Lenses, as a rule, have a spherical or closeto a spherical surface. They can be concave, convex or flat (the radius is equal to infinity). They have two surfaces through which light passes. They can be combined in different ways, forming different types of lenses (photo is given further in the article):
- If both surfaces are convex (curved outwards), the central part is thicker than at the edges.
- A lens with a convex and concave sphere is called a meniscus.
- A lens with one flat surface is called flat-concave or plane-convex, depending on the nature of the other sphere.
How to determine the type of lens? Let us dwell on this in more detail.
Collecting lenses: types of lenses
Regardless of the combination of surfaces, if theirthe thickness in the central part is greater than at the edges, they are called collectors. Have a positive focal length. There are the following types of collecting lenses:
- plane-convex,
- biconvex,
- concave-convex (meniscus).
They are also called "positive".
Scattering lenses: types of lenses
If their thickness in the center is thinner than at the edges, they are called scatterers. They have a negative focal length. There are such types of scattering lenses:
- flat-concave,
- biconcave,
- convex-concave (meniscus).
They are also called "negative".
Basic concepts
Rays from a point source diverge from onepoints. They are called a bundle. When the beam enters the lens, each beam is refracted, changing its direction. For this reason, the beam can leave the lens more or less divergent.
Some types of optical lenses changeThe direction of the rays is such that they converge at one point. If the light source is located at least at the focal length, then the beam converges at a point that is at least at the same distance.
Real and imaginary images
A point source of light is called a real object, and the point of convergence of the beam of rays emerging from the lens is its real image.
An important point is the array of point sources,distributed on, as a rule, a flat surface. An example is a picture on the frosted glass, highlighted at the back. Another example is a filmstrip, illuminated from behind so that the light from it passes through a lens, multiplying the image on a flat screen.
In these cases one speaks of a plane.Points on the image plane 1: 1 correspond to points on the plane of the object. The same applies to geometric figures, although the resulting picture may be inverted with respect to the object from top to bottom or from left to right.
The convergence of the rays at one point createsThe actual image, and the discrepancy is imaginary. When it is clearly outlined on the screen - it is real. If the image can be observed, only looking through the lens in the direction of the light source, it is called imaginary. Reflection in the mirror is imaginary. A picture that can be seen through a telescope - too. But the projection of the camera lens onto the film gives a real image.
Focal length
Focus of the lens can be found by passing through ita beam of parallel rays. The point at which they converge will be the focus of F. The distance from the focal point to the lens is called the focal length f. Parallel rays can also be missed on the other side and thus find F from both sides. Each lens has two F and two f. If it is relatively thin compared to its focal lengths, then the latter are approximately equal.
Divergence and convergence
Positive focal lengthCollecting lenses are characterized. Types of lenses of this type (plano-convex, biconvex, meniscus) reduce the rays emerging from them, more than they were reduced to before. Collecting lenses can form both a real and imaginary image. The first is formed only if the distance from the lens to the object exceeds the focal length.
Negative focal lengthcharacterized by scattering lenses. Types of lenses of this type (flat-concave, biconcave, meniscus) dilute the rays more than they were divorced before they hit their surface. Scattering lenses create an imaginary image. And only when the convergence of the incident rays is significant (they converge somewhere between the lens and the focal point on the opposite side), the formed rays can still converge, forming a real image.
Important differences
It should be very careful to distinguishconvergence or divergence of the rays from the convergence or divergence of the lens. Types of lenses and light beams may not coincide. Rays associated with an object or a point of the image are called divergent if they "scatter" and converge if they "assemble" together. In any coaxial optical system, the optical axis is the path of the rays. The beam along this axis passes without any change in the direction of motion due to refraction. This, in fact, a good definition of the optical axis.
A ray that moves away fromThe optical axis is called divergent. And the one that gets closer to it is called convergent. The rays parallel to the optical axis have zero convergence or divergence. Thus, when one speaks of the convergence or divergence of one ray, it is correlated with the optical axis.
