In this lesson, we will repeat the features of the propagation of light rays in homogeneous transparent media, as well as the behavior of the rays when they cross the border between the light separation of two homogeneous transparent media, which you already know. Based on the knowledge already gained, we will be able to understand what useful information about a luminous or light-absorbing object we can get.

Also, applying the laws of refraction and reflection of light already familiar to us, we will learn how to solve the main problems of geometric optics, the purpose of which is to build an image of the object in question, formed by rays falling into the human eye.

Let's get acquainted with one of the main optical devices - a lens - and the formulas of a thin lens.

2. Internet portal "CJSC "Opto-Technological Laboratory"" ()

3. Internet portal "GEOMETRIC OPTICS" ()

Homework

1. Using a lens on a vertical screen, a real image of a light bulb is obtained. How will the image change if the upper half of the lens is closed?

2. Construct an image of an object placed in front of a converging lens in the following cases: 1. ; 2.; 3.; 4. .

Target: introduce students to the types of lenses, geometric characteristics, characteristic rays, and imaging with lenses.

DURING THE CLASSES

1. Statement of the educational problem

Man has always dreamed of seeing small objects better and closer. But with the naked eye, it is extremely difficult to do this. To help a person come ... Lenses.

What is a lens?
What types of lenses are there?
How to use lenses to get different images?

2. Lesson plan

1. Lenses. Lens types.
2. Geometric characteristics of lenses. characteristic rays.
3. Image acquisition with a lens.

3. Learning new material

What is a lens?

Lenses are bodies that are transparent to light and bounded by spherical surfaces, one of which may be flat.

What types of lenses do you know (demonstration of lens types)?

There are six types of lenses based on the shape of the limiting surfaces:

Convex lenses are converging.

Converging lenses are lenses that convert a parallel beam of light rays into a converging beam.

Concave lenses are divergent.

Divergent lenses are lenses that convert a parallel beam of light into a divergent beam.

A thin lens is a lens whose thickness is negligibly small compared to the radii of curvature of its surface.

Geometric characteristics of lenses. characteristic rays.

O - main optical center of the lens
O 1 O 2 is the main optical axis of the lens
AB - secondary optical axis of the lens

Focus of a converging lens the point on the main optical axis at which rays incident parallel to the main optical axis are collected after they have been refracted in a lens.

Focus is real

Why is the focus of a divergent lens called virtual?

Focus of diverging lens- a point on the main optical axis through which the continuations of a divergent beam of rays pass, parallel to the main optical axis.

Focus is imaginary

Focal Plane Lens (MN)- a plane passing through the focus of the lens perpendicular to the main optical axis.

The optical power of the lens - the reciprocal of the focal length.

SI: [D] = 1/m = diopter (diopter)

Problem solving:

1. Practical task: Using a distant light source (the sun), use the lens to get a clear image on the screen. Measure the focal length and calculate the optical power of the lens.

Devices: lenses, screen.

Enter the results in the table:

2. Decide orally:

- The optical power of the glasses, respectively, is 1.25 diopters; 4 diopters What are the focal lengths of these lenses?
- How do lenses differ from each other, the optical power of one of which is +1.5 diopters, and the other -1.5 diopters?
– Can the optical power of a lens be equal to 0 diopters?

Building an image in a lens:

- A beam incident on a lens parallel to the optical axis, after refraction, goes through the focus of the lens.
– The beam passing through the optical center of the lens is not refracted.
- The beam, passing through the focus of the lens after refraction, goes parallel to the optical axis.

Problem solving:

1. Build images of objects in thin lenses and fill in the table:

2. Build the image and define its appearance:

Problems for construction in lenses

1 option

Option 2

1. Build an image in lenses:

2. Using constructions, determine the center of the lens, the type of lens and its focus:

3. Find the image of a luminous point lying on the main optical axis:

Fixing:

1. What lens is called a converging, divergent?
2. Does the focal length of a lens depend on the refractive index of the medium in which it is located?
3. Is it possible to obtain a virtual image of the source on a screen or photographic plate?
4. Is a biconcave lens always divergent?
5. How should two converging lenses be positioned so that a beam of parallel rays, passing through both lenses, becomes parallel again?

