L9 The optical instruments

Photographic chamber

The optical instruments, which generate images by means of lenses, include the eye. First of all, we will discuss the photographic chamber (camera obscura), because the optical apparatus of the steady eye is a natural, only not as simply constructed camera. Fig. 721 shows an early form of the photographer's box. The tube HJ contains the lenses L and L', which are to generate the image on the plate G. Since the image is at a different distance from the lens depending on the object's distance from it, you must be able to alter the distance of the plate G from the lens, whence the length of the box can be altered and the lens shifted with the tube. If the tube is directed at the object (its distance from the lens must be larger than its frontal, double, focal distance), you move G, a frosted glass disk, to the lens in such a manner that you see on it a sharp image of the object. It is a reduced image in natural colours, but inverted (upside down). If the object comes closer to the lens, the image moves away from it; if you leave the plate G where it is, you must push the lens away from it towards the object, in order to again make the picture sharp and correspondingly when the object moves away from the lens. Once focussing has been completed, you replace the frosted glass plate by a light sensitive plate on which the light generates the image.

Initially, the lens of the photographer was biconvex. A long sequence of improvements has led to systems (anastigmatic), in which faults, which disturb the images, can be considered to have been removed. However, no system is sufficient for all demands at the same time: Portraits demand more light intensive, that is, wider open bundles, because they are taken more quickly than landscapes; for these much less light intensive, that is, narrower bundles suffice, as you can take more time for taking them.

Projectors

Due to the invertibility of the light's path, object and image points can interchange their functions: Every image point, which as an object emits rays (in directions, opposite to those in which they were joined at it), is by the same optical arrangement mapped at it as conjugate object point. (Instead of saying that a point is the image of another, both are therefore said to be conjugate with reference to the optical means employed.) Imagine the complete image (G) to be an object and rays from it passing through the lens. If you then place a screen where previously was the object to be photographed, its image G appears on the screen - an enlargement of G. As far as the ray path is concerned, this is the optical mechanism in the projector, the purpose and action of which everybody knows from the laterna magica, lectures with projected photographs and cinemas. In order to obtain on the screen a sufficiently bright image, the object itself must be correspondingly bright, which demands special measures. A projector comprises a source of light, a condenser, a projecting lens and screen. We will not discuss the technical aspects of the source of light and the screen. You use an image projecting lenses inversely arranged photographic systems, that is, the back of the objective facing the object. During a moderate, about 15 - 20 fold enlargement, the light distributes itself from an object element into the system on to an element of the image with 225 - 400 times the area, and yet the intensity of the illumination is to be large enough, in order to evoke a sufficiently bright radiation (despite of all losses involved). Hence you must illuminate very strongly the object to be enlarged and shown on the screen. You must also select the objects correspondingly, opaque ones must be illuminated by incident light and depending on their albedo (or whiteness) - according to Lambert, it is the ratio of the reflected to the incident quantity of light in the case of a frosted surface - they reflect more or less of it, in the most favourable case (white paper) 40% and then again only a part of it into the system (since the radiation spreads out in all directions). For such demonstrations are most suitable black-white diagrams, writing on white paper, etc., due to the large differences in brightness. More bright than this image production in incident light (episcopy) is the penetrating one (diascopy), that is, the projection of glass images (diapositives), because in this case the object does not disperse rays. You only need to produce an illumination apparatus, which maps the source of light on to the entrance pupil of the projecting lens. The images become then bright enough and can be very much enlarged. Figs. 722 and Fig. 723 survey the principles of episcopy and diascopy.

The eye

An eye, which is not moved in its cavity, acts like a natural camera obscura. The eye's apple, covered by the black chortoid membrane corresponds to an internally blackened box (Fig. 724). Its outermost wall is a strong skin S, which is partly visible as the white of the eye. At the location where the photographer's box has the tube with the lenses, the eye's apple is closed by the completely translucent cornea C, vaulted like a sphere. Behind it (3.5 mm from it) lies the crystalline lens L; it forms together with the cornea the main section of the refracting system, corresponding to the photographer's lens. The blend in front of the lens in the camera, which is to raise the sharpness of the image, is matched in the eye by the iris J, due to which eyes are said to be brown, blue, etc. The opening in the iris - the pupil - widens or narrows automatically depending on whether it is met by weaker or stronger light as well as also during accommodation. On an average, is has a diameter of 4 mm; it enlarges at the most to 10 mm. The retina N between the chortoid membrane and the vitreous humor, which covers the eye's background like wall paper, corresponds to the light sensitive plate; between it and the crystalline lens, filling the space in between, lies the jelly like vitreous humor Q. The space between the crystalline lens and the retina is filled with fluid (frontal eye chamber K). Thus, the eye's refracting system extends from the cornea to the retina and comprises media which refract differently. For certain theoretical investigations, Johann Benedict Listing 1808-1882 has replaced it by the reduced eye, a homogeneous medium bounded by a single reflecting spherical surface with the index 103/77.

