Eyepiece in Galileo's spotting scope. Optical devices
The answer to the question "Who invented the telescope?" known to all of us from school: “Of course, G. Galileo!” - you will answer ... and you will be wrong. The first sample of a telescope (more precisely, a spotting scope) was made in Holland in 1608, and three people did it independently of each other - Johann Lipperschney, Zachary Jansen and Jakob Metius. All three were spectacle makers, so they used spectacle lenses for their pipes. They say that Lippershney was inspired by the idea of children: they combined lenses, trying to see the tower in the distance. Of the three inventors, it was he who went the furthest: he went with his invention to The Hague, where at that time negotiations were underway between Spain, France and Holland - and the heads of all three delegations immediately realized how useful the new device could bring in military affairs. In October of the same year, the Dutch parliament became interested in the telescope, the question was decided whether to give the inventor a patent or grant a pension - but the matter was limited to the allocation of 300 florins and an order to keep the invention secret.
But it was not possible to keep it secret: many people became aware of the Dutch "magic pipe", including the Venetian envoy in Paris, who told about it in a letter to G. Galileo. True, he told without details, but G. Galileo himself guessed about the structure of the device - and reproduced it. He also started with spectacle lenses, and he achieved a threefold increase - like the Dutch masters, but this result did not suit the scientist. The fact is that G. Galileo was one of the first to understand that such a device can be used not only in war or in maritime affairs - it can serve as astronomical research! And this is his undoubted merit. And for the observation of celestial bodies, such an increase was not enough.
And so Galileo improved the technology for making lenses (he preferred to keep it a secret) and made a telescope in which the lens facing the observed objects was convex (that is, it collected light rays), and concave towards the eye ( i.e. scattering). First, he made a telescope that gives a magnification of 14 times, then - at 19.5, and finally - at 34.6! In such a device it was already possible to observe celestial bodies. Therefore, one cannot agree with those who call the Italian astronomer, who received a patent for his telescope, a plagiarist: yes, he was not the first to construct such an instrument - but he was the first to make such a telescope that could become an astronomer's tool.
And he became one! The telescope of G. Galiei became famous not only for its power (fantastic for those times), but also for the discoveries that the scientist made with its help. He discovered spots on the Sun, the movement of which proved that the Sun rotates around its axis. He saw mountains on the Moon (and even calculated their height from the size of the shadows), found out that it always faces the Earth on one side. Galileo observed both changes in the apparent diameter of Mars and the phases of Venus.
The discovery of Jupiter's satellites was very important - of course, Galileo's telescope allowed us to see only four of them, the largest, but that was enough to say: you see, not everything in the Universe revolves around the Earth - Copernicus was right! True, G. Galileo's priority in this is also disputed: ten days before him, the satellites of Jupiter were seen by another astronomer, Simon Marius (it was he who gave them the names Callisto, Io, Ganymede and Europe), but S. Marius considered them stars, but G .Galileo guessed that these were the satellites of Jupiter.
Galileo also noticed the rings of Saturn. True, his telescope did not yet allow them to be clearly seen, he saw only some foggy spots on the sides of the planet and assumed that these were also satellites, but he was not sure - he even wrote it down in encryption.
And only in the XX century. it became known about one more observation of G. Galileo. In his notes, G. Galileo mentions a certain “weak unknown star with constant brightness”, observed on December 28, 1612 and January 27, 1613, and even a drawing is given showing where it was in the sky. In 1980, two astronomers - American Ch. Koval and Canadian S. Drake - calculated that at that time the planet Neptune should have been observed there!
True, G. Galileo mentions this object as a “star”, and not a planet, so it’s still impossible to consider him the discoverer of Neptune ... but there is no doubt that he, with his spotting scope, “opened the way” to all those who discovered the rings Saturn, and Neptune, and more.
Topics of the USE codifier: optical devices.
