DIOPTRICS
The First Part Containing Book One
Concerning the Explanation of the Principles, from which the Construction both of Telescopes as well as Microscopes is Desired.
This is one of Euler's major works, extending over most of his working life.
The chapters in the three volumes were produced mainly from his shorter articles
produced over many years, and assembled with the help of his co-workers.
At present, Volume 1 is now complete.
Chapter 1:
Concerning the spreading of the image shown by a single lens.
Ch. 1 is concerned with the spreading of the image by a single thick convex lens, (essentially the first ever treatment of spherical aberration),
Chapter 2:
The spreading of the image presented by several lenses.
Ch. 2 considers the spreading of the image by a number of such lenses on the same axis, with attempts to minimize this effect for two thin lenses.
Chapter 3:
Concerning multiple or composite lenses.
Ch. 3 is rather long, but gives a thorough discussion of how to minimize the spreading or confusion of the final image for two, three or four thin lenses.
The case for 4 lenses turns out to be especially relevant.
Chapter 4:
Concerning the confusion of vision both by the apparent magnitude and clarity of the image.
Ch. 4 is a compilation of the preceding chapters, and considers the combined effects on the image viewed by the eye due to magnification, confusion of image, and clarity.
Chapter 5:
Concerning the apparent field of view, with the eye at the most suitable place.
Ch. 5 is concerned with determining the field of view of an object seen through a number of lenses, and a convenient place for the eye.
Unfortunately, the treatment of the eye's accommodation was not understood at this time, and Euler considers the eye as a camera obscura.
In addition, the treatment of image formation is rather obscure in this work up to this point.
Chapter 6:
Concerning the confusion arising from the nature of diverse rays.
Ch. 6 is long and rather involved; in it Euler sets out formulas for the
distance and height of the image formed by a series of lenses. Note that here
and in the previous chapters, some of the lines do not refer to rays, but to
measurable lengths. The effect of lenses of differing refractive indices is
introduced, and finally a method is produced for producing an achromatic final
image from a series of such lenses, as well as being free of confusion.
These may be viewed by the modern reader with some suspicion.
Chapter 7:
Concerning the construction of dioptric instruments in general.
Ch. 7 is a summary of the preceding chapters, to which I have added the occasional notes.
It is in this chapter in particular that Euler advocated the removal of the colored fringes round the image of an object viewed through a combination of lenses, by careful
adjustments of the stops or diaphragms used.
This assertion detracted considerably from the value of the work, as it was of course complete nonsense.
E266 achromatic doublet:
Construction of objective lenses from two glasses.
The
Second Part Containing Book Two
The Construction of Telescopes
Section
I
Chapter 1:
Telescopes in general.
Ch. 1 is an updated summary of Book I.
Whether Euler understood Dollond's new approach for making achromatic lens doublets is not clear, though some clarification has been made of other matters.
Chapter 2:
Telescopes with composite perfect objective lenses.
Ch. 2 more or less gives Euler's recipies for making perfect composite objective lenses for telescopes, i.e., those with the minimum confusion or spherical aberration and free from colored fringes or achromatic.
Two or three lenses of differing refractive indices are used.
Chapter 3:
The division of telescopes into three particular kinds.
Ch. 3 gives an attempt to classify types of telescopes according to the number of real intermediate images produced.
Chapter 4:
Telescopes of the first kind are without real images and represent objects upright.
Ch. 4 is concerned with perhaps the simplest of telescopes, namely a convex objective followed by a concave eyepiece.
This kind of telescope is treated at length, although it would appear to be at variance with the actual devices produced by Dollond.
Yet, there appears to be much of value in this text, though Euler
seldom gets a mention in optics texts re telescopes.
Chapter 5:
Concerning the further perfection of
telescopes of the first kind, by the addition of one or more
lenses.
Ch. 5 is now complete,
It shows how to perfect simple upright image telescopes by the use of extra
lenses.
Section II
Sect. II, Chapter 1:
The construction of telescopes of the second kind, with a convex objective and the inverse image.
Sect. II, Chapter 2:
Concerning the further perfection of telescopes following the use of a single kind of glass.
Ch. 2 considers the advantages of inserting an extra lens to coincide with the primary image formed by the objective lens, and the nature of this lens to reduce confusion (i.e., aberrations).
Glass of the same refractive index is considered throughout at this stage.
Sect. II, Chapter 3:
Concerning the further perfection of telescopes following the use of a two kinds of glass.