When you look at an object, there arises on the retina its upside down, reduced image. The fact that you see the object upright in spite of the inversion of the retina images is a question of perception theory* and not of physics. In essence, the result, to which the empirical theory of visual perception leads, is: The viewing person is not at all conscious of the existence of the retina, whence it also cannot judge the positions of objects seen on the retina. (It senses the location of an object in its field of view, but not the location on the retina where it is mapped.) The images on the retina are only means for concentrating the rays of the light of individual points of the field of vision to individual nerve fibres; however, they do not have a role whatsoever for an assessment of the position of an object by a seeing person. Localization occurs in quite a different manner as Helmholtz describes: "Whenever two bright points are present in the field of vision while the eye is fixed, two different optic nerve fibres are excited by their light and there arise two sensations which must be differentiated by local signal characteristics, since we are able to differentiate them in our sensation. As the location on the retina of these local signals is concerned, we know to start with as little as we know of the location of the fibres, which conduct them, and whereto in the brain the sensation is conducted. However, we know through daily experience how we must extend our arm in order to touch one or the other bright object or cover up our eye. Hence we can discover directly by such motions the direction in the field of vision, where the objects are, and we learn directly to relate the specific local signals of the sensation to the object's location in the field of vision." (You understand by local signs of the sensation the instants, by which you can differentiate the stimulation of the, by the light of the object's point A incited, locaion of the retina from that of all other locations. We know nothing about the type of the local signals; we conclude that they must exist from the circumstance, that we can differentiate impressions of light at different locations of the retina.

* "What we call an image of the object in our eye is nothing but the fact that in our sensing organ neighbouring nerve ends are excited in the same order by rays of light with different colours in which these rays come from the objects themselves. However, this fact of an ordered neighbourhood of different excitations in different nerve fibres is not yet perception of this process, but only the process to be sensed itself, the possibility of which, to become in its entire order conscious, is the object of our question" (Rudolf Hermann Lotze 1871-1881).

Directing your eye at an object means to turn it so that it sees it as clearly as possible. The image of the object lies then on the macula M, which, due to its colour, is called the yellow patch. The retina is that location of the eye, where it is excited by light. This follows from the fact that the black chortoid membrane screens off the light and does not allow it to penetrate beyond the retina. The retina itself is a transparent membrane of neural substance, which while less than 0.5 mm thick has several layers (Fig. 725). Coming from the dioptric apparatus of the eye, the light penetrates the entire retina, but excites it only in the (most backward) layer of rods and uvulae. The rods, strongly light refracting cylinders, are about 63 - 81 m long and 1.8m thick. The uvulae, made of a similar substance, are thicker and shorter. They stand dispersed between the rods, more sparsely at the periphery of the retina, more densely towards the yellow spot; in the spot itself, there do not exist rods, that is, that location of the retina, which we employ for seeing, consists almost only of uvulae. It is suspected that there leads from every uvula an isolated nerve fibre through the optic nerve trunk to the brain, in order to transfer there the impression received, so that the state of excitation of every individual uvula can also be sensed individually. The magnitude of the diameter of an uvula determines therefore the magnitude of the spot of light, which appears to the eye as a point - dispersion point - and also determines the acuteness of the vision of the eye, that is, the distance of two points, which the eye still recognizes as being separate - not converging into a single point: The images of two points must lie on two uvulae, which are separated at least by a single, unexcited uvula a (Fig. 726). Imagine a line to have been drawn from from each of them to the centre of the pupil. The angle between the lines is the angle of vision, at which the distance of the two points appears: It must not lie below a certain size (which can be very different for different observers), in order that the two points will just still appear to be different. The border lies in the macula - location of the clearest vision -about at an angle of one minute; it corresponds to about 1/60 of the angle, at which you see the width of your index nail when you stretch out your arm as far as possible. Two horizontally neighbouring points, which lie 1 m from your eye, according to Helmholtz, must lie at least ½ mm apart, points which are further away, correspondingly further apart, in order to be recognized as two different points; at 100 m distance, it is 100·1/3 mm.