Homework:

Application of lenses (messages).

Bibliography:

1. Physics: Optics. The quantum physics. Grade 11. G.Ya. Myakishev. A.Z. Sinyakov.
2. Physics grade 11. V.A. Kasyanov.
3. Physics tutor. I.L. Kasatkin.
4. Collection of assignments and independent work grade 11. L.A. Kirik, Yu.I. Dick
5. Entertaining materials for lessons. Physics grade 8. A.I. Syomke.

Lenses, as a rule, have a spherical or near-spherical surface. They can be concave, convex or flat (the radius is infinity). They have two surfaces through which light passes. They can be combined in different ways, forming different types of lenses (the photo is given later in the article):

• If both surfaces are convex (curved outward), the center is thicker than the edges.
• A lens with a convex and concave sphere is called a meniscus.
• A lens with one flat surface is called plano-concave or plano-convex, depending on the nature of the other sphere.

How to determine the type of lens? Let's dwell on this in more detail.

Converging lenses: types of lenses

Regardless of the combination of surfaces, if their thickness in the central part is greater than at the edges, they are called collecting. They have a positive focal length. There are the following types of converging lenses:

• flat convex,
• biconvex,
• concave-convex (meniscus).

They are also called "positive".

Divergent lenses: types of lenses

If their thickness in the center is thinner than at the edges, then they are called scattering. They have a negative focal length. There are two types of diverging lenses:

• flat-concave,
• biconcave,
• convex-concave (meniscus).

They are also called "negative".

Basic concepts

Rays from a point source diverge from one point. They are called a bundle. When a beam enters a lens, each beam is refracted, changing its direction. For this reason, the beam may exit the lens more or less divergent.

Some types of optical lenses change the direction of the rays so that they converge at one point. If the light source is located at least at the focal length, then the beam converges at a point at least the same distance away.

Real and imaginary images

A point source of light is called a real object, and the point of convergence of the beam of rays emerging from the lens is its real image.

An array of point sources distributed over a generally flat surface is of great importance. An example is a pattern on frosted glass backlit. Another example is a filmstrip lit from behind so that the light from it passes through a lens that magnifies the image many times over on a flat screen.

In these cases, one speaks of a plane. Points on the image plane correspond 1:1 to points on the object plane. The same applies to geometric figures, although the resulting picture may be upside down with respect to the object or left to right.

The convergence of rays at one point creates a real image, and the divergence creates an imaginary one. When it is clearly outlined on the screen, it is valid. If the image can be observed only by looking through the lens towards the light source, then it is called imaginary. The reflection in the mirror is imaginary. The picture that can be seen through a telescope - too. But projecting a camera lens onto film produces a real image.

Focal length

The focus of a lens can be found by passing a beam of parallel rays through it. The point at which they converge will be its focus F. The distance from the focal point to the lens is called its focal length f. Parallel rays can also be passed from the other side and thus F can be found from both sides. Each lens has two f and two f. If it is relatively thin compared to its focal lengths, then the latter are approximately equal.

Divergence and Convergence

Converging lenses are characterized by positive focal length. The types of lenses of this type (plano-convex, biconvex, meniscus) reduce the rays coming out of them, more than they were reduced before. Converging lenses can form both real and virtual images. The first is formed only if the distance from the lens to the object exceeds the focal length.

Diverging lenses are characterized by negative focal length. The types of lenses of this type (plano-concave, biconcave, meniscus) spread the rays more than they were divorced before hitting their surface. Divergent lenses create a virtual image. And only when the convergence of the incident rays is significant (they converge somewhere between the lens and the focal point on the opposite side), the formed rays can still converge, forming a real image.

Important Differences

Care must be taken to distinguish convergence or divergence of beams from convergence or divergence of the lens. The types of lenses and beams of light may not match. Rays associated with an object or image point are said to be divergent if they "scatter", and convergent if they "gather" together. In any coaxial optical system, the optical axis is the path of the rays. The beam passes along this axis without any change in direction due to refraction. This is, in fact, a good definition of the optical axis.