Ch. 3 considers further improvements using two kinds of glass with differing refracting indices, forms of crystal and crown glass.
A formula for the dispersion of each kind is introduced and applied to the
individual lenses.
As mentioned above, defects in the final design are attributed to the poor artificier employed to implement the designs, which did not appear to work very well, and did not produce the sharp colour free images intended.
Section III
The translation of Sect. 3 of Book 2 is now complete, and we can now present Ch. 1, Ch. 2 and Ch. 3.
Sect. III, Chapter 1:
The construction of telescopes of the third kind, for which objects again are represented erect.
Ch. 1 is concerned with producing upright images, by the addition of extra
lenses.
I have included some notes here.
Sect. III, Chapter 2:
Concerning common terrestrial telescopes and their perfection.
Ch. 2 is occupied with terrestrial telescopes.
Euler's work was continually frustrated by the imperfect telescopes his artisans could make from his theoretical calculations.
The flaw would appear to arise from his use of a formula for the focal length of the objective which he produced in Ch. I of the first volume, long before the different forms of lens aberration were understood.
As it was, up to this point, he had not made use of Dollond's achromatic doublet, but used a separated pair of lenses, which did not produce very good results.
Sect. III, Chapter 3:
Concerning other kinds of telescopes of the third kind and their perfection.
In Ch.3, Euler is concerned with adapting his theory of terrestial telescopes to the innovations of John Dollond, where the chromatic aberration is reduced by using two lenses of differing refractive index, the first concave and the latter convex.
Finally, some worked examples are set out to ease the burden of understanding the theory, and to make the work more understandable.
The appendices on reflecting telescopes remains to be
translated.
Appendices
The translation of
the appendices of Book 2 is now complete, detailing the different kinds of
telescopes involving spherical mirrors.
Appendix I:
Concerning common terrestrial telescopes and their perfection.
Appendix II:
Concerning dual telescopes.
These have an objective mirror with a central hole plus smaller concave/convex mirror, and with focusing lenses for the eyepiece.
Discussion of the associated confusion (spherical aberration on axis) and their perfection.
Appendix III:
Concerning an example of a catadioptric telescope.
Initially some notes are provided on Euler's algebraic method of analysing such optical systems.
Appendix IV:
Concerning catadioptric telescopes constructed with a convex smaller mirror.
The
Third Part Containing Book Three
The Construction of Microscopes
Section
I
Chapter 1:
Ch. 1 is purely introductory.
However, it does contain a review of Euler's analytical method of treating
optical problems.
Chapter Ia:
Ch. Ia is is the actual first chapter.
This contains much interesting material on single lens microscopes.
Chapter 2:
Ch. 2gives a detailed introduction to the construction of simple microscopes involving a number of lenses
Chapter 3:
Ch. 3provides the formulas for the lenses to be used, according to Euler's
theories, either arising from the aperture size, and the use of one or two refractive indices for removing the confusion arising from the approx. image position.
Section
II
Chapter 1:
This chapter does not have the heading Ch. 1 as it is the only one present.
A concave lens is either present as the eyepiece or is added to the
objective, and has the title: Microscopes In Which No Real Images Occur.
Various systems are considered, including cases in which crown and crystal glass is used for a pair of lenses in the objective.
Euler does not consider the achromatic doublet, which had been
developed at this time, and he still erroneously considered removing the
coloured margins from images, rather than removing the confusion thoroughout
the image by such a lens.
Section
III
Chapter 1:
This chapter is concerned with simpler composite microscopes, in which a single real image is to be found, to which all microscopes of this kind are referred.
Chapter 2:
This chapter is a long chapter concerned with more complicated composite microscopes, in which a number of lenses are used to form the objective, resulting in higher possible magnifications.
A number of such microscopes, and also telescopes are set out from the principles established here.
Chapter 3:
This chapter is an addition to the second chapter, in which a concave lens is added to the objective, which is now a compound lens, in order to reduce the confusion of the image and to remove the colored fringe, at least according to Euler.
Chapter 4:
This chapter is a further addition in which the field of view is extended further, in addition to the benefits outlined above.
Section
IV
Chapter 1:
This chapter is concerned with composite microscopes with two intermediate real images.
An extension to terrestrial telescopes is made here.
Chapter 2:
This chapter is concerned with further composite microscopes with two intermediate real images.
Again, an extension to telescopes is made.
Chapter 3:
This final chapter is concerned with the further perfection of compound microscopes and with the confusion removed.
Ian Bruce.
June 8th, 2020 latest revision. Copyright: I reserve the
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