Lens examples. Optical lenses (physics): definition, description, formula and solution. Lighting and projection devices. Searchlights

Lenses. Optical devices

Lens is called a transparent body, which is bounded by two curved surfaces.

The lens is called thin if its thickness is much less than the radii of curvature of its surfaces.

The straight line passing through the centers of curvature of the lens surfaces is called the main optical axis of the lens. If one of the lens surfaces is a plane, then the optical axis runs perpendicular to it (Fig. 1).

The point on a thin lens through which rays pass without changing their direction is called optical center lenses. The main optical axis passes through the optical center.

Any other straight line passing through the optical center of the lens is called secondary axis lenses. The point at which the rays of light converge, running parallel to the main optical axis, is called focus.

The plane passing through the focus perpendicular to the main optical axis is called focal plane.

Thin lens formula (Fig. 2):

In formula (1), the quantities a 1 , a 2 , r 1 and r 2 are considered positive if their counting directions from the optical center of the lens coincide with the direction of light propagation; otherwise, these values ​​are considered negative.

Lenses are the main element of many optical devices.

The eye, for example, is an optical device, where the cornea and lens act as lenses, and the image of the object is obtained on the retina of the eye.

angle of view called the angle formed by the rays that pass from extreme points object or its image through the optical center of the lens of the eye.

Many optical devices are designed to obtain images of objects on screens, on light-sensitive films, or in the eye.

Apparent magnification of the optical device:

The lens in an optical device facing the object (object) is called the lens; the lens facing the eye is called the eyepiece. In technical instruments, the objective and the eyepiece consist of several lenses. This partially eliminates errors in the images.

Magnifier magnification (Fig. 3):

The reciprocal of the focal length is called optical power lenses: AT = 1/f. The unit of optical power of a lens is the diopter ( D) equal to the optical power of a lens with a focal length of 1 m.

The optical power of two thin lenses put together is equal to the sum of their optical powers.

Lens A transparent body bounded by two spherical surfaces is called. If the thickness of the lens itself is small compared to the radii of curvature of spherical surfaces, then the lens is called thin .

Lenses are part of almost all optical devices. Lenses are gathering and scattering . The converging lens in the middle is thicker than at the edges, the diverging lens, on the contrary, is thinner in the middle part (Fig. 3.3.1).

Straight line passing through the centers of curvature O 1 and O 2 spherical surfaces, called main optical axis lenses. In the case of thin lenses, we can approximately assume that the main optical axis intersects with the lens at one point, which is commonly called optical center lenses O. A beam of light passes through the optical center of the lens without deviating from its original direction. All lines passing through the optical center are called side optical axes .

If a beam of rays parallel to the main optical axis is directed to the lens, then after passing through the lens the rays (or their continuation) will gather at one point F, which is called main focus lenses. A thin lens has two main foci located symmetrically on the main optical axis relative to the lens. Converging lenses have real foci, diverging lenses have imaginary foci. Beams of rays parallel to one of the secondary optical axes, after passing through the lens, are also focused to a point F", which is located at the intersection of the side axis with focal plane F, that is, a plane perpendicular to the main optical axis and passing through the main focus (Fig. 3.3.2). Distance between the optical center of the lens O and main focus F called the focal length. It is denoted by the same F.

The main property of lenses is the ability to give images of objects . Images are direct and upside down , valid and imaginary , at magnified and reduced .

The position of the image and its nature can be determined using geometric constructions. To do this, use the properties of some standard rays, the course of which is known. These are rays passing through the optical center or one of the foci of the lens, as well as rays parallel to the main or one of the secondary optical axes. Examples of such constructions are shown in Figs. 3.3.3 and 3.3.4.

Note that some of the standard beams used in Fig. 3.3.3 and 3.3.4 for imaging do not pass through the lens. These rays do not really participate in the formation of the image, but they can be used for constructions.

The position of the image and its nature (real or imaginary) can also be calculated using thin lens formulas . If the distance from the object to the lens is denoted by d, and the distance from the lens to the image through f, then the thin lens formula can be written as:

the value D reciprocal of the focal length. called optical power lenses. The unit of optical power is diopter (dptr). Diopter - optical power of a lens with a focal length of 1 m:

The formula for a thin lens is similar to that for a spherical mirror. It can be obtained for paraxial rays from the similarity of triangles in Fig. 3.3.3 or 3.3.4.

It is customary to attribute the focal lengths of lenses certain signs: for converging lens F> 0, for scattering F < 0.