A beam that moves away from the optical axis with distance is called divergent. And the one that gets closer to it is called convergent. Rays parallel to the optical axis have zero convergence or divergence. Thus, when talking about the convergence or divergence of one beam, it is correlated with the optical axis.

Some types of which are such that the beam deviates to a greater extent towards the optical axis are converging. In them, converging rays approach even more, and diverging ones move away less. They are even able, if their strength is sufficient for this, to make the beam parallel or even convergent. Similarly, a diverging lens can spread the diverging rays even more, and make the converging ones parallel or divergent.

magnifying glasses

A lens with two convex surfaces is thicker in the center than at the edges and can be used as a simple magnifying glass or loupe. At the same time, the observer looks through it at a virtual, enlarged image. The camera lens, however, forms on the film or sensor the real, usually reduced in size compared to the object.

Glasses

The ability of a lens to change the convergence of light is called its power. It is expressed in diopters D = 1 / f, where f is the focal length in meters.

A lens with a power of 5 diopters has f \u003d 20 cm. It is the diopters that the oculist indicates when writing out a prescription for glasses. Let's say he recorded 5.2 diopters. The workshop will take a finished 5 diopter blank obtained at the factory and sand one surface a little to add 0.2 diopters. The principle is that for thin lenses in which two spheres are located close to each other, the rule is observed according to which their total power is equal to the sum of the diopters of each: D = D 1 + D 2 .

Trumpet of Galileo

During the time of Galileo (early 17th century), glasses were widely available in Europe. They were usually made in Holland and distributed by street vendors. Galileo heard that someone in the Netherlands put two kinds of lenses in a tube to make distant objects appear larger. He used a long focus converging lens at one end of the tube, and a short focus diverging eyepiece at the other end. If the focal length of the lens is equal to f o and the eyepiece f e , then the distance between them should be f o -f e , and the power (angular magnification) f o /f e . Such a scheme is called a Galilean pipe.

The telescope has a magnification of 5 or 6 times, comparable to modern hand-held binoculars. That's enough for many spectacular lunar craters, Jupiter's four moons, Venus phases, nebulae and star clusters, and faint stars in the Milky Way.

Kepler telescope

Kepler heard about all this (he and Galileo corresponded) and built another kind of telescope with two converging lenses. The one with the longest focal length is the lens, and the one with the shortest one is the eyepiece. The distance between them is f o + f e , and the angular increase is f o /f e . This Keplerian (or astronomical) telescope creates an inverted image, but for stars or the moon it doesn't matter. This scheme provided more uniform illumination of the field of view than Galileo's telescope, and was more convenient to use, as it allowed the eyes to be kept in a fixed position and see the entire field of view from edge to edge. The device made it possible to achieve a higher magnification than the Galilean tube, without serious deterioration in quality.

Both telescopes suffer from spherical aberration, which causes images to be out of focus, and chromatic aberration, which creates color halos. Kepler (and Newton) believed that these defects could not be overcome. They did not assume that achromatic species of which would become known only in the 19th century were possible.

mirror telescopes

Gregory suggested that mirrors could be used as lenses for telescopes, since they lack color fringing. Newton took this idea and created the Newtonian shape of a telescope from a concave silver-plated mirror and a positive eyepiece. He donated the specimen to the Royal Society, where it remains to this day.

A single lens telescope can project an image onto a screen or photographic film. Proper magnification requires a positive lens with a long focal length, say 0.5m, 1m or many meters. This arrangement is often used in astronomical photography. For people unfamiliar with optics, it may seem paradoxical that a weaker telephoto lens gives a greater magnification.

Spheres

It has been suggested that ancient cultures may have had telescopes because they made small glass beads. The problem is that it is not known what they were used for, and they certainly could not form the basis of a good telescope. Balls could be used to enlarge small objects, but the quality was hardly satisfactory.

The focal length of an ideal glass sphere is very short and forms a real image very close to the sphere. In addition, aberrations (geometric distortions) are significant. The problem lies in the distance between the two surfaces.

However, if you make a deep equatorial groove to block the rays that cause image defects, it goes from a very mediocre magnifier to a great one. This solution is attributed to Coddington, and an enlarger named after him can be purchased today as small hand-held magnifiers for examining very small objects. But there is no evidence that this was done before the 19th century.

