Types of lenses

Reflection and refraction of light are used to change the direction of rays or, as they say, to control light beams. This is the basis for the creation of special optical instruments, such as a magnifying glass, telescope, microscope, camera and others. The main part of most of them is the lens. For example, glasses are lenses enclosed in a frame. This example alone shows how important the use of lenses is for a person.

For example, in the first picture the flask is as we see it in life,

and on the second, if we look at it through a magnifying glass (the same lens).

Most often used in optics spherical lenses. Such lenses are bodies made of optical or organic glass, limited by two spherical surfaces.

Lenses are transparent bodies bounded on both sides by curved surfaces (convex or concave). The straight line AB passing through the centers C1 and C2 of the spherical surfaces limiting the lens is called the optical axis.

This figure shows cross sections of two lenses with centers at point O. The first lens shown in the figure is called convex, the second is called concave. Point O, lying on the optical axis at the center of these lenses, is called the optical center of the lens.

One of the two bounding surfaces may be flat.

On the left the lenses are convex,

on the right - concave.

We will consider only spherical lenses, that is, lenses bounded by two spherical surfaces.
Lenses bounded by two convex surfaces are called biconvex; lenses bounded by two concave surfaces are called biconcave.

By directing a beam of rays parallel to the main optical axis of the lens at a convex lens, we will see that after refraction in the lens, these rays are collected at a point called the main focus of the lens

- point F. The lens has two main foci, on both sides at the same distance from the optical center. If the light source is in focus, then after refraction in the lens the rays will be parallel to the main optical axis. Every lens has two focal points - one on each side of the lens. The distance from a lens to its focus is called the focal length of the lens.
Let us direct a beam of diverging rays from a point source lying on the optical axis to a convex lens. If the distance from the source to the lens is greater than the focal distance, then the rays, after refraction in the lens, will intersect the optical axis of the lens at one point. Consequently, a convex lens collects rays coming from sources located from the lens at a distance greater than its focal length. Therefore, a convex lens is otherwise called a converging lens.
When rays pass through a concave lens, a different picture is observed.
Let us send a beam of rays parallel to the optical axis onto a biconcave lens. We will notice that the rays will emerge from the lens in a diverging beam. If this diverging beam of rays enters the eye, then it will seem to the observer that the rays are coming out of point F. This point is called the imaginary focus of a biconcave lens. Such a lens can be called diverging.

Figure 63 explains the action of converging and diverging lenses. Lenses can be represented as a large number of prisms. Since prisms deflect rays, as shown in the figures, it is clear that lenses with thickening in the middle collect the rays, and lenses with thickening at the edges scatter them. The middle of the lens acts like a plane-parallel plate: it does not deflect rays in either the collecting or diverging lens

In the drawings, converging lenses are designated as shown in the figure on the left, and diverging lenses - in the figure on the right.

Among convex lenses there are: biconvex, plano-convex and concave-convex (respectively in the figure). All convex lenses have a wider middle cut than the edges. These lenses are called converging lenses. Among concave lenses there are biconcave, plano-concave and convex-concave (respectively in the figure). All concave lenses have a narrower middle section than the edges. These lenses are called diverging lenses.

Light is electromagnetic radiation, perceived by the eye by visual sensation.

• Law of rectilinear propagation of light: light propagates rectilinearly in a homogeneous medium
• A light source whose dimensions are small compared to the distance to the screen is called a point light source.

• The incident beam and the reflected beam lie in the same plane with the perpendicular restored to the reflecting surface at the point of incidence. Angle of incidence equal to angle reflections.
• If a point object and its reflection are swapped, the path of the rays will not change, only their direction will change.

A yawning reflecting surface is called a plane mirror if a beam of parallel rays incident on it remains parallel after reflection.

• A lens whose thickness is much less than the radii of curvature of its surfaces is called a thin lens.
• A lens that converts a beam of parallel rays into a converging one and collects it into one point is called a converging lens.
• A lens that converts a beam of parallel rays into a diverging one - diverging.

For a collecting lens

For a diverging lens:

For all positions of the object, the lens gives a reduced, virtual, direct image lying on the same side of the lens as the object.

Properties of the eye:

• accommodation (achieved by changing the shape of the lenses);
• adaptation (adaptation to different conditions illumination);
• visual acuity (the ability to separately distinguish two close points);
• field of view (the space observed when the eyes move but the head remains stationary)

Visual impairments

myopia (correction - diverging lens);

farsightedness (correction - converging lens).

A thin lens represents the simplest optical system. Simple thin lenses are used mainly in the form of glasses for glasses. In addition, the use of a lens as a magnifying glass is well known.

