surfaces, d₁, d₂, da, d
the thicknesses of the lenses in the optical axis of the system, L, L, L, L, the
different lenses.
The following two tables corresponding to Figures 3 and 4 respectively take
reference to these letters and to the diameter D common to all components of a
lens system, the radii, thicknesses and diameters of the lenses being represented
by numbers which relate to the focal length of the total lens system as to the
unit. Therefore the dimensions of the components of an object glass of any required
focal length are obtained by multiplying the numbers given in the table by the
amount of the focal length. The kinds of glass are distinguished firstly by the
refractive indices nD relating to the D-line of the solar spectrum and nG, relating
to the Hy line of hydrogene spectrum and secondly by the value ✓ of the so-
called relative dispersion, in which ratio An is taken between D and Hy, whilst
the amount of nD has been used as n.
FIRST EXAMPLE.-FIGURE 3.
An
Spherically and chromatically corrected object glass allowing a relative
opening 0, 333 and consisting of 4 single lenses cemented together, viz. a biconvex
collecting lens L₁, a biconcave dispersing lens L, and two collecting lenses L
and L, the lenses L₁ and L, being made of kinds of glass which have nearly equal
refractive indices and such dispersive powers that by the combination of those
lenses a hyperchromatic negative lens is formed.
Radii:
10, 492
-
0, 795
-
Thicknesses:
d₁
0, 047
d₁
=
0, 014

page_text: are the components of the hyperchromatic dispersing lens, whilst L, is a collecting
lens made of a glass of a comparatively high refractive index.
Having now particularly described and ascertained the nature of my said inven-
tion, and in what manner the same is to be performed, I declare that what I
claim is :-
In a chromatically and spherically corrected lens system in which all the
components are cemented together, a hyperchromatic negative compound lens.
consisting of a flint glass dispersing lens and a collecting lens made of glass having
about the same refractive but a less dispersive power than the glass of the dispersing:
lens.
Dated thie 41st dor of January 1897
JOHNSONS & WILLCOX,
47 Lincoln's Inn Fields, London, W.C., Agents..