Quantities d and f also subject to certain rule signs:

d> 0 and f> 0 - for real objects (that is, real light sources, and not continuations of rays converging behind the lens) and images;

d < 0 и f < 0 - для мнимых источников и изображений.

For the case shown in Fig. 3.3.3, we have: F> 0 (converging lens), d = 3F> 0 (real item).

According to the thin lens formula, we get: so the image is real.

In the case shown in Fig. 3.3.4, F < 0 (линза рассеивающая), d = 2|F| > 0 (real item), , that is, the image is imaginary.

Depending on the position of the object in relation to the lens, the linear dimensions of the image change. Linear zoom lens Γ is the ratio of the linear dimensions of the image h" and subject h. size h", as in the case of a spherical mirror, it is convenient to assign plus or minus signs depending on whether the image is upright or inverted. Value h always considered positive. Therefore, for direct images Γ > 0, for inverted images Γ< 0. Из подобия треугольников на рис. 3.3.3 и 3.3.4 легко получить формулу для линейного увеличения тонкой линзы:

In the considered example with a converging lens (Fig. 3.3.3): d = 3F > 0, , Consequently, - the image is inverted and reduced by 2 times.

In the diverging lens example (Figure 3.3.4): d = 2|F| > 0, ; therefore, the image is straight and reduced by 3 times.

optical power D lens depends on both the radii of curvature R 1 and R 2 of its spherical surfaces, and on the refractive index n the material from which the lens is made. In optics courses, the following formula is proved:

The radius of curvature of a convex surface is considered positive, and that of a concave surface is negative. This formula is used in the manufacture of lenses with a given optical power.

In many optical instruments, light passes sequentially through two or more lenses. The image of the object given by the first lens serves as the object (real or imaginary) for the second lens, which builds the second image of the object. This second image can also be real or imaginary. The calculation of an optical system of two thin lenses is reduced to applying the lens formula twice, with the distance d 2 from the first image to the second lens should be set equal to the value l - f 1 , where l is the distance between the lenses. The value calculated from the lens formula f 2 determines the position of the second image and its character ( f 2 > 0 - real image, f 2 < 0 - мнимое). Общее линейное увеличение Γ системы из двух линз равно произведению линейных увеличений обеих линз: Γ = Γ 1 · Γ 2 . Если предмет или его изображение находятся в бесконечности, то линейное увеличение утрачивает смысл, изменяются только угловые расстояния.

A special case is the telescopic path of rays in a system of two lenses, when both the object and the second image are at infinity. long distances. The telescopic path of the rays is realized in spotting scopes - Kepler astronomical tube and Galileo's earth tube .

Thin lenses have a number of disadvantages that do not allow obtaining high-quality images. Distortions that occur during image formation are called aberrations . The main ones are spherical and chromatic aberrations. Spherical aberration manifests itself in the fact that in the case of wide light beams, rays far from the optical axis cross it out of focus. The thin lens formula is valid only for rays close to the optical axis. The image of a distant point source, created by a wide beam of rays refracted by a lens, is blurred.

Chromatic aberration occurs because the refractive index of the lens material depends on the wavelength of light λ. This property of transparent media is called dispersion. The focal length of the lens is different for light with different lengths waves, which leads to blurring of the image when using non-monochromatic light.

Modern optical instruments do not use thin lenses, but complex multilens systems in which various aberrations can be approximately eliminated.

The formation of a real image of an object by a converging lens is used in many optical devices, such as a camera, a projector, etc.

Camera is a closed light-tight chamber. The image of photographed objects is created on photographic film by a lens system called lens . A special shutter allows you to open the lens during exposure.

A feature of the operation of the camera is that on a flat photographic film, sufficiently sharp images of objects located at different distances should be obtained.

In the plane of the film, only images of objects that are at a certain distance are sharp. Focusing is achieved by moving the lens relative to the film. Images of points that do not lie in the sharp pointing plane are blurred in the form of circles of scattering. The size d these circles can be reduced by aperture of the lens, i.e. decrease relative borea / F(Fig. 3.3.5). This results in an increase in the depth of field.

projection apparatus designed for large scale imaging. Lens O projector focuses the image of a flat object (transparency D) on the remote screen E (Fig. 3.3.6). Lens system K called condenser , designed to concentrate the light source S on a diapositive. Screen E creates a truly enlarged inverted image. The magnification of the projection apparatus can be changed by zooming in or out of the screen E while changing the distance between the transparencies D and lens O.

Most important application refraction of light is the use of lenses, which are usually made of glass. In the figure you see cross sections of various lenses. Lens called a transparent body bounded by spherical or flat-spherical surfaces. Any lens that is thinner in the middle than at the edges will, in a vacuum or gas, diverging lens. Conversely, any lens that is thicker in the middle than at the edges will converging lens.