The action of many optical instruments - a projection lamp, a camera and other devices - can be schematically compared to the action of thin lenses. However, a thin lens gives a good image only in that relatively in a rare case, when you can limit yourself to a narrow single-color beam coming from the source along the main optical axis or at a large angle to it. In most practical problems, where these conditions are not met, the image produced by a thin lens is rather imperfect.
Therefore, in most cases, they resort to constructing more complex optical systems that have a large number of refractive surfaces and are not limited by the requirement of proximity of these surfaces (a requirement that is satisfied by a thin lens). [4]

4.2 Photographic apparatus. Optical instruments.

All optical instruments can be divided into two groups:

1) devices with which they obtain optical images on the screen. These include projection devices, cameras, movie cameras, etc.

2) devices that operate only in conjunction with through human eyes and do not form images on the screen. These include a magnifying glass, a microscope and various instruments of the telescope system. Such devices are called visual.

Camera.

Modern cameras have a complex and varied structure, but we will look at what basic elements a camera consists of and how they work.

Unlike prismatic and other diffusers, lenses in lighting devices are almost always used for spot lighting. As a rule, optical systems using lenses, they consist of a reflector (reflector) and one or more lenses.

Converging lenses direct light from an object located in focal point source into a parallel beam of light. As a rule, they are used in lighting structures together with a reflector. The reflector directs the light flux in the form of a beam in the desired direction, and the lens concentrates (collects) the light. The distance between the converging lens and the light source is usually varied, allowing you to adjust the angle you want to achieve.

A system of both a light source and a collecting lens (left) and a similar system of a source and a Fresnel lens (right). The angle of the light flux can be changed by changing the distance between the lens and the light source.

Fresnel lenses consist of separate concentric ring-shaped segments adjacent to each other. They received their name in honor of the French physicist Augustin Fresnel, who first proposed and put into practice such a design in lighthouse lighting fixtures. The optical effect of such lenses is comparable to the effect of using traditional lenses of similar shape or curvature.

However, Fresnel lenses have a number of advantages due to which they are found wide application in lighting structures. In particular, they are much thinner and cheaper to manufacture compared to converging lenses. Designers Francisco Gomez Paz and Paolo Rizzatto did not fail to take advantage of these features when working on a bright and magical range of models.

Made from lightweight, thin polycarbonate, Hope “sheets,” as Gomez Paz calls them, are nothing more than thin and large diffusion Fresnel lenses that create a magical, sparkling, and dimensional glow by being coated with a polycarbonate film textured with microprisms.

Paolo Rizzatto described the project this way:
“Why have crystal chandeliers lost their relevance? Because they are too expensive, very difficult to handle and produce. We broke down the idea itself into its components and modernized each of them.”

Here's what his colleague said about this:
“Several years ago, our attention was drawn to the wonderful capabilities of Fresnel lenses. Their geometric features make it possible to obtain the same optical properties as regular lenses, but on a completely flat surface of the petals.

However, the use of Fresnel lenses to create such unique products, combining an excellent design project with modern technological solutions, is still rare.

Such lenses are widely used in lighting scenes with spotlights, where they allow you to create an uneven light spot with soft edges, blending perfectly with the overall light composition. Nowadays, they have also become widespread in architectural lighting schemes, in cases where individual adjustment of the angle of light is required, when the distance between the illuminated object and the lamp can change.

The optical performance of a Fresnel lens is limited by the so-called chromatic aberration that forms at the junctions of its segments. Because of it, a rainbow border appears on the edges of images of objects. The fact that what appears to be a disadvantage of a lens has been turned into an advantage in once again highlights the strength of the authors' innovative thought and their attention to detail.

Lighthouse lighting design using Fresnel lenses. The image clearly shows the ring structure of the lens.

Projection systems consist of either an elliptical reflector or a combination of a parabolic reflector and a condenser that directs the light to a collimator, which can also be equipped with optical accessories. After which the light is projected onto the plane.

Spotlight systems: a uniformly illuminated collimator (1) directs the light flux through a lens system (2). On the left is a parabolic reflector, with high rate light output, on the right is a condenser that allows you to achieve high resolution.

The size of the image and the angle of light are determined by the features of the collimator. Simple curtains or iris diaphragms shape light rays different sizes. Contour masks can be used to create different contours for a light beam. You can project logos or images using a gobo lens with designs printed on them.

Different light angles or image size can be selected depending on the focal length of the lenses. Unlike lighting devices using Fresnel lenses, it is possible to create light rays with clear contours. Soft contours can be achieved by shifting the focus.