As we know from the previous topic, for a more detailed examination of the object, you need to increase the angle of view. Then the image of the object on the retina will be larger, and this will lead to irritation of a larger number of nerve endings. optic nerve; more visual information will be sent to the brain, and we will be able to see new details of the object in question.
Why is the angle of view small? There are two reasons for this: 1) the object itself is small; 2) the object, although large enough in size, is located far away.
Optical devices - These are devices for increasing the angle of view. A magnifying glass and a microscope are used to examine small objects. To view distant objects, spotting scopes are used (as well as binoculars, telescopes, etc.)
Naked eye.
We start by looking at small objects with the naked eye. Hereinafter, the eye is considered normal. Recall that a normal eye in an unstressed state focuses a parallel beam of light on the retina, and the distance best vision for a normal eye, see
Let a small object in size be at the distance of best vision from the eye (Fig. 1). An inverted image of an object appears on the retina, but, as you remember, this image then turns over again in the cerebral cortex, and as a result, we see the object normally - not upside down.
Due to the smallness of the object, the angle of view is also small. Recall that a small angle (in radians) is almost the same as its tangent: . That's why:
. (1)
If a r distance from the optical center of the eye to the retina, then the size of the image on the retina will be equal to:
. (2)
From (1) and (2) we also have:
. (3)
As you know, the diameter of the eye is about 2.5 cm, so. Therefore, it follows from (3) that when a small object is viewed with the naked eye, the image of the object on the retina is about 10 times smaller than the object itself.
Magnifier.
You can enlarge the image of an object on the retina using a loupe (magnifying glass).
magnifying glass - it's just a converging lens (or lens system); The focal length of a magnifying glass is usually in the range of 5 to 125 mm. An object viewed through a magnifying glass is placed in its focal plane (Fig. 2). In this case, the rays emanating from each point of the object, after passing through the magnifying glass, become parallel, and the eye focuses them on the retina without experiencing tension.
Now, as we see, the angle of view is . It is also small and approximately equal to its tangent:
. (4)
The size l images on the retina is now equal to:
. (5)
or, taking into account (4) :
. (6)
As in fig. 1, the red arrow on the retina also points down. This means that (taking into account the secondary reversal of the image by our consciousness) through a magnifying glass we see an unreversed image of the object.
Magnifying glass is the ratio of the image size when using a magnifying glass to the size of the image when viewing an object with the naked eye:
. (7)
Substituting expressions (6) and (3) here, we get:
. (8)
For example, if the focal length of a magnifying glass is 5 cm, then its magnification is . When viewed through such a magnifying glass, an object appears five times larger than when viewed with the naked eye.
We also substitute relations (5) and (2) into formula (7):
Thus, the magnification of a magnifying glass is an angular magnification: it is equal to the ratio of the angle of view when viewing an object through a magnifying glass to the angle of view when viewing this object with the naked eye.
Note that the magnification of a magnifying glass is a subjective value - after all, the value in formula (8) is the distance of the best vision for a normal eye. In the case of a near-sighted or far-sighted eye, the distance of best vision will be correspondingly smaller or larger.
From formula (8) it follows that the magnification of the magnifying glass is the greater, the smaller its focal length. Reducing the focal length of a converging lens is achieved by increasing the curvature of the refractive surfaces: the lens must be made more convex and thereby reduce its size. When the magnification reaches 40-50, the size of the magnifier becomes equal to several millimeters. With an even smaller size of the magnifying glass, it will become impossible to use it, therefore it is considered the upper limit of magnifying glass.
Microscope.
In many cases (for example, in biology, medicine, etc.) it is necessary to observe small objects with a magnification of several hundred. You can't get by with a magnifying glass, and people resort to using a microscope.
The microscope contains two converging lenses (or two systems of such lenses) - an objective and an eyepiece. It's easy to remember: the lens is facing the object, and the eyepiece is facing the eye (eye).
