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 one can see from the center of the device extreme points subject.

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 a 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.

On the drawings thin lenses depicted as a line 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 rule signs:
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 turns out to be different for light with different lengths waves, 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. Value is given appearance 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. This lens is 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 an 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 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 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 removed item, 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 sign shows that the image is upside down. In astronomical telescopes it remains so; Telescopes for observing terrestrial objects use an inverting system to view normal rather than inverted images. The wrapping 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 get high magnification in a wide field of view, free from lens aberrations, and therefore a significant viewing angle (6-9°), binoculars require a very high-quality eyepiece, more advanced than a telescope with a narrow viewing angle. 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 a 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. Usually optical sight is calculated so that the pupil of its exit is removed from the last surface of the eyepiece at a sufficient distance 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: on a known side (base) and two known angles of a 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 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.

Currently, most lenses compact cameras 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.

Simple lenses There are two different types: positive and negative. These two types are also known as converging and diverging because positive lenses collect light and form an image of the source, while negative lenses scatter light.

Characteristics of simple lenses

Depending on the forms there are collecting(positive) and scattering(negative) lenses. The group of collecting lenses usually includes lenses whose middle is thicker than their edges, and the group of diverging lenses includes lenses whose edges are thicker than the middle. It should be noted that this is only true if the refractive index of the lens material is greater than that of the surrounding medium. If the refractive index of the lens is lower, the situation will be reversed. For example, an air bubble in water is a biconvex diverging lens.

Lenses are typically characterized by their optical power (measured in diopters), or focal length.

To build optical devices with corrected optical aberration (primarily chromatic, caused by light dispersion - achromats and apochromats), other properties of lenses and their materials are also important, for example, refractive index, dispersion coefficient, transmittance of the material in the selected optical range.

Sometimes lenses/lens optical systems (refractors) are specifically designed for use in environments with a relatively high refractive index (see immersion microscope, immersion liquids).

Types of lenses: Collecting: 1 - biconvex 2 - plano-convex 3 - concave-convex (positive (convex) meniscus) Scattering: 4 - biconcave 5 - flat-concave 6 - convex-concave (negative (concave) meniscus)

Using a lens to change the shape of the wavefront. Here a plane wavefront becomes spherical as it passes through the lens

A convex-concave lens is called meniscus and can be collective (thickens towards the middle), diffuse (thickens towards the edges) or telescopic (focal length is infinity). So, for example, the lenses of glasses for myopia are, as a rule, negative menisci.

Contrary to popular misconception, the optical power of a meniscus with equal radii is not zero, but positive, and depends on the refractive index of the glass and the thickness of the lens. A meniscus, the centers of curvature of the surfaces of which are located at one point, is called a concentric lens (optical power is always negative).

A distinctive property of a collecting 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 - optical axis - a straight line passing through the centers of the spherical surfaces delimiting the lens; O - optical center - the point that for biconvex or biconcave (with the same surface radii) lenses is located on the optical axis inside the lens (at its center). Note. The path of rays is shown as in an idealized (thin) lens, without indicating refraction at the real interface. Additionally, a somewhat exaggerated image of a biconvex lens is shown

If a luminous point S is placed at a certain distance in front of the collecting lens, then a ray of light directed along the axis will pass through the lens without being refracted, and rays passing not 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 point S. This point is called the conjugate focus, or simply focus.

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

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

Imaginary focus of a diverging lens

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

Collective lenses can be directed towards an object from either side, as a result of which rays passing through the lens can be collected from both one and the other side. Thus, the lens has two focuses - front And rear. They are located on the optical axis on both sides of the lens at the focal length from the main points of the lens.

a) Types of lenses.

Optical lenses that are thicker in the middle than at the edge are called converging lenses; on the contrary, if the edge is thicker than the middle, then the lenses act as

scattering. By shape cross section distinguish: biconvex, plano-convex, concave-convex collecting lenses; biconcave, flat-concave, convex-concave diverging lenses.

Thin lenses, to a first approximation, can be considered as two folded thin prisms (Fig. 217, 218). The course of the rays can be traced on the Hartl puck.

Converging lens concentrates parallel rays at one point behind the lens, at the focus (Fig. 219)

diverging lens turns a parallel beam of rays into a diverging beam that appears to be coming out of focus (Fig. 220).