1. Laws of reflection and refraction of light.

2. Total internal reflection. fiber optics.

3. Lenses. The optical power of the lens.

4. Lens aberrations.

5. Basic concepts and formulas.

6. Tasks.

When solving many problems related to the propagation of light, one can use the laws of geometric optics based on the concept of a light beam as a line along which the energy of a light wave propagates. In a homogeneous medium, light rays are rectilinear. Geometric optics is the limiting case of wave optics as the wavelength tends to zero (λ →0).

23.1. Laws of reflection and refraction of light. Total internal reflection, light guides

Laws of reflection

reflection of light- a phenomenon that occurs at the interface between two media, as a result of which the light beam changes the direction of its propagation, remaining in the first medium. The nature of the reflection depends on the ratio between the dimensions (h) of the irregularities of the reflecting surface and the wavelength (λ) incident radiation.

diffuse reflection

When the irregularities are located randomly, and their sizes are of the order of the wavelength or exceed it, there is diffuse reflection- scattering of light in various directions. It is due to diffuse reflection that non-luminous bodies become visible when light is reflected from their surfaces.

Mirror reflection

If the dimensions of the irregularities are small compared to the wavelength (h<< λ), то возникает направленное, или mirror, reflection of light (Fig. 23.1). In this case, the following laws are fulfilled.

The incident beam, the reflected beam and the normal to the interface between two media, drawn through the point of incidence of the beam, lie in the same plane.

The angle of reflection is equal to the angle of incidence:β = a.

Rice. 23.1. The course of rays in specular reflection

Laws of refraction

When a light beam falls on the interface between two transparent media, it is divided into two beams: reflected and refracted(Fig. 23.2). The refracted beam propagates in the second medium, changing its direction. The optical characteristic of the medium is absolute

Rice. 23.2. The course of rays at refraction

refractive index, which is equal to the ratio of the speed of light in vacuum to the speed of light in this medium:

The direction of the refracted beam depends on the ratio of the refractive indices of the two media. The following laws of refraction are fulfilled.

The incident beam, the refracted beam and the normal to the interface between two media, drawn through the point of incidence of the beam, lie in the same plane.

The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant value equal to the ratio of the absolute refractive indices of the second and first media:

23.2. total internal reflection. fiber optics

Consider the transition of light from a medium with a high refractive index n 1 (optically denser) to a medium with a lower refractive index n 2 (optically less dense). Figure 23.3 shows the rays incident on the glass-air interface. For glass, the refractive index n 1 = 1.52; for air n 2 = 1.00.

Rice. 23.3. The occurrence of total internal reflection (n 1 > n 2)

An increase in the angle of incidence leads to an increase in the angle of refraction until the angle of refraction becomes 90°. With a further increase in the angle of incidence, the incident beam is not refracted, but fully reflected from the interface. This phenomenon is called total internal reflection. It is observed when light is incident from a denser medium on the boundary with a less dense medium and consists in the following.

If the angle of incidence exceeds the limiting angle for these media, then there is no refraction at the interface and the incident light is completely reflected.

The limiting angle of incidence is determined by the relation

The sum of the intensities of the reflected and refracted beams is equal to the intensity of the incident beam. As the angle of incidence increases, the intensity of the reflected beam increases, while the intensity of the refracted beam decreases, and for the limiting angle of incidence becomes equal to zero.

fiber optics

The phenomenon of total internal reflection is used in flexible light guides.

If light is directed to the end of a thin glass fiber surrounded by a cladding with a lower refractive index of the angle, then the light will propagate through the fiber, experiencing total reflection at the glass-cladding interface. Such a fiber is called light guide. The bends of the light guide do not interfere with the passage of light

In modern light guides, the loss of light as a result of its absorption is very small (on the order of 10% per km), which makes it possible to use them in fiber-optic communication systems. In medicine, bundles of thin light guides are used to make endoscopes, which are used for visual examination of hollow internal organs (Fig. 23.5). The number of fibers in the endoscope reaches a million.

With the help of a separate light guide channel, laid in a common bundle, laser radiation is transmitted for the purpose of therapeutic effects on internal organs.