For clarification, refer to the drawings. On the left, it is shown that the rays traveling parallel to the main optical axis of the converging lens, after it "converge", passing through the point F - valid main focus converging lens. On the right, the passage of light rays through a diverging lens is shown parallel to its main optical axis. The rays after the lens "diverge" and seem to come from the point F ', called imaginary main focus diverging lens. It is not real, but imaginary because the rays of light do not pass through it: only their imaginary (imaginary) extensions intersect there.

In school physics, only the so-called thin lenses, which, regardless of their "sectional" symmetry, always have two main foci located at equal distances from the lens. If the rays are directed at an angle to the main optical axis, then we will find many other foci in the converging and / or diverging lens. These, side tricks, will be located away from the main optical axis, but still in pairs at equal distances from the lens.

A lens can not only collect or scatter rays. Using lenses, you can get enlarged and reduced images of objects. For example, thanks to a converging lens, an enlarged and inverted image of a golden figurine is obtained on the screen (see figure).

Experiments show: a distinct image appears, if the object, lens and screen are located at certain distances from each other. Depending on them, images can be inverted or straight, enlarged or reduced, real or imaginary.

The situation when the distance d from the object to the lens is greater than its focal length F, but less than the double focal length 2F, is described in the second row of the table. This is exactly what we observe with the figurine: its image is real, inverted and enlarged.

If the image is real, it can be projected onto a screen. In this case, the image will be visible from any place in the room from which the screen is visible. If the image is imaginary, then it cannot be projected onto the screen, but can only be seen with the eye, positioning it in a certain way in relation to the lens (you need to look “into it”).

Experiences show that diverging lenses give a reduced direct virtual image at any distance from the object to the lens.

A lens is an optical part bounded by two refractive surfaces, which are the surfaces of bodies of revolution, one of which may be flat. Lenses are usually round shape, but may also have a rectangular, square, or some other configuration. As a rule, the refractive surfaces of a lens are spherical. Aspherical surfaces are also used, which can be in the form of surfaces of revolution of an ellipse, hyperbola, parabola and curves. higher order. In addition, there are lenses whose surfaces are part of the lateral surface of the cylinder, called cylindrical. Also used are toric lenses with surfaces having different curvature in two mutually perpendicular directions.

As individual optical parts, lenses are almost never used in optical systems, with the exception of simple magnifiers and field lenses (collectives). They are usually used in various complex combinations, such as glued two or three lenses and sets of a number of single and glued lenses.

Depending on the shape, there are collective (positive) and diverging (negative) lenses. The group of converging lenses usually includes lenses, in which the middle is thicker than their edges, and the group of diverging lenses is lenses, the edges of which are thicker than the middle. It should be noted that this is true only if the refractive index of the lens material is greater than that of environment. If the refractive index of the lens is less, the situation will be reversed. For example, an air bubble in water is a biconvex diffusing lens.

Lenses are characterized, as a rule, by their optical power (measured in diopters), or focal length, as well as aperture. For the construction of optical devices with corrected optical aberration (primarily chromatic aberration due to light dispersion, achromats and apochromats), other properties of lenses / their materials are also important, for example, the refractive index, the dispersion coefficient, the transmittance of the material in the selected optical range.

Sometimes lenses/lens optical systems(refractors) are specifically designed for use in media with a relatively high refractive index.

Types of lenses

Collective:

1 -- biconvex

2 -- flat-convex

3 -- concave-convex (positive meniscus)

Scattering:

4 -- biconcave

5 -- flat-concave

6 -- convex-concave (negative meniscus)

A convex-concave lens is called a meniscus and can be converging (thickens towards the middle) or divergent (thickens towards the edges). The meniscus, whose surface radii are equal, has optical power, zero(used for dispersion correction or as a cover lens). So, the lenses of myopic glasses are usually negative menisci. A distinctive property of a converging lens is the ability to collect rays incident on its surface at one point located on the other side of the lens.

The main elements of the lens

NN - the main optical axis - a straight line passing through the centers of spherical surfaces limiting the lens; O - optical center - a point that, for biconvex or biconcave (with the same surface radii) lenses, is located on the optical axis inside the lens (in its center).

If a luminous point S is placed at some distance in front of the converging lens, then a beam of light directed along the axis will pass through the lens without being refracted, and rays that do not pass through the center will be refracted towards the optical axis and intersect on it at some point F, which and will be the image of the point S. This point is called the conjugate focus, or simply the focus.