An object at a yet smaller angle of view, whatever its shape, appears to be round and and does not display details to the mere eye. - Starting from the macula, the sharpness of view drops rapidly towards the edges**. In order to to bring another part of the field of vision into the range of clearest perception, you move the eye in its cavity like in a ball joint (you scan the field of vision with your view). For the same reason, you must also employ optical instruments with the viewing eye when a field of view of larger extent arises; you connect a fixed optical instrument to an eye, which moves while it is in use - just think of spectacles and an opera glass.

**"Hence the eye is an optical tool with a large field of vision; however, only at a small, very narrowly bounded place of this field of vision are images distinct. The entire image corresponds to a drawing, in which, while the most important part is carefully executed, the environment is only outlined, and indeed the more roughly indicated the further away it is from the main object. However, the movability of the eye allows you to focus sequentially every individual point of the field of vision" (Helmholtz).

To see something does not yet mean seeing it sharply. For this purpose, the image on the retina itself must be sharp, and hence the lens must be at a definite distance from the retina as well as the object. In the photographer's box, the lens can be moved between the plate and the object, in order to focus closer or further away objects. or you can displace the plate relative to the lens. It is quite different with the eye! It changes the shape of its lens depending on whether it is to map a closer or further away object. The front surface of the lens becomes more strongly curved as it maps a close object, it becomes flatter for a further away one. The focussing ability of the eye is called accommodation, the bounds within which it can do so its accommodation depth. You feel the changing of shape as an effort when you look quickly and consecutively at a very close and far away object. The accommodation width decreases with advancing age. It can be measured by the ability to refract of that convex lens, which, when placed in front of an eye at rest and focussing infinity, makes rays from the nearest point of clear vision axis parallel. The eye of a twenty years old person demands for this a focal length of 10 cm (in the now used terminology 10 dptr. The ten years old child has an accommodation depth of 15 dptr, the fifty years person only of 2.5 dptr.

Gullstrand's numbers for the surveying eye
These number are millimetres from the vertex of the cornea, positive inward, negative to air.

Front focal length is the distance of the front focal point from the first principal point (and correspondingly for the rear). The focal lengths of a refracting system are equal to each other when the system lies in one and the same medium (air), they differ otherwise. The eye's optical system is bounded on its one side by air, but not on the other side, whence there arises the displacement of focal lengths. The narrowing of the pupil during accommodation sharpens the mapping: It blends off the edge rays, the spherical aberration of which would make the image unclear, and reduces the sizes of the dispersion circles.

The eye's optical apparatus has certain deficiencies. The retina does not have at the location, where the optical nerve enters, rods and maculae, and is therefore blind there; however, as a rule, the blind spot is not noticed by the viewing eye. Moreover, the cornea of most eyes is differently curved at its different meridians and, in addition, it and the crystalline lens are mostly not formed for the same axis (centred). These two deviations cause the mostly stronger and weaker astigmatism of eyes. It causes an eye not to see simultaneously clearly horizontal and vertical lines at the same distance. You correct this by means of spectacles - combinations of spherical and cylindrical surfaces. Moreover: Also the properly sighted eye develops sharp images on its retina only of such objects which do not lie closer to it than 25 cm (central near point) and even within the range of normal vision not every eye can see an object sharply, for example, the distant point O in Fig. 727 a, b, c. This means physically that the faulty (ametropic, opposite: emmetropic) eye cannot vault the lens so that the rays from O exactly join on the retina. The point O' where they join lies then in front of or behind the retina (Fig. 727 a). In both cases, there arises on the retina a dispersion circle. Such eyes are said to be short-sighted (c) and long-sighted (b): myopic, when the point of intersection O' lies ahead of, hyperopic when it lies behind the retina.

Spectacles

In order to assist the short-sighted eye, you must ensure that the rays are less strongly refracted, for the far-sighted eye, they must be refracted more strongly. For this purpose, you place an auxiliary lens in front of the eye - a spectacle lens (Fig. 727 b and c). It acts as follows: Rays which enter in parallel, the normal eye (a) refracts so that after refraction their joining point lies on the retina; hence the short-sighted eye refracts them too strongly the far-sighted eye too weakly. In order to to join also parallel incident rays on the retina, you deprive them before entry into the eye of their parallelism: You make them divergent (c) before they enter a short-sighted, convergent (b)before they enter a far-sighted eye - the former by letting them pass through a concave lens (its focal length is negative, whence there is a minus sign in front of the number** in the spectacle prescription), the latter through a convex lens. Depending on the degree of short-sightedness and farsightedness, the strength of that lens must be assessed, which makes the divergence or convergence of the rays sufficiently large, in order to shift the point of intersection to the retina.