Examples additional accessories(from left to right): a lens to create a wide beam of light, a sculpted lens to give the beam an oval shape, a grooved deflector and a honeycomb lens to reduce glare.

Stepped lenses transform light rays so that they fall somewhere between the "flat" light of a Fresnel lens and the "hard" light of a plano-convex lens. Stepped lenses retain their convex surface, but on the side of the flat surface there are stepped recesses that form concentric circles.

The front parts of the steps (steps) of concentric circles are often light-proof (either painted over or have a chipped matte surface), which makes it possible to cut off the scattered radiation of the lamp and form a beam of parallel rays.

Spotlights with a Fresnel lens create an uneven light spot with soft edges and a faint halo around the spot, making it easy to mix with other light sources, creating a natural light pattern. This is why spotlights with Fresnel lenses are used in cinema.

Spotlights with a plano-convex lens, compared to spotlights with a Fresnel lens, form a more uniform spot with a less pronounced transition at the edges of the light spot.

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LENS

(German Linse, from Latin lens - lentil), a transparent body, limited by two surfaces that refract light rays, capable of forming optical. images of objects glowing with their own or reflected light. L. yavl. one of the main optical elements systems The most commonly used are lamellas, both surfaces of which have a common axis of symmetry, and of these, spherical laminas. surfaces, the production of which is most simple. Less common are lenses with two mutually perpendicular planes of symmetry; their surfaces are cylindrical. or toroidal. These are L. in glasses prescribed for astigmatism of the eye, L. for anamorphic attachments, etc.

The material for lasers is usually optical. and organic glass. Specialist. Lenses intended for use in the UV region of the spectrum are made from crystals of quartz, fluorite, lithium fluoride, etc., in the IR - from special types of glass, silicon, germanium, fluorite, lithium fluoride, cesium iodide, etc.

Describing optical properties of an axisymmetric lens, most often they consider rays incident on it at a small angle to the axis, the so-called. the paraxial beam is beamed.

The action of the light on these rays is determined by the position of its cardinal points - the so-called main points H and H, where the main planes of the light intersect with the axis, as well as the front and rear main foci F and F (Fig. 1 ). The segments HF=f and H"F"=f are called. focal lengths of the lens (if the media with which the lens borders have the same refractive indices, always f = f"); the points of intersection of the O and O" surfaces of the lens with the so-called axis. its vertices, and the distances between the vertices are the thickness of L. d.

If the directions of the focal length coincide with the direction of the light rays, then it is considered positive, so, for example, in Fig. 1, the rays pass through L. to the right and the segment H "F" is oriented in the same way. Therefore, here f">0, and f

L. change the directions of the rays incident on it. If a laser transforms a parallel beam into a convergent beam, it is called collecting; If a parallel beam turns into a divergent one, the beam is called scattering. At the main focus F" of a collecting lens, rays intersect, which before refraction were parallel to its axis. For such a lens, f" is always positive. In a scattering lens, F" is the point of intersection not of the rays themselves, but of their imaginary extensions in the direction opposite to the direction of propagation of light. Therefore, for them it is always f"

A measure of the refractive effect of a lens is its Ф, a value reciprocal to the focal length (Ф=1/f") and measured in diopters (m-1). For collecting lenses, Ф>0, which is why they are also called positive, scattering lenses ( F focal length is equal to infinity). They do not collect or scatter rays, but create aberrations (see ABERRATIONS OF OPTICAL SYSTEMS) and are used in mirror-lens (and sometimes in lens) lenses as aberration compensators.

All parameters that determine optical St. L., limited spherical. surfaces, can be expressed through the radii of curvature r1 and r2 of its surfaces, the thickness of the sheet along the d and n axis of its material. For example, optical and the focal length of the lens are given by the relation (true only for paraxial rays):

Radii r1 and r2 are considered positive if the direction from the vertices of the line to the center of the corresponding surface coincides with the direction of the rays (in Fig. 1 r1=OF">0, r2=O"F

The first three are positive, the last three are negative. L. called thin if its thickness d is small compared to r1 and r2. A fairly accurate expression for optical the forces of such a laser are obtained without taking into account the second term in (1).

Provision of Ch. planes of the plane relative to its vertices (the distances OH and O"H") can also be determined by knowing r1, r2, n and d. The distance between the main planes depends little on the shape and optical properties. L. strength and approximately equal to d(n-1)/n. In the case of a thin line, this distance is small and practically one can assume that the main planes coincide.