Some types of lenses, the physics of which is such thatThe beam deviates more towards the optical axis, are collecting. In them the convergent rays converge even more, and the divergent rays retreat less. They are even able, if their strength is sufficient for this, to make the beam parallel or even converging. Similarly, the scattering lens can dilute the divergent rays even more, and the converging ones can be made parallel or divergent.
Magnifying glasses
A lens with two convex surfaces is thicker incenter than the edges, and can be used as a simple magnifying glass or magnifying glass. At the same time, the observer looks through it to an imaginary, enlarged image. The camera lens, however, forms a real, usually reduced in size, on the film or sensor in comparison with the object.
Glasses
The ability of a lens to change the convergence of light is called its strength. It is expressed in diopters D = 1 / f, where f is the focal length in meters.
For a lens with a force of 5 diopters f = 20 cm.It is the diopter that the oculist points out, prescribing a prescription for glasses. Say, he recorded 5.2 diopters. In the workshop, take a ready stock of 5 diopters obtained at the factory, and polish a little one surface to add 0.2 diopters. The principle is that for thin lenses in which two spheres are located close to each other, the rule is observed, according to which their total force is equal to the sum of dioptries of each: D = D1 + D2.
The Galileo Pipe
In the time of Galileo (the beginning of the XVII century), glasses inEurope was widely available. They, as a rule, were made in Holland and distributed by street vendors. Galileo heard that someone in the Netherlands put two kinds of lenses in the tube, so that distant objects seemed bigger. He used a long-focus collecting lens at one end of the tube, and a short-focus diffusing eyepiece at the other end. If the focal length of the lens is fabout and the eyepiece fe, then the distance between them must be fabout-fe, and the force (angular magnification) fabout/ fe. Such a scheme is called the Galilean pipe.
The telescope has an increase of 5 or 6 times,comparable to modern hand-held binoculars. This is enough for many exciting astronomical observations. You can easily see the lunar craters, the four moons of Jupiter, the rings of Saturn, the phases of Venus, the nebulae and star clusters, and the weak stars in the Milky Way.
Kepler's telescope
Kepler heard about all this (he and Galileo conductedcorrespondence) and built another kind of telescope with two collecting lenses. The one with the large focal length is the lens, and the one with the smaller focal length is an eyepiece. The distance between them is fabout + fe, and the angular magnification is fabout/ fe. This Keplerian (or astronomical)The telescope creates an inverted image, but for stars or the moon it does not matter. This scheme provided a more uniform illumination of the field of view than the Galilean telescope, and was more convenient to use, since it allowed to keep the eyes in a fixed position and to see the entire field of view from edge to edge. The device allowed to achieve a higher increase than the Galileo pipe, without serious deterioration in quality.
Both telescopes suffer from spherical aberration,as a result of which the images are not fully focused, and chromatic aberration creating color halos. Kepler (and Newton) believed that these defects can not be overcome. They did not assume that achromatic types of lenses are possible, the physics of which will be known only in the XIX century.
Mirror Telescopes
Gregory suggested that as lensesTelescopes can use mirrors, as they lack a colored border. Newton took advantage of this idea and created the Newtonian shape of the telescope from a concave silvered mirror and a positive eyepiece. He handed the sample to the Royal Society, where it is to this day.
Single-lens telescope can projectimage on the screen or film. A proper magnification requires a positive lens with a long focal length, say, 0.5 m, 1 m, or many meters. Such an arrangement is often used in astronomical photography. People unfamiliar with optics may find it paradoxical when a weaker long-focus lens gives a greater magnification.
Spheres
It has been suggested that the ancientscultures may have had telescopes because they made small glass balls. The problem is that it is unknown what they were used for, and of course they could not form the basis of a good telescope. The balls could be used to increase small objects, but the quality was hardly satisfactory.
Focal length of an ideal glass spherevery short and forms a real image very close to the sphere. In addition, aberrations (geometric distortions) are significant. The problem lies in the distance between the two surfaces.
However, if you make a deep equatorialthe groove to block the rays that cause image defects, it turns from a very mediocre magnifier to a beautiful one. Such a decision is attributed to Coddington, and the enlarger of his name can be purchased today in the form of small hand-held loops to study very small objects. But there is no evidence that this was done before the 19th century.