If light from a very distant source falls on the lens, the rays of which can be represented as traveling in a parallel beam, then upon exiting the lens, the rays will be refracted at a large angle and the point F will move closer to the lens on the optical axis. Under these conditions, the point of intersection of the rays emerging from the lens is called the main focus F, and the distance from the center of the lens to the main focus is called the main focal length.

Rays incident on a diverging lens, upon exiting it, will be refracted towards the edges of the lens, that is, they will be scattered. If these rays continue in the opposite direction as shown in the figure by the dotted line, then they will converge at one point F, which will be the focus of this lens. This focus will be imaginary.

What has been said about the focus on the main optical axis applies equally to those cases when the image of a point is located on a secondary or inclined optical axis, i.e., a line passing through the center of the lens at an angle to the main optical axis. The plane perpendicular to the main optical axis, located at the main focus of the lens, is called the main focal plane, and at the conjugate focus, simply the focal plane.

Collecting lenses can be directed to the object by any side, as a result of which the rays passing through the lens can be collected from one or the other side of it. Thus, the lens has two focuses - front and rear. They are located on the optical axis on both sides of the lens.

A lens is an optical part that is made from transparent material(optical glass or plastic) and has two refractive polished surfaces (flat or spherical). The oldest lens found by archaeologists at Nimrud is about 3,000 years old.

This suggests that people from very ancient times were interested in optics and tried to use it to create various equipment that helps in Everyday life. The Roman military used lenses to make fire in field conditions, and the emperor Nero used a concave emerald as a remedy for his myopia.

Over time, optics became closely integrated into medicine, which made it possible to create devices for vision correction such as eyepieces, glasses and contact lenses. In addition, the lenses themselves are widely used in various high-precision technology, which has made it possible to radically change a person's ideas about the world around him.

What is a lens, what properties and features does it have?

Any lens in a section can be represented as two prisms placed on top of each other. Depending on which side they are in contact with each other, the optical effect of the lens will also differ, as well as its appearance (convex or concave).

Consider what a lens is in more detail. For example, if we take a piece of ordinary window glass, the edges of which are parallel, we will get a completely insignificant distortion. visible image. That is, a ray of light entering the glass will be refracted, and after passing through the second face and entering the air, it will return the previous value of the angle with a slight shift, which depends on the thickness of the glass. But if the glass planes are at an angle relative to each other (for example, as in a prism), then the beam, regardless of its angle, after hitting the given glass body, will be refracted and exit at its base. This rule, which allows you to control the luminous flux, is the basis of all lenses. It is worth noting that all the features of lenses and optical devices based on them.

What are the types of lenses in physics?

There are only two main types of lenses: concave and convex, also called diverging and converging. They allow you to split the beam of light or vice versa to concentrate it at one point at a certain focal length.

A convex lens has thin edges and a thicker center, making it easier to see through
represented as two prisms connected by bases. This feature of it allows you to collect all the rays of light falling at different angles to one point in the center. It was these devices that the Romans used to kindle fires, since focused beams sunlight allowed to create a very high temperature on a small area of ​​​​a highly flammable object.

In what devices and what are lenses used for?

Since ancient times, people have known what a lens is. This detail was used in the first glasses, which appeared in the 1280s in Italy. Later, spyglasses, telescopes, binoculars and many other devices were created, which consisted of many different lenses and made it possible to significantly expand the possibilities human eye. Microscopes were built on the same principles, which had a significant impact on the development of science as a whole.

The first televisions were equipped with huge lenses that magnified the image.
from miniature screens and made it possible to examine the picture in more detail. All video and photographic equipment, starting from the very first devices, is equipped with lenses. They are installed in the lens so that the operator or photographer can focus or zoom in / out of the image in the frame.

Most modern mobile phones have autofocus cameras that use miniature lenses that allow you to take sharp pictures of objects that are a couple of centimeters or several kilometers from the lens of the device.

Do not forget about modern space telescopes (such as Hubble) and laboratory microscopes, which also have high-precision lenses. These devices give humanity the opportunity to see what was previously inaccessible to our vision. Thanks to them, we can study the world around us in more detail.

What is a contact lens and why is it needed?

Contact lenses are small, clear lenses made from soft or
rigid materials that are intended to be worn directly on the eye in order to correct vision. They were designed by Leonardo da Vinci in 1508, but were made only in 1888. Lenses were originally made from hard materials, but over time, new polymers were synthesized, which made it possible to create soft lenses almost imperceptible with daily use.

If you want to purchase contact lenses, then read the article to learn more about this device.