When the position of the cardinal points is known, the position of the optical points. the image of a point given by L. (Fig. 1) is determined by the following formulas:

where V is the linear magnification of the lens (see OPTICAL MAGNIFICATION); l and l" - distances from the point and its image to the axis (positive if they are located above the axis); x - distance from the front focus to the point; x" - distance from the back focus to the image. If t and t" are the distances from the main points to the planes and the image, respectively, then

because x=t-f, x"=t"-f")

f"/t"+f/t=1 or 1/t"-1/t=1/f". (3)

In thin sheets, t and t" can be counted from the corresponding surfaces of the sheet.

Physical encyclopedic dictionary. - M.: Soviet Encyclopedia. . 1983 .

LENS

(German Linse, from Latin lens - lentil) - the simplest optical lens. an element made of a transparent material, limited by two refractive surfaces having a common axis or two mutually perpendicular planes of symmetry. When making L. for the visible area, use optical glass or organic glass (mass replication of non-precision parts), in the UV range - fluorite, etc., in the IR range - special. types of glass, germanium, a number of salts, etc.

L.'s working surfaces are usually spherical. shape, less often - cylindrical, toroidal, cone-shaped or with specified small deviations from the sphere (aspherical). L. with spherical surfaces max. are easy to manufacture and are basic. elements of most optical devices. systems

In the paraxial approximation (the angles between the rays and the optical axis are so small that sin and can be replaced by the properties of lenses with spherical surfaces can be unambiguously characterized by the position of the main planes and optical powerФ, which is expressed in dioptres the reciprocal of the focal length (in m). The connection of these characteristics with geo. The parameters of the light are clear from the figure, in which, for clarity, the angles of inclination of the rays are depicted as exaggeratedly large. Distances from the first lens surface along the ray path to the first chapter. plane I and from the second surface to the second chapter. plane H" are equal respectively

S 1, 2

Focal length from H to front focus ( F)f= -1/F, from to back focus I optical. The force of light, which is a measure of its refractive action, is equal to

Here p - refractive index of the substance of L. (or the ratio of this index to the refractive index environment, if the last one is 1), d- L thickness measured along the axis, r 1 and r 2 - radii of curvature of its surfaces (considered positive if the centers of curvature are located further along the course of the rays; for example, for the biconvex L shown in the figure. r 1 >0, r 2 <0), расстояния отсчитываются вдоль направления распространения света.

A method for constructing and calculating the trajectories of meridional (lying in the axial plane) rays passing through a lens using Ch. planes is clear from Fig. After passing, the lens appears to emanate from a point at the same distance from the axis h, same as the point of intersection of the original ray with I. The angle between the ray and the axis changes to To find the trajectory of an arbitrary non-meridional ray, the latter is projected onto two mutually perpendicular axial planes. Each projection is essentially a meridional ray and behaves in the manner described above.

The position of the point image given by L. is determined by the formulas

Where l And - distances from the main planes to the planes of the object and image, respectively (Fig.), b and are the distances of the point and its image from the axis (counted upward).

If L. is called. positive or collecting, with - negative or scattering; lenses with Ф=0 name. afocal and are used by ch. arr. to correct aberrations of other optical devices. elements. Positive lenses give real images of all real objects located before the front focus (in the figure - to the left F), and all imaginary objects located behind the lens. Scattering lenses produce a direct, virtual, reduced image located between the lens and the front focus. objects.

Distance between ch. planes of the lens almost does not depend on its optical properties. strength and shape and approximately equal d(1-1/n). When it is negligible compared to L. called. thin. Thin lenses have an optical sign. force Ф coincides with the sign of the difference 1/ r 1 -1/r 2 ; At the same time, the thickness of the collecting lamps decreases with distance from the axis, and the thickness of the scattering ones increases. Both ch. The planes of thin lenses can be considered coinciding with the plane of the lens and the distances introduced above can be counted /, l, straight from the last one. There is no clear boundary between thick L. (when it cannot be neglected) and thin ones - it all depends on the specific applications.

To convert highly coherent light beams (usually of laser origin), predominant ones are used. thin L. They are often called. quadratic phase correctors: when a coherent beam passes through a thin laser, the value where is added to the phase distribution over its cross section k= - wave vector, = ( p- 1) - introduced L. will add. , which is a quadratic removal function r from the axis. The distribution of the complex field amplitude in the focal plane of the lens, up to the phase factor, is Fourier-like distribution of the field amplitude in front of the laser, calculated for spatial frequencies (x, y - transverse coordinates on the focal plane). The intensity distribution in the same plane is similar to angle. distribution of radiation with coefficient. Therefore, L. are widely used in systems spatial filtering radiation, usually representing a combination of lasers with those installed in their focal planes apertures, rasters, and in devices for measuring angle. radiation.