**You call the fraction 1/f with f the focal length of (equally sided thin) spectacle lenses their strength. You measure the strength in dioptrics. One dioptric (dptr) is defined by a lens of 1 m focal length; lenses of 1/2 1/3 ··· 1/n m focal length are called lenses of 2, 3, ···, n dptr.

Another fault in the eye's optical apparatus causes a point of light to be seen actinomorphicly, for example, flames, and especially stars. The common occurrence of this fault is the description of a figure with rays as being starlike. Eyes without a lens (cataract operation) see stars without rays. Helmholtz deduced from this fact that the rays of stars arise in the crystalline lens of the eye and looked for the reason in the structure of the lens. According to Gullstrand 1862-1930, while you can explain in this way six-ray star figures, you cannot explain those with eight rays, which Helmholtz describes. According to Gullstrand, the rays are coincide with the directions of certain lines of curvature, which at one point align with the axis of a not astigmatic eye; he explains the corresponding character of the crystalline lens by its not tension free suspension at the ciliar body.

Magnifying glass

The closer we bring an object to the eye, the larger becomes its angle of vision; however, as it eventually lies nearer to the eye than the near point, the eye cannot map it any more sharply on the retina (accommodate) and demands help. This auxiliary tool must take the image of the object to a distance from the eye, at which it can see it sharply. The eye sees then the object at a larger view angle. The ratio of this angle to the smaller one, at which it would appear to the mere eye at the same location, is called the subjective enlargement of the magnifying glass. The armoured eye works best whenever it need not accommodate, that is, the normal eye then, when the image lies very far from it (the rays enter it parallel), that is, the object viewed under the magnifying glass lies close to its frontal focal point in between it and the magnifying glass (Fig. 728, repeated from Fig. 695 b). The angle at which the eye sees the object through the magnifying glass is w'; its size follows from y/f' = tan w'. The unarmoured eye sees the object at the distance l, just about at the near point, at the angle w; its size is determined by tan w=y/l, whence follows the enlargement number of the magnifying glass N = tan w'/tan w = l/f'. Accordingly, the enlargement N depends on the distance, at which one can accommodate for a longer period. You assume that the mean near point distance of the normal eye is 250 mm. Hence the enlargement of the magnifying glass is N = 250/f'. (For enlargements up to N = 20, you speak of magnifying glasses, for enlargements beyond of simple microscopes.)

This formula shows that a magnifying glass enlarges the more, the smaller is f'. However, if you make the focal distance smaller, you soon arrive at lenses, the images of which are useless partly due to too large enlargement, partly due to their darkness. You can bypass these deficiencies by a combination of several lenses as shown in Fig. 729 - an old type of Zeiss lens with 2 mm focal length.- In general, you use magnifying glasses of at most 30 fold enlargement and beyond that microscopes.

Microscope

A microscope comprises two optical systems Ob and Oc, which are separate and differ completely in their optical action, but are joined into a single system, just about like the lenses in a binocular. The two systems - they are called the objective and the eye piece - because the one faces the object, the other the eye - are fitted at the ends of a cylindrical tube. Each of them comprises several lenses, which, however, have a common optical axis - axis of the tube. The tube - tubus (made mostly out of brass) - is blackened dull inside, in order to avoid reflections of light.

The focal points, facing each other, - the posterior (upper) of the objective and the frontal (lower) of the eye piece - are given a certain distance from each other - in Zeiss microscopes about 180 mm, the optical tubus length. (This must not be mixed up with tubus length, that is, the length of the tube at the ends of which are located the objective and the eye piece, which is in Zeiss microscopes about 160 mm long and varies from manufacturer to manufacturer from 150 - 300 mm.)

Already this combination of two optical systems and the motion of their facing focal points to a certain distance makes the microscope superior to the magnifying glass. Calling the focal lengths of the systems F and f and the distance between their focal points d, one finds for the combined focal length F·f /d. For example, if each system has the focal length 15 mm and the optical tubus length is 180 mm, their combination has the focal length 5/4 mm. (In order to be able to enlarge d, that is, to reduce the focal length yet further, you make the tubus extendable like a telescope.) An instrument, which is to have so small a focal length, is more simply combined out of two systems, each of which has a much larger focal length. - The moving apart of the two system displaces the object further away from the eye than the magnifying glass, which is desirable for the protection of the eye. - Moreover: You are not tied to a single objective and also not to a single eye piece; you can insert objectives and eye pieces of different focal lengths into the tubus, that is, you can attain with the same microscope a wide range of enlargements.