Rice. 23.4. Propagation of light rays through a fiber

Rice. 23.5. endoscope

There are also natural light guides. For example, in herbaceous plants, the stem plays the role of a light guide that brings light to the underground part of the plant. The cells of the stem form parallel columns, which is reminiscent of the design of industrial light guides. If

to illuminate such a column, examining it through a microscope, it is clear that its walls remain dark, and the inside of each cell is brightly lit. The depth to which light is delivered in this way does not exceed 4-5 cm. But even such a short light guide is enough to provide light to the underground part of a herbaceous plant.

23.3. Lenses. Optical power of the lens

Lens - a transparent body, usually bounded by two spherical surfaces, each of which can be convex or concave. The straight line passing through the centers of these spheres is called main optical axis of the lens(word home usually omitted).

A lens whose maximum thickness is much less than the radii of both spherical surfaces is called thin.

Passing through the lens, the light beam changes direction - it is deflected. If the deviation is to the side optical axis, then the lens is called collecting otherwise the lens is called scattering.

Any ray incident on a converging lens parallel to the optical axis, after refraction, passes through a point on the optical axis (F), called main focus(Fig. 23.6, a). For a diverging lens, through the focus passes continuation refracted beam (Fig. 23.6, b).

Each lens has two foci located on either side of it. The distance from the focus to the center of the lens is called main focal length(f).

Rice. 23.6. Focus of converging (a) and diverging (b) lenses

In the calculation formulas, f is taken with the “+” sign for gathering lenses and with a "-" sign for scattering lenses.

The reciprocal of the focal length is called optical power of the lens: D = 1/f. Unit of optical power - diopter(dptr). 1 diopter is the optical power of a lens with a focal length of 1 m.

optical power thin lens and focal length depend on the radii of the spheres and the refractive index of the lens substance relative to the environment:

where R 1 , R 2 - radii of curvature of the lens surfaces; n is the refractive index of the lens substance relative to the environment; the "+" sign is taken for convex surface, and the sign "-" - for concave. One of the surfaces may be flat. In this case, take R = ∞ , 1/R = 0.

Lenses are used to take images. Consider an object located perpendicular to the optical axis of the converging lens, and construct an image of its upper point A. The image of the entire object will also be perpendicular to the lens axis. Depending on the position of the object relative to the lens, two cases of refraction of rays are possible, shown in Fig. 23.7.

1. If the distance from the object to the lens exceeds the focal length f, then the rays emitted by point A, after passing through the lens intersect at point A, which is called actual image. The actual image is obtained upside down.

2. If the distance from the object to the lens is less than the focal length f, then the rays emitted by point A, after passing through the lens race-

Rice. 23.7. Real (a) and imaginary (b) images given by a converging lens

walk around and at point A" their extensions intersect. This point is called imaginary image. The imaginary image is obtained direct.

A diverging lens gives a virtual image of an object in all its positions (Fig. 23.8).

Rice. 23.8. Virtual image given by a divergent lens

To calculate the image is used lens Formula, which establishes a connection between the provisions points and her Images

where f is the focal length (for a diverging lens it negative) a 1 - distance from the object to the lens; a 2 is the distance from the image to the lens (the "+" sign is taken for a real image, and the "-" sign for a virtual image).

Rice. 23.9. Lens Formula Options

The ratio of the size of an image to the size of an object is called linear increase:

The linear increase is calculated by the formula k = a 2 / a 1. lens (even thin) will give the "correct" image, obeying lens formula, only if the following conditions are met:

The refractive index of a lens does not depend on the wavelength of the light, or the light is sufficient monochromatic.

When using imaging lenses real subjects, these restrictions, as a rule, are not met: there is dispersion; some points of the object lie away from the optical axis; the incident light beams are not paraxial, the lens is not thin. All this leads to distortion images. To reduce distortion, the lenses of optical instruments are made of several lenses located close to each other. The optical power of such a lens is equal to the sum of the optical powers of the lenses:

23.4. Lens aberrations

aberrations is a general name for image errors that occur when using lenses. aberrations (from Latin "aberratio"- deviation), which appear only in non-monochromatic light, are called chromatic. All other types of aberrations are monochromatic since their manifestation is not associated with the complex spectral composition of real light.