The idea of a microscope is simple. The object in question is between the focus and double focus of the lens, so the lens gives an enlarged (actually inverted) image of the object. This image is located in the focal plane of the eyepiece and then viewed through the eyepiece as if through a magnifying glass. As a result, it is possible to achieve a final increase of much more than 50.
The path of the rays in the microscope is shown in Fig. 3 .
The designations in the figure are clear: - lens focal length - eyepiece focal length - object size; - the size of the image of the object given by the lens. The distance between the focal planes of the objective and the eyepiece is called tube optical length microscope.
Note that the red arrow on the retina is pointing up. The brain will turn it over again, and as a result, the object will appear upside down when viewed through a microscope. To prevent this from happening, the microscope uses intermediate lenses that additionally flip the image.
The magnification of a microscope is determined in exactly the same way as for a magnifier: . Here, as above, and are the size of the image on the retina and the angle of view when the object is viewed through a microscope, and are the same values when the object is viewed with the naked eye.
We still have , and the angle , as can be seen from Fig. 3 is equal to:
Dividing by , we get to magnify the microscope:
. (9)
This, of course, is not the final formula: it contains and (values related to the object), but I would like to see the characteristics of the microscope. We will eliminate the relation that we do not need using the lens formula.
First, let's take a look at Fig. 3 and use the similarity of right triangles with red legs and :
Here is the distance from the image to the lens, - a- distance from object h to the lens. Now we use the lens formula for the lens:
from which we get:
and we substitute this expression in (9) :
. (10)
This is the final expression for the magnification given by the microscope. For example, if the focal length of the lens is cm, the focal length of the eyepiece is cm, and the optical length of the tube is cm, then according to formula (10)
Compare this with the magnification of the lens alone, which is calculated by formula (8) :
The magnification of the microscope is 10 times greater!
Now we move on to objects that are large enough but too far away from us. To view them better, spotting scopes are used - spyglasses, binoculars, telescopes, etc.
The objective of the telescope is a converging lens (or lens system) with a sufficiently large focal length. But the eyepiece can be both a converging and a diverging lens. Accordingly, there are two types of spotting scopes:
Kepler tube - if the eyepiece is a converging lens;
- Galileo's tube - if the eyepiece is a diverging lens.
Let's take a closer look at how these spotting scopes work.
Kepler tube.
The principle of operation of the Kepler tube is very simple: the lens gives an image of a distant object in its focal plane, and then this image is viewed through the eyepiece as if through a magnifying glass. Thus, the rear focal plane of the objective coincides with the front focal plane of the eyepiece.
The course of rays in the Kepler tube is shown in Fig. four .
 |
| Rice. four |
The object is a distant arrow pointing vertically upwards; it is not shown in the picture. The beam from the point goes along the main optical axis of the objective and the eyepiece. From the point there are two rays, which, due to the remoteness of the object, can be considered parallel.
As a result, the image of our object given by the lens is located in the focal plane of the lens and is real, inverted and reduced. Let's denote the size of the image.
An object is visible to the naked eye at an angle. According to fig. four :
, (11)
where is the focal length of the lens.
We see the image of the object in the eyepiece at an angle , which is equal to:
, (12)
where is the focal length of the eyepiece.
Telescope magnification is the ratio of the angle of view when viewed through a tube to the angle of view when viewed with the naked eye:
According to formulas (12) and (11) we get:
(13)
For example, if the focal length of the objective is 1 m and the focal length of the eyepiece is 2 cm, then the magnification of the telescope will be: .
The path of the rays in the Kepler tube is fundamentally the same as in the microscope. The image of the object on the retina will also be an arrow pointing up, and therefore in the Kepler tube we will see the object upside down. To avoid this, special inverting systems of lenses or prisms are placed in the space between the lens and the eyepiece, which once again invert the image.
Trumpet of Galileo.
Galileo invented his telescope in 1609, and his astronomical discoveries shocked his contemporaries. He discovered the satellites of Jupiter and the phases of Venus, made out the lunar relief (mountains, depressions, valleys) and spots on the Sun, and the seemingly solid Milky Way turned out to be a cluster of stars.