The illumination of the object depends on whether it is transparent or opaque. Opaque objects do not demand lighting other than magnifying glasses, transparent ones - most of them - must be illuminated . For ordinary observations, the in all directions adjustable mirror S under the object table t is sufficient. However, strong microscopes and observations extending to the limits of microscopy demand special systems of illumination such as Abbe's condenser. In essence these are objectives which you place, like in Fig. 730, below the object tables in such a manner that they present their lenses to the light in inverse order like the objective in the tubus.

An explanation of the action of the microscope follows (Fig. 731): The objective (here comprising two lenses) behaves towards the object O₁O₂ - we assume that it provides its own light* - like a photographic lens towards an object to be photographed. It creates (disregarding for the moment the eye piece) of the object the inverted image O'₁O'₂, which is real, that is, can be intercepted by a plate (useable for micro-photography - another advantage compared with the magnifying glass).

*An image arises, like in the photographic chamber, only if the object provides its own light. According to Abbe, the microscopic image of an illuminated object is a dispersion image.

However, there exists an essential difference between the lens of the photographer and the objective of the microscope: The former generates under normal conditions a reduced image of the object, the latter an enlarged one. In fact, while using the microscope, the object lies so close to the objective, that it is only a little further away than the focal length, while during photography the object is by more than twice the focal length away from the lens. The real image floating in the air, generated by the objective, serves the eye piece as an object. The eye piece (here consisting of two lenses) acts for the image as a magnifying glass: It generates an upright, enlarged, virtual image O"₂O"₁, that is, the image generated by the microscope's objective remains inverted, whence what you see in the microscope's image on the right hand side, lies in the object on the left hand side; what appears to lie ahead of the axis of the tubus lies, in fact, lies behind it.

Fig. 731 (taken from "Foundations of the theory of optical instruments according to Abbe" by Czapski-Eppenstein) displays the ray path, that is, the path of the principal rays in the microscope, which generate of the object O₁O₂ the image O"₂O"₁, seen by the eye: The objective (here two lenses), if there were no eye piece, would generate a real image at O'₂O'₁. However, the lower lens of the eye piece takes it to the position O*₂O*₁. This image is seen by the eye through the upper lens of the eye piece. It sees its virtual image O"₂O"₁. The opening of the ray bundle coming from the object is always buonded in the objective. For this purpose, the blend BB lies in the ray paths of Fig. 731 between the lenses of the objective; its image (dotted above) forms the EP of the objective. This is not the case in every microscope. In strong microscopes, the bounding is achieved by the lowest lens of the objective (frontal lens) or also just by the casings of one of the other objective lenses. - At P"₂P"₁ arises the AP of the microscope; if you place your eye there, all effective rays coming out of the microscope appear. If you look at the eye piece from some distance above, you see the AP as a small circle above it. The field of vision, that is, the size of the mapped part of the object is always bounded by the eye piece, and indeed in the way that the place, where the real image O"₂O"₁ is formed, holds a blend, which leaves free as much of the image as during observation through the eye piece as magnifying glass appears uniformly bright, that is, the darker edge region is covered up.

From the focal length of the microscope F·f /d follows for the total enlargement N - the proof is omitted - the formula N = d/F·l/f, where, like in the case of the magnifying glass, l is the near point distance (250mm). An objective with a focal width of 2 mm together with an eye piece with a 10 mm focal width yields the enlargement

N = (180/2)·(250/10) = 2250.

However, it is senseless to increase the enlargement beyond about N = 1700. Particles with sizes below (about) 0.003 mm cannot be recognized even under the most favourable circumstances. This phenomenon is linked to the formation of the microscopic image as a refracted image. The magnification must be distributed in a certain manner between the objective and the eye piece.

You can only compute the magnification, when you know F and f, otherwise you must measure them, for example, with an object micrometer, a measurement ruler subdivided into 0.01 mm of length 1 mm as microscopic object. If you look at it in a microscope and draw with a camera lucinda its image. you can measure the distance of two neighbouring subdivisions of the image with an ordinary ruler and discover by how much this distance is larger then the corresponding one of the millimetre ruler in the microscope. We want to enlarge the object as much as is possible, whence we give the objective and the eye piece the shortest possible focal lengths. However, the microscope is to make accessible extreme details of an object - resolve them. Experiments have shown - all being equal - that the microscope with the largest opening angle - realizes this aim, that is, that in which the opening of the ray bundles, sent from the object points into the objective, is largest*. However, enlargement of this opening raises the difficulty experienced in making the image sharp, that is, removal of aberrations. Theory and experiments have led to the construction of the objective for strong microscopes essentially in the form of Fig. 732. This form (Giovanni Battista Amici 1786-1863) is the start of the development of the modern microscope objective.