L. have all the aberrations inherent in centers. optical systems (see Aberrations of optical systems). The problem of aberrations is especially important when using broadband and large-angle lenses. apertures of light beams from conventional (incoherent) sources. Spherical and chromatic aberrations, and may also be in the mean. degrees corrected by combining two L. decomposition. shapes and from materials with different dispersion. Such two-lens systems are widely used as lenses for spotting scopes, etc. Sometimes spherical. aberrations are eliminated using lasers with an aspherical, in particular paraboloidal, surface shape.

To correct differences. eye defects, L. is used not only with spherical, but also with cylindrical. and Torich. surfaces. Cylindrical. Lenses are relatively often used in cases where the image of a point source must be “stretched” into a strip or line (for example, in spectral instruments).

Lit.: Born M., Wolf E., Fundamentals of Optics, trans. from English, 2nd ed., M., 1973; Goodman J., Introduction to Fourier Optics, trans. from English. M.. 1970. Yu. A. Ananyev.

Physical encyclopedia. In 5 volumes. - M.: Soviet Encyclopedia. Editor-in-chief A. M. Prokhorov. 1988 .

Transparent bodies with at least one curved surface are called lenses. Most often, there are lenses that are symmetrical about the optical axis. The optical properties of the lens depend on the radius and type of curvature.

Converging lens

Convex, or convex, lenses have a thicker center than the edges. A parallel beam of light, such as a ray of sunlight, falls on a convex lens. The lens collects a beam of light at a focus F. The distance from the middle plane to the focus is called the focal length of the lens f. The shorter it is, the greater the optical power of the lens. This power is measured in diopters.

Let's take a lens with a focal length of 0.5 meters. Then the optical power of the lens is equal to one divided by the focal length: 1/0.5 m = 2 diopters.

diverging lens

Concave or diverging lenses are those whose edges are thicker than the middle.

In this case, the parallel beam of light will be scattered. In this case, it will seem that the light beam comes out from one point, which is called the imaginary focus. The focal length in this case will be negative and, accordingly, the optical power of the diverging lens will also be negative.

Let's take a lens with a focal length of -0.25 meters. Then the optical power will be equal to: 1/-0.25 = -4 diopters.

The principle of constructing an image using a converging lens

A converging lens produces a real image. Only it will be turned upside down.

If we want to get a more accurate image, then knowing the focal length, we can construct this image. For this we need three rays.

A ray propagating parallel to the optical axis, refracted in a lens and passing through the focus is called a parallel ray.

The ray passing through the center of the lens is called the main ray. It doesn't refract.

The ray that passes in front of the lens through the focus and then propagates parallel to the optical axis is called the focal ray. At the point where all three rays intersect, the clearest image will be.

If the distance from the object to the lens is very large, then the distance from the image of this object to the lens will be much smaller, i.e. the image will be reduced in size.

If the distance from the object is twice the focal length, then the image will be the same size as the object itself, and it will be at double the focal length behind the lens.

If we bring an object closer to the focus, we get a magnified image located at a great distance on the other side of the lens.

If the object is directly in focus or even closer to the lens, then we will get a blurry image.

Optical instruments- devices in which radiation from any region of the spectrum(ultraviolet, visible, infrared) transforms(transmitted, reflected, refracted, polarized).

Paying tribute to historical tradition, Optical devices are usually called devices that operate in visible light..

During the initial assessment of the quality of the device, only basic his characteristics:

• aperture- ability to concentrate radiation;
• resolving power- the ability to distinguish adjacent image details;
• increase- the ratio of the size of an object and its image.
• For many devices, the defining characteristic turns out to be field of view- the angle at which the extreme points of the object are visible from the center of the device.

Resolving power (ability)- characterizes the ability of optical instruments to produce separate images of two points of an object close to each other.

The smallest linear or angular distance between two points, from which their images merge, is calledlinear or angular resolution limit.

The ability of the device to distinguish between two close points or lines is due to the wave nature of light. The numerical value of the resolving power of, for example, a lens system depends on the designer's ability to cope with lens aberrations and carefully center these lenses on the same optical axis. The theoretical limit of resolution of two adjacent imaged points is defined as the equality of the distance between their centers to the radius of the first dark ring of their diffraction pattern.

Increase. If an object of length H is perpendicular to the optical axis of the system, and the length of its image is h, then the magnification m is determined by the formula:

m = h/H .

The magnification depends on the focal lengths and the relative position of the lenses; There are corresponding formulas to express this dependence.