The eyepiece of Galileo's tube is a diverging lens; the rear focal plane of the lens coincides with the rear focal plane of the eyepiece (Fig. 5).
 |
| Rice. 5. |
If there were no eyepiece, then the image of the remote arrow would be in
focal plane of the lens. In the figure, this image is shown by a dotted line - after all, in reality it is not there!
But it is not there because the rays from the point, which, after passing through the lens, became converging to the point, do not reach and fall on the eyepiece. After the eyepiece, they again become parallel and therefore are perceived by the eye without tension. But now we see the image of the object at an angle , which is greater than the angle of view when viewing the object with the naked eye.
From fig. 5 we have
and to increase the Galilean tube, we get the same formula (13) as for the Kepler tube:
Note that at the same magnification, the Galilean tube is smaller than the Kepler tube. Therefore, one of the main uses of Galileo's tube is theater binoculars.
Unlike the microscope and Kepler's tube, in Galileo's tube we see objects upside down. Why?
In paragraph 71, it was noted that Galileo's telescope consists (Fig. 178) of a positive objective and a negative eyepiece and therefore gives a direct image of the observed objects. The intermediate image obtained in the combined focal planes, other than the image in the Kepler tube, will be imaginary, so there is no reticle.
Let us consider formula (350) as applied to the Galilean tube. For a thin eyepiece, we can assume that then this formula can be easily converted to the following form:
As you can see, the removal of the entrance pupil in the Galilean tube is positive, i.e., the entrance pupil is imaginary and it is located far to the right behind the observer's eye.
The position and dimensions of the aperture diaphragm and the exit pupil in the Galilean tube determine the pupil of the observer's eye. The field in the Galilean tube is limited not by the field diaphragm (it is formally absent), but by the vignetting diaphragm, the role of which is played by the lens barrel. As a lens, a two-lens design is most often used, which allows having a relative aperture and an angular field of no more than. However, to provide such angular fields at a significant distance from the entrance pupil, the lenses must have large diameters. As an eyepiece, a single negative lens or a two-lens negative component is usually used, which provide an angular field of no more, provided that the field aberrations are compensated by the objective.
Rice. 178. Calculation scheme of Galileo's telescope
Rice. 179. Dependence of the angular field on the apparent magnification in Galileo's telescopes
Thus, it is difficult to obtain a large increase in the Galilean tube (usually it does not exceed more often). The dependence of the angle on the magnification for the Galilean tubes is shown in Fig. 179.
Thus, we note the advantages of Galileo's telescope: direct image; simplicity of design; the length of the tube is shorter by two eyepiece focal lengths compared to the length of a similar Kepler tube.
However, we must not forget the disadvantages: small margins and magnification; the absence of a valid image and, consequently, the impossibility of sighting and measurements. The calculation of Galileo's telescope is performed according to the formulas obtained for the calculation of the Kepler's telescope.
1. Focal lengths of the lens and eyepiece:
2. Entrance pupil diameter
With the help of telescopes, distant objects are usually considered, the rays from which form almost parallel, weakly divergent beams. The main task is to increase the angular divergence of these beams so that their sources turn out to be resolved on the retina (not merging into a point).
The figure shows the path of the rays in Kepler tube, consisting of two converging lenses, the back focus of the lens coincides with the front focus of the eyepiece. Suppose we are considering two points of a remote body, such as the Moon. The first point emits a beam parallel to the main optical axis (not shown), and the second, an oblique beam drawn in the drawing, going at a small angle φ to the first. If the angle φ is less than 1', then the images of both points on the retina will merge. It is necessary to increase the angle of divergence of the beams. How to do this is shown in the drawing. The oblique beam is collected in a common focal plane and then diverges. But then it is converted by the second lens into a parallel one. After the second lens, this parallel beam goes at a much larger angle φ' to the axial beam. Simple geometric reasoning allows us to find the instrumental (angular) magnification.