1. Spherical aberration- monochromatic aberration due to the fact that the extreme (peripheral) parts of the lens deviate rays coming from a point source more strongly than its central part. As a result, the peripheral and central regions of the lens form different images (S 2 and S "2, respectively) of a point source S 1 (Fig. 23.10). Therefore, at any position of the screen, the image on it is obtained in the form of a bright spot.

This type of aberration is eliminated by using concave and convex lens systems.

Rice. 23.10. Spherical aberration

2. Astigmatism- monochromatic aberration, consisting in the fact that the image of a point has the form of an elliptical spot, which, at certain positions of the image plane, degenerates into a segment.

Astigmatism oblique beams manifests itself when the rays emanating from a point make significant angles with the optical axis. In Figure 23.11, a the point source is located on the secondary optical axis. In this case, two images appear in the form of segments of straight lines located perpendicular to each other in planes I and II. The image of the source can only be obtained in the form of a blurry spot between planes I and II.

Astigmatism due to asymmetry optical system. This type of astigmatism occurs when the symmetry of the optical system with respect to the beam of light is broken due to the design of the system itself. With this aberration, the lenses create an image in which contours and lines oriented in different directions have different sharpness. This is observed in cylindrical lenses (Fig. 23.11, b).

A cylindrical lens forms a linear image of a point object.

Rice. 23.11. Astigmatism: oblique beams (a); due to the cylindricity of the lens (b)

In the eye, astigmatism is formed when there is an asymmetry in the curvature of the lens and cornea systems. To correct astigmatism, glasses are used that have different curvature in different directions.

3. Distortion(distortion). When the rays sent by the object make a large angle with the optical axis, another kind is found monochromatic aberrations - distortion. In this case, the geometric similarity between the object and the image is violated. The reason is that in reality the linear magnification given by the lens depends on the angle of incidence of the rays. As a result, the square grid image takes either pillow-, or barrel-shaped view (Fig. 23.12).

To combat distortion, a lens system with opposite distortion is selected.

Rice. 23.12. Distortion: a - pincushion, b - barrel

4. Chromatic aberration manifests itself in the fact that a beam of white light emanating from a point gives its image in the form of a rainbow circle, violet rays intersect closer to the lens than red ones (Fig. 23.13).

The reason for chromatic aberration is the dependence of the refractive index of a substance on the wavelength of the incident light (dispersion). To correct this aberration in optics, lenses made from glasses with different dispersions (achromats, apochromats) are used.

Rice. 23.13. Chromatic aberration

23.5. Basic concepts and formulas

Table continuation

End of table

23.6. Tasks

1. Why do air bubbles shine in water?

Answer: due to the reflection of light at the water-air interface.

2. Why does a spoon seem enlarged in a thin-walled glass of water?

Answer: The water in the glass acts as a cylindrical converging lens. We see an imaginary magnified image.

3. The optical power of the lens is 3 diopters. What is the focal length of the lens? Express your answer in cm.

Solution

D \u003d 1 / f, f \u003d 1 / D \u003d 1/3 \u003d 0.33 m. Answer: f = 33 cm.

4. The focal lengths of the two lenses are equal, respectively: f = +40 cm, f 2 = -40 cm. Find their optical powers.

6. How can you determine the focal length of a converging lens in clear weather?

Solution

The distance from the Sun to the Earth is so great that all the rays falling on the lens are parallel to each other. If you get an image of the Sun on the screen, then the distance from the lens to the screen will be equal to the focal length.

7. For a lens with a focal length of 20 cm, find the distances to the object at which the linear size of the actual image will be: a) twice as large as the size of the object; b) equal to the size of the object; c) half the size of the object.

8. The optical power of the lens for a person with normal vision is 25 diopters. Refractive index 1.4. Calculate the radii of curvature of the lens if it is known that one radius of curvature is twice the other.

Construction of images obtained using lenses Objectives: to form practical skills to apply knowledge about the properties of lenses to find images using a graphical method; Learn how to build the path of rays in lenses, analyze images obtained with lenses.