An important characteristic of visual observation devices is apparent increase M. It is determined from the ratio of the size of the images of an object that are formed on the retina of the eye when directly observing the object and viewing it through a device. Usually the apparent increase in M ​​is expressed as the ratio M = tgb/tga, where a is the angle at which the observer sees the object with the naked eye, and b is the angle at which the observer's eye sees the object through the device.

The main part of any optical system is the lens. Lenses are part of almost all optical instruments.

Lens – an optically transparent body bounded by two spherical surfaces.

If the thickness of the lens itself is small compared to the radii of curvature of spherical surfaces, then the lens is called thin.

There are lenses collecting 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.

Types of lenses:

• convex:
  • biconvex (1)
  • plano-convex (2)
  • concave-convex (3)

• concave:
  • biconcave (4)
  • flat-concave (5)
  • convex-concave (6)

Basic designations in the lens:

A straight line passing through the centers of curvature O 1 and O 2 of spherical surfaces is called main optical axis of the lens.

In the case of thin lenses, we can approximately assume that the main optical axis intersects with the lens at one point, which is usually called optical center of the lens O. The light beam passes through the optical center of the lens without deviating from its original direction.

Optical center of the lens- the point through which light rays pass without being refracted in the lens.

Main optical axis– a straight line passing through the optical center of the lens, perpendicular to the lens.

All straight lines passing through the optical center are called secondary optical axes.

If a beam of rays parallel to the main optical axis is directed at a lens, then after passing through the lens the rays (or their continuation) will converge at one point F, which is called the main focus of the lens. A thin lens has two main focuses, located symmetrically on the main optical axis relative to the lens. Converging lenses have real foci, while diverging lenses have imaginary foci.

Beams of rays parallel to one of the secondary optical axes, after passing through the lens, are also focused at point F", which is located at the intersection of the secondary axis with the focal plane Ф, that is, the plane perpendicular to the main optical axis and passing through the main focus.

Focal plane– a straight line, perpendicular to the main optical axis of the lens and passing through the focus of the lens.

The distance between the optical center of the lens O and the main focus F is called focal length. It is designated by the same letter F.

Refraction of a parallel beam of rays in a collecting lens.

Refraction of a parallel beam of rays in a diverging lens.

Points O 1 and O 2 are the centers of spherical surfaces, O 1 O 2 is the main optical axis, O is the optical center, F is the main focus, F" is the secondary focus, OF" is the secondary optical axis, Ф is the focal plane.

In the drawings, thin lenses are depicted as a segment with arrows:

collecting: scattering:

The main property of lenses– ability to give images of objects. Images come straight And upside down, valid And imaginary, enlarged And reduced.

The position of the image and its character 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 focal points of the lens, as well as rays parallel to the main or one of the secondary optical axes. To construct an image in a lens, any two of three rays are used:

A ray incident on a lens parallel to the optical axis passes through the focus of the lens after refraction.

The ray passing through the optical center of the lens is not refracted.

The ray, passing through the focus of the lens after refraction, goes parallel to the optical axis.

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

The value of D, the reciprocal of the focal length, is called optical power of the lens.

The unit of measurement for optical power is diopter (dopter). Diopter – optical power of a lens with a focal length of 1 m: 1 diopter = m –1

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

The quantities d and f also obey a certain sign rule:
d > 0 and f > 0 – for real objects (that is, real light sources, and not extensions of rays converging behind the lens) and images;
d< 0 и f < 0 – для мнимых источников и изображений.

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 aberration.

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, turns out to be blurred.

Chromatic aberration occurs due to the fact that 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 of different wavelengths, which leads to blurring of the image when using non-monochromatic light.

Modern optical devices do not use thin lenses, but complex multi-lens 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 instruments, such as a camera, projector, etc.

If you want to create a high-quality optical device, you should optimize a set of its main characteristics - aperture ratio, resolution and magnification. You cannot make a good telescope, for example, by achieving only high apparent magnification and leaving the aperture ratio (aperture) small. It will have poor resolution since it directly depends on the aperture. The designs of optical devices are very diverse, and their features are dictated by the purpose of specific devices. But when implementing any designed optical system into a finished optical-mechanical device, it is necessary to arrange all optical elements in strict accordance with the adopted scheme, securely fasten them, ensure precise adjustment of the position of moving parts, and place diaphragms to eliminate unwanted background scattered radiation. It is often necessary to maintain specified temperature and humidity values ​​inside the device, minimize vibrations, normalize weight distribution, and ensure heat removal from lamps and other auxiliary electrical equipment. Importance is attached to the appearance of the device and ease of handling.

Microscope, magnifying glass, magnifying glass.