The focal plane point at which the oblique beam is collected is determined by the central beam of the beam passing through the first lens without refraction. To determine the angle of passage of this beam through the second lens, it suffices to consider an auxiliary source at this point in the focal plane. The rays emitted by it will turn after the second lens into a parallel beam. It will be parallel to the central beam of the second lens (figure). This means that the beam drawn in the upper figure will go at the same angle φ' to the optical axis. It can be seen that and , therefore . The instrument magnification of the Kepler tube is equal to the ratio of the focal lengths, so the lens always has a much larger focal length. For a correct description of the action of the pipe, it is necessary to consider inclined beams. A beam parallel to the axis is converted by the pipe into a beam of smaller diameter.
Therefore, more light energy enters the pupil of the eye than when directly observing, for example, stars. Stars are so small that their images are always formed on one "pixel" of the eye. With a tube, we cannot get an extended image of a star on the retina. However, the light from faint stars can be "concentrated". Therefore, through the tube you can see stars invisible to the eye. In the same way, it is explained why stars can be observed through a tube even during the day, when, when observed with a simple eye, their weak light is not visible against the background of a brightly luminous atmosphere.
The Kepler tube has two shortcomings, corrected in Galileo's trumpet. First, the length of the Kepler tube tube is equal to the sum of the focal lengths of the objective and the eyepiece. That is, this is the maximum possible length. Secondly, and most importantly, this tube is inconvenient to use in terrestrial conditions, since it gives an inverted image. The downward beam of rays is transformed into an upward beam. For astronomical observations, this is not so important, and in spotting scopes for observing terrestrial objects it is necessary to make special “flipping” systems of prisms.
Trumpet of Galileo arranged differently (left figure).
It consists of a converging (objective) and a diverging (eyepiece) lens, with their common focus now on the right. Now the length of the tube is not the sum, but the difference between the focal lengths of the lens and the eyepiece. In addition, since the rays deviate from the optical axis in one direction, the image is straight. The path of the beam and its transformation, the increase in the angle φ is shown in the figure. Having carried out a slightly more complex geometric reasoning, we will come to the same formula for instrumental magnification of Galileo's tube. .
To observe astronomical objects, one more problem has to be solved. Astronomical objects, as a rule, are weakly luminous. Therefore, a very small light flux enters the pupil of the eye. To increase it, it is necessary to "collect" light from the largest possible surface on which it falls. Therefore, the diameter of the objective lens is made as large as possible. But large-diameter lenses are very heavy, and in addition, they are difficult to manufacture and are sensitive to temperature changes and mechanical deformations that distort the image. Therefore, instead of refracting telescopes(refract-refract), began to use more often reflecting telescopes(reflect- reflect). The principle of operation of the reflector is that the role of the lens that gives a real image is played not by a converging lens, but by a concave mirror. The figure on the right shows Maksutov's ingenious portable reflecting telescope. A wide beam of rays is collected by a concave mirror, but before reaching the focus, it is turned by a flat mirror so that its axis becomes perpendicular to the tube axis. Point s is the focus of the eyepiece, a small lens. After that, the beam, which has become almost parallel, is observed by the eye. The mirror almost does not interfere with the light flux entering the pipe. The design is compact and convenient. The telescope is directed to the sky, and the viewer looks into it from the side, and not along the axis. Therefore, the line of sight is horizontal and convenient for observation.
In large telescopes, it is not possible to create lenses with a diameter of more than a meter. A high-quality concave metal mirror can be made up to 10 m in diameter. Mirrors are more resistant to temperature effects, therefore all the most powerful modern telescopes are reflectors.
Determining the magnification of a spotting scope with a rod. If you point the pipe at a nearby rail, then you can count how many divisions of the rail N, visible to the naked eye, correspond to n divisions of the rail visible through the pipe. To do this, you need to look alternately into the pipe and at the rail, projecting the divisions of the rail from the field of view of the pipe onto the rail visible to the naked eye.
