Lenses, as a rule, have a spherical or close to spherical surface. They can be concave, convex or flat (radius equals infinity). They have two surfaces through which light passes. They can be combined in different ways, forming different types of lenses (photo is given later in the article):
- If both surfaces are convex (curved outward), the central part is thicker than at the edges.
- A lens with a convex and concave spheres is called a meniscus.
- A lens with one flat surface is called flat-concave or flat-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 their thickness in the central part is greater than at the edges, they are called collecting. Have a positive focal length. The following types of collecting lenses are distinguished:
- flat 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, then they are called scattering. 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 one point. They are called a bunch. When the beam enters the lens, each ray is refracted, changing its direction. For this reason, the beam can exit the lens to a greater or lesser extent diverging.
Some types of optical lenses change the direction of the rays so much that they converge at one point. If the light source is located at least at the focal length, the beam converges at a point remote at least by 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 actual image.
An array of point sources distributed on a generally flat surface is important. An example is a pattern on frosted glass, backlit. Another example is a filmstrip lit from behind so that light from it passes through a lens that magnifies the image on a flat screen many times.
In these cases, they speak of a plane. Points on the image plane 1: 1 correspond to points on the plane of the object. The same applies to geometric shapes, although the resulting image may be turned upside down or from left to right with respect to the object.
The convergence of the rays at one point creates a real image, and the difference is imaginary. When it is clearly outlined on the screen, it is valid. If the image can be observed only by looking through the lens towards the light source, then it is called imaginary. The reflection in the mirror is imaginary. The picture that can be seen through the telescope is also. But the projection of the camera lens onto the film gives a valid image.
Focal length
The focus of the lens can be found by passing a beam of parallel rays through it. The point at which they converge will be its focus F. The distance from the focal point to the lens is called its focal length f. Parallel rays can also be skipped on the other hand and thus find F on 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
A positive focal length is characterized by collecting lenses. Types of lenses of this type (flat-convex, biconvex, meniscus) reduce the rays coming out of them, more than they were reduced to this. Collecting lenses can form both a real and an imaginary image. The first is formed only if the distance from the lens to the object exceeds the focal length.
Negative focal lengths are characterized by scattering lenses. Types of lenses of this type (flat-concave, biconcave, meniscus) produce more rays than they were diluted before reaching 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
Care should be taken to distinguish convergence or divergence of rays from convergence or divergence of the lens. Types of lenses and light beams may not match. Rays associated with an object or image point are called diverging if they “scatter” and converging if they “gather” together. In any coaxial optical system, the optical axis is the path of the rays. A beam along this axis passes without any change in direction of motion due to refraction. This is essentially a good definition of the optical axis.
A beam that moves away from the optical axis with distance is called diverging. And the one that gets closer to her is called convergent. Rays parallel to the optical axis have zero convergence or divergence. Thus, when talking about the convergence or divergence of one beam, it is correlated with the optical axis.
Some types of lenses, the physics of which is such that the beam deviates to a greater extent to the optical axis, are collecting. In them, converging rays approach each other even more, and diverging rays move away less. They are even able, if their strength is sufficient for this, to make the beam parallel or even converging. Similarly, a scattering lens can dilute diverging rays even more, and converging - make parallel or diverging.
Magnifying glasses
A lens with two convex surfaces is thicker in the center than at the edges, and can be used as a simple magnifying glass or magnifier. In this case, the observer look through it at an imaginary, enlarged image. The camera lens, however, forms on the film or sensor the actual, usually reduced in size compared 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 power of 5 diopters, f = 20 cm. It is the diopter that the optometrist indicates when writing out a prescription for glasses. Say he recorded 5.2 diopters. In the workshop, they will take the finished workpiece of 5 diopters, obtained at the manufacturer, 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 strength is equal to the sum of each diopter: D = D 1 + D 2 .
Galileo's pipe
In the days of Galileo (beginning of the XVII century), glasses in Europe were widely available. They were usually made in Holland and distributed by street vendors. Galileo heard that someone in the Netherlands put two kinds of lenses in a tube so that distant objects seemed larger. He used a telephoto lens at one end of the tube, and a telephoto lens at the other end. If the focal length of the lens is f o and the eyepiece f e , then the distance between them should be f o -f e , and the force (angular increase) f o / f e . Such a scheme is called the Galileo pipe.
The telescope has a magnification of 5 or 6 times, comparable to modern manual binoculars. This is enough for many exciting astronomical observations. You can easily see lunar craters, the four moons of Jupiter, the rings of Saturn, the phases of Venus, nebulae and star clusters, as well as faint stars in the Milky Way.
Kepler telescope
Kepler heard about all this (he and Galileo corresponded) and built another view of the telescope with two collecting lenses. The one with a large focal length is the lens, and the one with less is the eyepiece. The distance between them is f o + f e , and the angular increase is f o / f e . This Keplerian (or astronomical) 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 Galileo telescope, and was more convenient to use, since it allowed you to keep your eyes in a fixed position and see the entire field of view from edge to edge. The device allowed to achieve a higher magnification than the Galileo pipe, without serious deterioration.
Both telescopes suffer from spherical aberration, resulting in images that are not fully focused, and chromatic aberration, which creates color halos. Kepler (and Newton) believed that these defects could not be overcome. They did not assume that achromatic types of lenses are possible , the physics of which will become known only in the 19th century.
Reflex telescopes
Gregory suggested that mirrors can be used as telescope lenses, since they lack color fringing. Newton took advantage of this idea and created the Newtonian form of a telescope from a concave silver-plated mirror and a positive eyepiece. He handed the sample to the Royal Society, where it is to this day.
A single-lens telescope can project an image onto a screen or film. For proper magnification, a positive lens with a large focal length of, say, 0.5 m, 1 m or many meters is required. This arrangement is often used in astronomical photography. To people unfamiliar with optics, a paradoxical situation may appear when a weaker telephoto lens gives a larger increase.
Spheres
It has been suggested that ancient cultures may have had telescopes because they made small glass beads. The problem is that it is not known what they were used for, and they, of course, could not form the basis of a good telescope. Balls could be used to enlarge small objects, but the quality was hardly satisfactory.
The focal length of an ideal glass sphere is very 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 equatorial groove to block the rays that cause image defects, it turns from a very mediocre magnifier into a beautiful one. Such a decision is attributed to Coddington, and a magnifier for his name can be purchased today in the form of small hand loops for studying very small objects. But there is no evidence that this was done before the 19th century.