If an object located behind the lens no further than its focal point is viewed through a positive (converging) lens, then an enlarged virtual image of the object is visible. Such a lens is a simple microscope and is called a magnifying glass or magnifying glass.

The size of the enlarged image can be determined from the optical design.

When the eye is tuned to a parallel beam of light (the image of the object is at an indefinitely large distance, which means that the object is located in the focal plane of the lens), the apparent magnification M can be determined from the relation: M = tgb /tga = (H/f)/( H/v) = v/f, where f is the focal length of the lens, v is the distance of best vision, i.e. the shortest distance at which the eye sees well with normal accommodation. M increases by one when the eye is adjusted so that the virtual image of the object is at the distance of best vision. Accommodation abilities are different for all people, and they worsen with age; 25 cm is considered to be the distance of best vision in a normal eye. In the field of view of a single positive lens, as one moves away from its axis, image sharpness quickly deteriorates due to transverse aberrations. Although there are loupes with a magnification of 20x, their typical magnification is from 5 to 10. The magnification of a compound microscope, usually called simply a microscope, reaches up to 2000x.

Telescope.

A telescope increases the apparent size of distant objects. The simplest telescope circuit includes two positive lenses.

Rays from a distant object, parallel to the axis of the telescope (rays a and c in the diagram), are collected at the rear focus of the first lens (objective). The second lens (eyepiece) is removed from the focal plane of the lens at its focal length, and rays a and c emerge from it again parallel to the axis of the system. Some ray b, emanating from different points of the object from which rays a and c came, falls at an angle a to the axis of the telescope, passes through the front focus of the lens and after it goes parallel to the axis of the system. The eyepiece directs it to its back focus at an angle b. Since the distance from the front focus of the lens to the observer's eye is negligible compared to the distance to the object, from the diagram we can obtain an expression for the apparent magnification M of the telescope: M = -tgb /tga = -F/f" (or F/f). Negative the sign indicates that the image is inverted. In astronomical telescopes it remains so; in telescopes for observing terrestrial objects, an inverting system is used to view normal, rather than inverted, images. The inverting system may include additional lenses or, as in binoculars, prisms.

Binoculars.

A binocular telescope, commonly referred to as binoculars, is a compact instrument for observing with both eyes at the same time; its increase is usually from 6 to 10 times. Binoculars use a pair of wraparound systems (most often Porro), each of which includes two rectangular prisms (with a base at 45°), oriented towards each other with rectangular edges.

To obtain high magnification over a wide field of view free from lens aberrations, and therefore a significant viewing angle (6-9°), binoculars need a very high-quality eyepiece, more advanced than a telescope with a narrow angle of view. The eyepiece of the binoculars provides for image focusing, and with vision correction - its scale is marked in diopters. In addition, in binoculars the position of the eyepiece is adjusted to the distance between the observer's eyes. Typically, binoculars are labeled according to their magnification (in multiples) and lens diameter (in millimeters), for example, 8*40 or 7*50.

Optical sight.

Any telescope for ground-based observations can be used as an optical sight if clear marks (grids, marks) corresponding to the given purpose are applied in any plane of its image space. The typical design of many military optical installations is such that the telescope lens is openly looking at the target, and the eyepiece is in a shelter. This scheme requires a bend in the optical axis of the sight and the use of prisms to shift it; these same prisms convert the inverted image into a direct one. Systems with a displacement of the optical axis are called periscopic. Typically, an optical sight is designed so that the pupil of its exit is located at a sufficient distance from the last surface of the eyepiece to protect the gunner's eye from hitting the edge of the telescope during recoil of the weapon.

Rangefinder.

Optical rangefinders, which measure distances to objects, come in two types: monocular and stereoscopic. Although they differ in design details, the main part of the optical design is the same and the principle of operation is the same: using the known side (base) and two known angles of the triangle, its unknown side is determined. Two parallel oriented telescopes, separated by a distance b (base), build images of the same distant object so that it appears to be observed from them in different directions (the size of the target can also serve as the base). If, using some suitable optical device, the image fields of both telescopes are combined so that they can be viewed simultaneously, it turns out that the corresponding images of the object are spatially separated. There are rangefinders not only with full field overlap, but also with half field overlap: the upper half of the image space of one telescope is combined with the lower half of the image space of the other. In such devices, using a suitable optical element, spatially separated images are combined and the measured value is determined from the relative shift of the images. Often the shearing element is a prism or a combination of prisms.