*Enlargement of this angle is the first demand to be met during the construction of a microscope to raise its performance (Czapski), click here for the reason

The object point F sends a widely opened ray bundle to the forward lens. It refracts the rays so that, as they leave, they seem to come from the point F¹, that is, it generates the virtual image F¹. This image becomes the object for the second lens; it develops from F¹ the virtual image F², and only the third lens generates the real image, which is viewed through the eye piece. Everyone of the three lenses reduces the divergence of the ray bundle, as is indicated by the angles at F, F¹ and F² becoming ever smaller. The individual lenses are achromatic - bring the focal points of two colours of the spectrum to the same point - for observation by eye of green and yellow, for photography blue and violet. Hence they remove the coloured edges, which would confuse the image. - The achromates are surpassed by far by the apochromates (Abbe 1886). They take the focal points of three colours of the spectrum into a single point and remove an image's falsifying colouring to a practically negligible remainder. They remove in addition the spherical aberration for three and thereby practically all colours of the visible spectrum, while in other objectives it is only removed for a single colour.

In order to improve the performance of a microscope as far as it is possible, you must, first of all, increase the angle of the ray bundle entering the frontal lens . Moreover, the independent theoretical studies of Abbe 1873 and Helmholtz 1874 have shown that the smallest distance d between two points, which can still be identified with an optically perfect objective is l/n·sina, where a is half the opening angle (Fig. 738) of the incident bundle, n the refractive index of the substance, which separates the object from the frontal lens (as a rule it is air - n = 1) and l is the wave length of the light, illuminating the object. Following Abbe, the denominator is called the numerical aperture - one of the most important concepts in the theory of the microscope. Briefly speaking, you push the border of the performance of the microscope as far as possible by making its numerical aperture n·sin a as large as possible and the wave length l as small as possible.

In order to make n·sina large, you must make n and sina large. While a grows from 0º to 90º, sin a increases from 0 to 1. Since the objective and object must be a certain distance apart, you can increase a at the best to about 70º, that is, sin a to about 0.95. You can only increase the aperture yet further by means of n. For this purpose, you fill the space between the object and the objective by a substance with a larger refractive index than air. You employ for this purpose certain fluids, one drop of which you place between the frontal lens and the cover glass (on top of the object), so that both are moistened. In this manner you obtain an immersion system (the opposite is a dry system).

Initially - before recognition of the significance of the numerical aperture - water was used instead of air between the object and objective (Amici 1850), because the light, on its way from the object to the objective, experiences then less reflection from the frontal lens and is also weakened less. Later on (in 1877, following a suggestion by I.W.Stephenson), Abbe introduced the homogeneous immersion, that is, immersion which is homogeneous in optical respects. The refractive indices of the frontal lens, of the immersion fluid (cedarwood oil with n = 1.51 - 1,52) and the cover glass are then equally large and obnoxious reflection is completely avoided and the refractive index n is still larger than that of water. The aperture n·sin a is then at the most 1.40 (water immersion 1.25). The strongest aperture achieved by 1935 (Czapski) was 1.60 with mono-chrome-naphtaline, the destructive action of which has restricted its use to special cases.

In order to make the wave length l as small as possible, you must use blue light. The retina does not react to shorter waves. While you can still photograph with ultraviolet light, there too exists a limit. Wave lengths below 0.28 are absorbed. However, much finer structures have been photographed with X-rays. - The limits of the presently with microscopes attainable have been widened in a certain sense by making visible ultra-microscopic particles.

The objective decides the performance of the microscope. However, also the eye piece must meet definite demands* in order to achieve a required image quality. Almost everywhere, Huygens' eyepiece is in use (Fig. 734).The image, generated by the objective, falls between the two lenses. The lens facing the object - the collective lens - intervenes in a certain manner with the path of the rays from the object, in order to transfer the image to a location, demanded for the observation. Only the lens, facing the eye - the eye lens - acts as a magnifying glass.

*The demands on the objective and the eye piece as generator of the image differ as follows: The objective is to map an object, which is very small compared to the objective's focal length, but is to use a very widely opened bundle. In contrast, the eye piece is to map an object which sends a very marrow bundle to the lens, but is large compared with the eye piece's focal length (cf. comments to Fig. 731).