High-precision geodetic instruments have interchangeable eyepieces with different focal lengths, and changing the eyepiece allows you to change the magnification of the tube depending on the observation conditions.
The magnification of the Kepler tube is equal to the ratio of the focal length of the objective to the focal length of the eyepiece.
Let us denote by γ the angle at which n divisions are visible in the pipe and N divisions without the pipe (Fig. 3.8). Then one division of the rail is visible into the pipe at an angle:
α = γ / n,
and without a pipe - at an angle:
β = γ / N.
Fig.3.8
Hence: V = N / n.
The increase in the pipe can be approximately calculated by the formula:
V = D / d, (3.11)
where D is the input diameter of the lens;
d is the diameter of the outlet of the pipe (but not the diameter of the eyepiece).
The field of view of the pipe. The field of view of the pipe is the area of space visible through the pipe when it is stationary. The field of view is measured by the angle ε, the apex of which lies in the optical center of the lens, and the sides touch the edges of the diaphragm opening (Fig. 3.9). Aperture with a diameter of d1 is installed inside the tube in the focal plane of the lens. Figure 3.11 shows that:
where
Fig.3.9.
Usually, in geodetic instruments, d1 = 0.7 * fok is taken, then in radian measure:
ε = 0.7 / V.
If ε is expressed in degrees, then:
ε = 40o / V . (3.12)
The greater the magnification of the pipe, the smaller its angle of view. So, for example, at V = 20x ε = 2o, and at V = 80x ε = 0.5o.
The resolution of the pipe is estimated by the formula:
For example, at V = 20x ψ = 3″; at such an angle, an object 5 cm in size is visible at a distance of 3.3 km; the human eye can see this object at a distance of only 170 m.
Net of threads. The correct aiming of the telescope at the object is considered to be when the image of the object is exactly in the center of the field of view of the telescope. To eliminate the subjective factor when finding the center of the field of view, it is designated by a grid of threads. A grid of threads is, in the simplest case, two mutually perpendicular strokes applied to a glass plate, which is attached to the pipe diaphragm. The net of threads happens different types; Figure 3.10 shows some of them.
The net of threads has correction screws: two lateral (horizontal) and two vertical. The line connecting the center of the reticle and the optical center of the lens is called the line of sight or line of sight of the tube.
Fig.3.10
Placement of the tube on the eye and on the subject. When pointing the pipe at an object, you must simultaneously clearly see the grid of threads and the image of the object in the eyepiece. By installing a pipe over the eye, a clear image of the grid of threads is achieved; to do this, move the eyepiece relative to the grid of threads by rotating the corrugated ring on the eyepiece. Setting the pipe on the subject is called focusing the pipe. The distance to the objects under consideration varies, and according to formula (3.6), when a changes, the distance b to its image also changes. In order for the image of an object to be clear when viewed through the eyepiece, it must be located in the plane of the grid of threads. By moving the ocular part of the tube along the main optical axis, the distance from the reticle to the objective is changed until it becomes equal to b.
Tubes that focus by changing the distance between the lens and the reticle are called external focusing tubes. Such pipes have a large and, moreover, variable length; they are leaky, so dust and moisture get inside them; they do not focus on close objects at all. Spotting scopes with external focusing are not used in modern measuring instruments.
More perfect are pipes with internal focusing (Fig. 3.11); they use an additional movable diverging lens L2, which together with the lens L1 forms an equivalent lens L. When the lens L2 is moved, the distance between the lenses l changes and, consequently, the focal length f of the equivalent lens changes. The image of an object located in the focal plane of the lens L also moves along the optical axis, and when it hits the plane of the reticle, it becomes clearly visible in the eyepiece of the tube. Pipes with internal focusing are shorter; they are sealed and allow you to observe close objects; in modern measuring instruments, such spotting scopes are mainly used.
