Lenses and their use in working with light. Optical lenses (physics): definition, description, formula and solution

Everyone knows that a photographic lens consists of optical elements. Most photographic lenses use lenses as such elements. The lenses in a photographic lens are located on the main optical axis, forming the optical design of the lens.

Optical spherical lens - is a transparent homogeneous element bounded by two spherical or one spherical and the other flat surfaces.

In modern photographic lenses we have widespread, Also, aspherical lenses whose surface shape differs from a sphere. In this case, there may be parabolic, cylindrical, toric, conical and other curved surfaces, as well as surfaces of revolution with an axis of symmetry.

The materials used to make lenses can be various types of optical glass, as well as transparent plastics.

The whole variety of spherical lenses can be reduced to two main types: Collecting(or positive, convex) and Scattering(or negative, concave). Converging lenses in the center are thicker than at the edges, on the contrary, diverging lenses in the center are thinner than at the edges.

In a converging lens, parallel rays passing through it are focused at one point behind the lens. In diverging lenses, rays passing through the lens are scattered to the sides.

Ill. 1. Converging and diverging lenses.

Only positive lenses can produce images of objects. In optical systems that produce a real image (in particular lenses), diverging lenses can only be used together with collective ones.

There are six main types of lenses based on their cross-sectional shape:

1. biconvex converging lenses;
2. plano-convex converging lenses;
3. concave-convex collecting lenses (menisci);
4. biconcave diverging lenses;
5. flat-concave diverging lenses;
6. convex-concave diverging lenses.

Ill. 2. Six types of spherical lenses.

The spherical surfaces of the lens may have different curvature(degree of convexity/concavity) and different axial thickness.

Let's look at these and some other concepts in more detail.

Ill. 3. Elements of a biconvex lens

In Figure 3 you can see a diagram of the formation of a biconvex lens.

• C1 and C2 are the centers of the spherical surfaces limiting the lens, they are called centers of curvature.
• R1 and R2 are the radii of the spherical surfaces of the lens or radii of curvature.
• The straight line connecting points C1 and C2 is called main optical axis lenses.
• The points where the main optical axis intersects the lens surfaces (A and B) are called the vertices of the lens.
• Distance from point A to the point B called axial lens thickness.

If a parallel beam of light rays is directed at a lens from a point lying on the main optical axis, then after passing through it they will converge at a point F, which is also located on the main optical axis. This point is called main focus lenses, and the distance f from the lens to this point - main focal length.

Ill. 4. Main focus, main focal plane and focal length of the lens.

Plane MN perpendicular to the main optical axis and passing through the main focus is called main focal plane. This is where the photosensitive matrix or photosensitive film is located.

The focal length of a lens directly depends on the curvature of its convex surfaces: the smaller the radii of curvature (i.e., the larger the convexity), the shorter the focal length.

A lens is an optical part delimited by two refractive surfaces, which are the surfaces of bodies of revolution, one of which may be flat. Lenses are typically round in shape, but can also be rectangular, square, or some other configuration. Typically, the refractive surfaces of a lens are spherical. Aspherical surfaces are also used, which can take the form of surfaces of revolution of an ellipse, hyperbola, parabola and higher order curves. In addition, there are lenses whose surfaces are part of the side surface of a cylinder, called cylindrical. Toric lenses with surfaces having different curvatures in two mutually perpendicular directions are also used.

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

Depending on the shape, a distinction is made between collecting (positive) and diverging (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 environment. 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 usually characterized by their optical power(measured in diopters), or focal length, as well as aperture. To build optical devices with corrected optical aberration (primarily chromatic, caused by light dispersion - achromats and apochromats), other properties of lenses/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.

Types of lenses

Collective:

1 -- biconvex

2 -- flat-convex

3 -- concave-convex (positive meniscus)

Scattering:

4 -- biconcave

5 -- flat-concave

6 -- convex-concave (negative meniscus)

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

Basic lens elements

NN -- main 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).

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 that do not pass through the center will be refracted towards the optical axis and intersect on it at some point F, which and will be the image of 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 traveling in a parallel beam, then upon exiting it the rays will refract at a large 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 the main focus F", and the distance from the center of the lens to the main focus is called the main focal length.

Rays incident on a diverging lens will be refracted toward 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 the focus of this lens. This focus will be imaginary.

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

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 back. They are located on the optical axis on both sides of the lens.

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 line of sight- 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 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 foci, 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 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 is different for light with different wavelengths, which leads to blurring of the image when using non-monochromatic light.

Modern optical instruments 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 withstand set values temperature and humidity inside the device, minimize vibration, normalize weight distribution, 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.

From the optical design you can determine the size of the enlarged image.

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 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 points other than those on 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 used 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 obtain 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: 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), construct 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 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 objects being photographed 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.

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.

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 a source located at the focal point into a parallel beam of light. As a rule, they are used in lighting structures together with a reflector. The reflector directs the luminous flux in the form of a beam into in the right direction, and the lens concentrates (collects) 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. Optical effect from 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 conventional lenses, but on a completely flat surface of the petals.

However, the use of Fresnel lenses to create such unique products, combining excellent design 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 supplemented 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 of optional 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 opaque (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.

Visit our blog to learn new things about lamps and lighting design.

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 lenses whose edges are thicker than the middle thickness.

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. Focal length in 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 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.