Telescope

The magnifying glass and microscope clarify for the eye objects, which due to their smallness would have to be brought closer to it (in order to show them at a sufficiently large view angle) than its accommodation allows. In contrast, the telescope clarifies for the eye objects like stars which it sees, due to their distance, at too small an angle of vision and which cannot be approached more closely. Also a telescope (we disregard here those with mirrors) comprises (Fig. 735) a collective lens Ob as objective and an eye piece Oc at the ends of a cylindrical tube, the axis of which is simultaneously the optical axis of the lenses. The objective behaves with respect to the object AB, at which it is directed, like a

photographer's lens: It generates close to its rear focussing point its image ba - inverted -, real and reduced (because the object is much further away from the lens than the frontal focus point). In Kepler's telescope (1611), the eye piece acts with respect to the image ba (as in the microscope) as magnifying glass: It generates its image - virtual, enlarged and upright, whence the telescope's image remains inverse. You see through it right and left, up and down interchanged and use it for this reason only as astronomical telescope. For terrestrial observations, you employ a telescope (mostly hand held), which once again inverts the image into the object's directions. But the system of lenses (John Dollond 1706-1761, Fraunhofer) between the objective and the eye piece makes the terrestrial telescope very long and heavy (Fig. 736). Another trick leads to an upright image. You employ a bi-concave lens B as eye piece and, indeed, at such a distance from the objective O that the exiting rays meet the eye piece before they intersect each other (discovered first by the Dutchman Johann Hans Lipperhey ?-1619 1608, and one year later, but independently, by Gallilei. The image becomes inverted only when the rays intersect and a virtual, upright image is formed. This Dutch (or Gallilean) telescope is known to everyone from the use of binoculars. It is today only of historical interest; the Zeiss prism telescope (1893), an astronomical one, has displaced it more or less.

In the astronomical telescope, you almost place the back focal point F' of the objective together with the front one of the eye piece, in order to be able to look at the real image at the focal point of the objective with the eye piece acting like a magnifying glass. Its length is therefore almost equal to the sum of the two focal lengths. (Fig. 737 right) As a rule, the eye piece of Jesse Ramsden is used; it is similar to Huygens' eye piece (Fig. 734) and consists of two plane convex lenses. You can imagine it for the following considerations to be replaced by a bi-convex lens.

In the Dutch telescope, the back focal point of the objective falls almost together with the front one of the bi-concave eye piece. Hence its length is almost equal to the difference of the two focal lengths. The front focal point of the bi-concave lens lies on the right hand side, when the light comes from the left hand side (opposite to the bi-convex lens).

The rays reach the tube only through the objective. As far as the eye piece is concerned, the frame of the objective is the object - and the rays coming from the telescope must pass through the image, which the eye piece forms of the objective or, better, of the objective's frame. (Whether all of them reach the observer's eye is another question, discussed below.) This image is real in the astronomical telescope and lies on this side of the eye piece (at AP), that is, outside the tube, so that you can introduce your pupil's eye. (If you look from some distance at the eye piece in the direction of the telescope's axis, you see it float in front of the eye piece as a circular disk.) It is smaller than the pupil, whence there enter into the eye, as it looks through the telescope, all ray bundles which intersect each other in the image, that is, all rays entering through the objective. This image of the frame of the objective is the exit pupil of the astronomical telescope, whence the opening of the objective is the entry pupil. Its diameter determines the opening of the ray bundle from the object, which contributes to the image - its brightness and its resolution; it is for the astronomical telescope what the aperture is for the microscope. Hence you have the giant refractors as in the Yerkes Obervatory (Winconsin) and the Lick Observatory (California) with objective diameters of 91 cm.

In the Dutch telescope, the image of the objective opening is virtual and lies (Fig. 738) beyond the eye piece (at P¹P²), inside the tube, whence you cannot bring you eye's pupil to its location. The image is larger than the eye's pupil, it dips into the cone of light and cuts out from it as much as it can accept: Hence it becomes the exit pupil and the image, which the telescope generates from it, its entry pupil; it is virtual and enlarged and lies far behind the eye at EP. The ray path in the Dutch telescope (Szapski 1887) is therefore for the eye at rest as shown in Fig. 738 (for the searching eye as in Fig. 707). The ray path differs fundamentally from that of the astronomical telescope. As a consequence, for example, all effective bundles of parallel rays in the astronomical telescope intersect in the objective, they intersect each other in the image of the eye piece in the Dutch telescope, that is, they meet the objective at different locations (a,b).