Unlike prismatic and other diffusers, lenses in lighting devices are almost always used for spot lighting. Typically, optical systems using lenses 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 the convex surface, but on the side of the flat surface there are stepped recesses forming 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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We know that light, falling from one transparent medium to another, is refracted - this is the phenomenon of light refraction. Moreover, the angle of refraction is less than the angle of incidence when light enters a denser optical medium. What does this mean and how can it be used?

If we take a piece of glass with parallel edges, such as window glass, we will get a slight shift in the image seen through the window. That is, upon entering the glass, the rays of light will be refracted, and upon entering the air again, they will again refract to the previous values ​​of the angle of incidence, only at the same time they will shift slightly, and the amount of displacement will depend on the thickness of the glass.

Obviously, from such a phenomenon practical benefit A little. But if we take glass whose planes are inclined to each other, for example, a prism, then the effect will be completely different. Rays passing through a prism are always refracted towards its base. It's easy to check.

To do this, draw a triangle and draw a ray entering any of its sides. Using the law of light refraction, we will trace the further path of the beam. After performing this procedure several times under different meanings angle of incidence, we will find out that no matter at what angle the beam enters the prism, taking into account the double refraction at the output, it will still deviate towards the base of the prism.

Lens and its properties

This property of the prism is used in very simple device, allowing you to control the direction of light flows - the lens. A lens is a transparent body bounded on both sides by curved surfaces of the body. They consider the structure and principle of operation of lenses in an eighth-grade physics course.

In fact, a cross-section of a lens can be depicted as two prisms placed on top of each other. The optical effect of the lens depends on which parts of these prisms are located to each other.

Types of lenses in physics

Despite the enormous diversity, there are only two types of lenses in physics: convex and concave, or converging and diverging lenses, respectively.

A convex lens, that is, a converging lens, has much thinner edges than the middle. A converging lens in section is two prisms connected by bases, so all rays passing through it converge to the center of the lens.

On the contrary, the edges of a concave lens are always thicker than the middle. A diverging lens can be represented as two prisms connected at the tops, and, accordingly, the rays passing through such a lens will diverge from the center.

People discovered similar properties of lenses a long time ago. The use of lenses has allowed man to design a wide variety of optical instruments and devices that make life easier and help in everyday life and production.

Lens is a 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 .

Lenses are part of almost all optical instruments. 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 (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 usually called optical center lenses O. The light beam passes through the optical center of the lens without deviating from its original direction. 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 main focus lenses. 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 into a point F", which is located at the intersection of the secondary 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 optical center of lens O and main focus F called focal length. It is denoted by the same letter F.

The main property of lenses is the ability to provide images of objects . Images come straight And upside down , valid And imaginary , at exaggerated 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. Examples of such constructions are presented in Fig. 3.3.3 and 3.3.4.

It should be noted that some of the standard rays used in Fig. 3.3.3 and 3.3.4 for imaging do not pass through the lens. These rays do not actually 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:

Size D, the inverse of the focal length. called optical power lenses. 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.

The formula for a thin lens is similar to the formula 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 assign certain signs to the focal lengths of lenses: for a converging lens F> 0, for scattering F < 0.

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.

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

Using the thin lens formula we get: , therefore, the image is real.

In the case shown in Fig. 3.3.4, F < 0 (линза рассеивающая), d = 2|F| > 0 (real subject), , 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 increase lenses 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. Magnitude h is 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, , hence, - the image is inverted and reduced by 2 times.

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

Optical power D lenses depends both on 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 proven:

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

In many optical instruments, light passes through two or more lenses in succession. The image of the object given by the first lens serves as an object (real or imaginary) for the second lens, which constructs the second image of the object. This second image can also be real or imaginary. The calculation of an optical system consisting of two thin lenses comes down to applying the lens formula twice, while the distance d 2 from the first image to the second lens should be set equal to the value l - f 1 where l- distance between lenses. The value calculated using 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 infinitely large distances. The telescopic beam path is implemented in spotting scopes - Kepler astronomical tube And Galileo's earth pipe .

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, turns out to be 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 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.

Camera It is a closed, light-tight chamber. The image of photographed objects is created on photographic film by a system of lenses called 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. Size d These circles can be reduced by stopping down the lens, i.e. decrease relative holea / F(Fig. 3.3.5). This results in an increase in depth of field.

Figure 3.3.5. Camera

Projection apparatus designed for obtaining large-scale images. Lens O projector focuses the image of a flat object (slide D) on the remote screen E (Fig. 3.3.6). Lens system K, called condenser , 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 lens O.