A lens is a transparent body bounded by two curvilinear (most often spherical) or curved and flat surfaces. A lens is a transparent body bounded by two curvilinear (most often spherical) or curved and flat surfaces. The first mention of lenses can be found in the ancient Greek play "Clouds" by Aristophanes (424 BC), where fire was made using convex glass and sunlight. A lens (German Linse, from Latin lentil) is usually a disk of transparent homogeneous material, bounded by two polished spherical or flat surfaces. What is a lens?

The main elements of the lens MAIN OPTICAL AXIS - a straight line passing through the centers of the spherical surface of the lens OPTICAL CENTER - the intersection of the main optical axis with the lens Secondary optical axis - any straight line passing through the optical center Main optical axis Secondary optical axis O O - optical center

If a beam of rays parallel to the main optical axis falls on a converging lens, then after refraction in the lens they are collected in one optical axis, then after refraction in the lens they are collected at one point F, which is called the main focus of the lens. At the focus of the diverging lens, the continuations of the rays intersect, which before refraction were parallel to its main optical axis. The focus of a diverging lens is imaginary. There are two main focuses; they are located on the main optical axis at the same distance from the optical center of the lens on opposite sides. What is the focus of a lens? F- focus of the lens optical center of the lens main optical axis of the lens

Rule To obtain an image of any point of an object, it is necessary to use TWO "remarkable" beams: 1. A beam passing through the center of the lens. It is never refracted, always straight 2. A beam parallel to the main optical axis. After the lens, it will definitely pass through the focus

Building an image Building an image F F We draw a lens, the main optical axis, Object AB, we draw the first ray from point A through the optical center of the lens, it is not refracted! The second beam is drawn from the same point A parallel to the main optical axis, it is refracted and always passes through the focus of the lens. At the intersection of these two rays, we obtain an image of point A A B From point A1 we draw a perpendicular to the main optical axis. A1B1 is an image of the object AB A1 B1

The converging lens of the object is behind the double focus The converging lens of the object is behind the double focus A We draw two “remarkable” beams from point A and get its image Using the same two beams, we get the image of point B Connecting the obtained points, we get the image of the object Image of the object: reduced, inverted F F A B B

Converging lens Converging lens A We draw two "wonderful" beams from point A and get its image Using two beams, we also get an image of point B Connecting the points obtained, we get an image of the object Image of the object: enlarged, inverted FF A B B the object is between the focus and the double focus the object is between focus and double focus

Converging lens A We draw two “remarkable” beams from point A In the same way we get an image of point B By connecting the obtained points, we get an image of the object Image of the object: enlarged, direct, imaginary FF A B B the object is between the focus and the lens What to do? and the rays spread out! We continue the rays after the lens in the opposite direction. At the intersection of the imaginary rays, we get the image of point A

Diverging lens A We draw a beam from point A through the center of the lens, it will not be refracted Similarly, we obtain an image of point B By connecting the obtained points, we get an image of the object The image of the object is always imaginary, reduced, direct B FFA B We draw a beam from point A parallel to the axis, it will be refracted so that its imaginary continuation will pass through the focus At the intersection of two rays, we get the image of point A

A converging lens used as a magnifying glass gives... Question 1. Question 2

Using a lens, an inverted image of a candle flame is obtained on the screen. How will the size of the image change if part of the lens is obscured by a sheet of paper? 1.part of the image will disappear;part of the image will disappear 2.image dimensions will not change;image dimensions will not change; 3. sizes will increase; sizes will increase; 4.dimensions will decrease.dimensions will decrease. Question 2. Question 3

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The use of lenses. The use of lenses. Lenses are a universal optical element of most optical systems. Lenses are a universal optical element of most optical systems. Biconvex lenses are used in most optical devices, the lens of the eye is the same lens. Biconvex lenses are used in most optical devices, the lens of the eye is the same lens. Lenses - menisci are widely used in glasses and contact lenses. In a converging beam behind a converging lens, the light energy is concentrated at the focus of the lens. Burning with a magnifying glass is based on this principle. Lenses - menisci are widely used in glasses and contact lenses. In a converging beam behind a converging lens, the light energy is concentrated at the focus of the lens. Burning with a magnifying glass is based on this principle.