Field of vision of telescope

As a rule, you understand by the field of vision of a telescope just the apparent (image sided) one. The true (object sided) field of vision is the angle, at which the eye would see the object from the centre of the entry pupil. (The ratio of the first angle to the second one - of the apparent field of vision to the true one - yields the enlargement of the telescope. The image sided field of vision is that of the eye piece, which as a magnifying glass enlarges the real image in the focal plane of the objective. However, the field of vision of the magnifying glass is only uniformly bright in a circular disk with a certain diameter and becomes darker towards the edge. Hence you place at the location, where arises the real image (Fig. 737) a blend which only displays the uniformly bright, central (brightest) part. It borders the (apparently) image sided field of vision; it is the angle at which it appears seen from the exit pupil. The ray path in the astronomical telescope - the path of the principal rays through the centre of the exit pupil AP and the entry pupil EP - is then as shown in Fig. 737.

In the Dutch telescope, the true field of vision is the view angle, at which the opening of the objective appears, if you imagine the eye to be inside the entry pupil. The apparent field of vision, that is, the one immediately known to the eye, is given by the angle, at which the eye sees the image of the objective opening when it uses the telescope. The blend of the field of vision is not located at the place of the image itself, whence the field of vision has (as has been discussed when dealing with the field of vision of the magnifying glass) a central, circular part of constant and maximal brightness and around it a ring, within which the brightness decreases to zero at the edge. The ray path in the Dutch telescope indicates the size of the field of vision in dependence on that of the objective. Two separate points of an object (Fig. 738), like a and b, use for their mapping separate sections a and b of the objective. Hence, if the field of vision is not to be too small, the objective must be made large. However, for reasons concerning the eye piece, the limit of this is soon reached.

The telescope's enlargement in the astronomical as well as in the Dutch telescope equals - we will not give the proof - the focal length F of the objective, divided by the focal length f of the eye piece: F/f, whence you make F as large and f as small as possible. You make the enlargement of opera glasses about 3-fold, those of the refractors up to 250-fold*.

*Normal enlargement of a given astronomical telescope is that enlargement, at which the ray bundle leaving the eye piece has at most the same diameter as the pupil of the observing eye (at darkness about 8 mm), that is, at which all the light entering the objective reaches the retina. At smaller enlargement, the exiting bundle has a larger diameter than the pupil, that is, one part of the rays bypass the pupil. At stronger enlargement, also all of the light, entering the objective, reaches the retina, whence the brightness of a star should also be equal to that at normal enlargement. However, in fact, then also substantially weaker stars become visible than at normal enlargement (due to the weakening of the sky background?). For example, a telescope with an objective opening of 16 cm diameter has a normal enlargement of 20.

Zeiss prism telescope (Abbe 1893)

The field of vision of the Dutch telescope is irregularly bright and its diameter at the most used enlargement (in the theatre about 3-fold) is only about 2/5 that of a strongly enlarging astronomical telescope. Stronger enlargements reduce its field of vision so that is becomes useless. A terrestrial telescope, which is still handier than the Dutch one, has an equally large and in addition uniformly bright field of vision and enlarges as strongly as the astronomical one, is Zeiss' prism telescope (also as double telescope for manual usage, Fig. 739). It is an astronomical prism telescope in which a prism system (Ignazio Porro 1801-1875 1850) inverts the image, generated by the objective (Fig. 740). Its basic idea is: An upright 90º angular mirror reflects an object in front of it: Its right half lies on the left hand side in the image and its left hand side lies on the right hand side, up and down remain unchanged, whence it maps a in Fig. 741 into b. If you place the mirror horizontally in front of the object, it interchanges up and down, left and right remain unchanged, that is, it maps a into c. Hence, if you first reflect the object a in a vertical, then in a horizontal 90º angular mirror, it attains the position d. Von Abbe has employed this trick by reflecting in the astronomical telescope the image generated by the objective in a combination of two such correspondingly positioned angular mirrors and looking at it then through the eye piece. In practice, you do not let first the inverted image form and reflect it then, but you let (Fig. 739) the angular mirror change the direction correspondingly of the rays before they form the image so that it forms upright. The mirrors are planes in totally reflecting prisms. The multiple reflections make the ray path have the form , whence the tube becomes very short. However, the deformation of the ray path displaces the image (and with it the eye piece) sidewards against the axis of the objective. Hence, in a prism-double-telescope, the objectives are located further apart than the eye pieces, whence it has the form shown in Fig. 739. This move of the objectives improves considerably the depth action of the double telescope.

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