MONOCULAR RANGE FINDER. A - rectangular prism; B - pentaprisms; C - lens objectives; D - eyepiece; E - eye; P1 and P2 are fixed prisms; P3 - movable prism; I 1 and I 2 - images of halves of the field of view

In the monocular rangefinder circuit shown in the figure, this function is performed by prism P3; it is associated with a scale graduated in measured distances to the object. Pentaprisms B are used as light reflectors at right angles, since such prisms always deflect the incident light beam by 90°, regardless of the accuracy of their installation in the horizontal plane of the device. In a stereoscopic rangefinder, the observer sees the images created by two telescopes with both eyes at once. The base of such a rangefinder allows the observer to perceive the position of an object three-dimensionally, at a certain depth in space. Each telescope has a reticle with marks corresponding to the range values. The observer sees a distance scale going deep into the depicted space, and uses it to determine the distance of the object.

Lighting and projection devices. Spotlights.

In the optical design of the spotlight, the light source, for example the crater of an electric arc discharge, is located at the focus of a parabolic reflector. Rays emanating from all points of the arc are reflected by a parabolic mirror almost parallel to each other. The beam of rays diverges slightly because the source is not a luminous point, but a volume of finite size.

Diascope.

The optical design of this device, designed for viewing transparencies and transparent color frames, includes two lens systems: a condenser and a projection lens. The condenser evenly illuminates the transparent original, directing the rays into the projection lens, which builds an image of the original on the screen. The projection lens provides focusing and replacement of its lenses, which allows you to change the distance to the screen and the size of the image on it. The optical design of the film projector is the same.

DIASCOPE DIAGRAM. A - slide; B - lens condenser; C - projection objective lenses; D - screen; S - light source

Spectral devices.

The main element of a spectral device can be a dispersion prism or a diffraction grating. In such a device, the light is first collimated, i.e. is formed into a beam of parallel rays, then decomposed into a spectrum, and finally, the image of the input slit of the device is focused onto its output slit at each wavelength of the spectrum.

Spectrometer.

In this more or less universal laboratory device, the collimating and focusing systems can be rotated relative to the center of the stage on which the element is located that decomposes light into a spectrum. The device has scales for reading the angles of rotation, for example, a dispersion prism, and the angles of deflection after it of different color components of the spectrum. Based on the results of such readings, for example, the refractive indices of transparent solids are measured.

Spectrograph.

This is the name of a device in which the resulting spectrum or part of it is recorded on photographic material. You can obtain a spectrum from a prism made of quartz (range 210-800 nm), glass (360-2500 nm) or rock salt (2500-16000 nm). In those spectral ranges where the prisms weakly absorb light, the images of spectral lines in the spectrograph are bright. In spectrographs with diffraction gratings, the latter perform two functions: they decompose the radiation into a spectrum and focus the color components onto the photographic material; Such devices are also used in the ultraviolet region.

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

A special feature of the camera is that flat film should produce fairly sharp images of objects located at different distances.

In the film plane, only images of objects located 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 appear blurred in the form of scattering circles. The size d of these circles can be reduced by stopping down the lens, i.e. reducing the relative aperture a / F. This leads to an increase in the depth of field.

The lens of a modern camera consists of several lenses combined into optical systems (for example, the Tessar optical design). The number of lenses in the lenses of the simplest cameras is from one to three, and in modern expensive cameras there are up to ten or even eighteen.

Optical design of Tessar

There can be from two to five optical systems in the lens. Almost all optical circuits are designed and work the same way - they focus light rays passing through the lenses onto a photosensitive matrix.

The quality of the image in the photo depends only on the lens, whether the photo will be sharp, whether the shapes and lines in the photo will be distorted, whether it will convey colors well - all this depends on the properties of the lens, which is why the lens is one of the most important elements of a modern camera.

Objective lenses are made from special types of optical glass or optical plastic. Creating lenses is one of the most expensive parts of creating a camera. When comparing glass and plastic lenses, it is worth noting that plastic lenses are cheaper and lighter. Currently, most lenses on inexpensive amateur compact cameras are made of plastic. But such lenses are susceptible to scratches and are not so durable; after about two to three years they become cloudy, and the quality of photographs leaves much to be desired. The optics of more expensive cameras are made of optical glass.

Nowadays, most compact camera lenses are made of plastic.

The objective lenses are glued or connected to each other using very precisely calculated metal frames. Gluing lenses can be found much more often than metal frames.

Projection apparatus designed for obtaining large-scale images. The projector lens O focuses the image of a flat object (slide D) on a distant screen E. A lens system K, called a condenser, is designed to concentrate the light of the source S on the slide. On screen E a real enlarged inverted image is created. The magnification of the projection apparatus can be changed by moving the screen E closer or further away while simultaneously changing the distance between the slide D and the lens O.