What condition do biconvex lenses help with? Optical system of the eye

Who does not know the usual magnifying glass, similar to a grain of lentils. If such a glass - it is also called a biconvex lens - is placed between an object and the eye, then the image of the object seems to be magnified several times to the observer.

What is the secret of such an increase? How to explain that objects, when viewed through a biconvex lens, seem to us larger than their actual size?

To understand well the cause of this phenomenon, we must remember how the rays of light propagate.

Everyday observations convince us that light travels in a straight line. Remember, for example, how sometimes the sun, hidden by clouds, pierces them with direct, clearly visible beams of rays.

But are the rays of light always straight? It turns out not always.

Do, for example, such an experiment.

In the shutter that tightly covers the window of your room, make Fig. 6< прямолинейный

Small hole. A ray of light, a ray of light, hitting another -

Having passed through this hole, “I pass through the environment - Into the water, FROM -

Draws "in a dark room directly - changes its direction,

G "and 1 is refracted,

Linear trace. But put on to

The path of the beam to a jar of water, and you will see that the beam, hitting the water, will change its direction, or, as they say, "refract" (Fig. 6).

Thus, the refraction of light rays can be observed when they enter another medium. So, as long as the rays are in the air, they are rectilinear. But as soon as some other medium, such as water, is encountered in their path, the light is refracted.

This is the same refraction experienced by a ray of light in the case when it passes through a biconvex magnifying glass. In this case, the lens collects light rays
into a narrow pointed beam (this, by the way, explains the fact that with the help of a magnifying glass that collects rays of light into a narrow beam, you can set fire to cigarettes, paper, etc. in the sun).

But why does a lens enlarge the image of an object?

Here's why. Look with the naked eye at an object, such as a leaf of a tree. Rays of light bounce off the leaf and converge in your eye. Now place a biconvex lens between the eye and the leaf. Light rays passing through the lens will be refracted (Fig. 7). However, they do not appear broken to the human eye. The observer still feels the straightness of the rays of light. It seems to continue them further, beyond the lens (see the dotted lines in Fig. 7), and the object observed through the biconvex lens seems enlarged to the observer!

Well, what happens if the rays of light, instead of falling into the eye of the observer, continue

Farther? After crossing at one point, called the focus of the lens, the rays will diverge again. If we put a mirror on their way, we will see in it an enlarged image of the same sheet (Fig. 8). However, it will present itself to us in an inverted form. And this is quite understandable. After all, after crossing at the focus of the lens, the light rays go further in the same rectilinear direction. yeste

It is obvious that in this case the rays from the top of the sheet are directed downward, and the rays coming from its base are reflected in the upper part of the mirror.

This property of a biconvex lens - the ability to collect rays of light at one point - is used in a photographic apparatus.

USE codifier topics: lenses

The refraction of light is widely used in various optical instruments: cameras, binoculars, telescopes, microscopes. . . An indispensable and most essential part of such devices is the lens.

Lens - this is an optically transparent homogeneous body, bounded on both sides by two spherical (or one spherical and one flat) surfaces.

Lenses are usually made of glass or special transparent plastics. Speaking about the material of the lens, we will call it glass - it does not play a special role.

Biconvex lens.

Consider first a lens bounded on both sides by two convex spherical surfaces (Fig. 1). Such a lens is called biconvex. Our task now is to understand the course of rays in this lens.

The easiest way is with a ray going along main optical axis- axes of symmetry of the lens. On fig. 1 this ray leaves the point . The main optical axis is perpendicular to both spherical surfaces, so this beam passes through the lens without being refracted.

Now let's take a beam running parallel to the main optical axis. At the point of fall
the beam to the lens is drawn normal to the surface of the lens; as the beam passes from air to optically denser glass, the angle of refraction is less than the angle of incidence. Consequently, the refracted beam approaches the main optical axis.

A normal is also drawn at the point where the beam exits the lens. The beam passes into optically less dense air, so the angle of refraction is greater than the angle of incidence; Ray
refracts again towards the main optical axis and intersects it at the point .

Thus, any ray parallel to the main optical axis, after refraction in the lens, approaches the main optical axis and crosses it. On fig. 2 shows the refraction pattern is enough wide light beam parallel to the main optical axis.

As you can see, a wide beam of light not focused lens: the farther from the main optical axis the incident beam is located, the closer to the lens it crosses the main optical axis after refraction. This phenomenon is called spherical aberration and refers to the disadvantages of lenses - after all, I would still like the lens to reduce a parallel beam of rays to one point.

A very acceptable focus can be achieved using narrow a light beam passing near the main optical axis. Then spherical aberration almost imperceptible - look at fig. 3 .

It is clearly seen that a narrow beam parallel to the main optical axis is collected at approximately one point after passing through the lens. For this reason, our lens is called collecting.

The point is called the focus of the lens. In general, a lens has two foci located on the main optical axis to the right and left of the lens. The distances from the foci to the lens are not necessarily equal to each other, but we will always deal with situations where the foci are located symmetrically with respect to the lens.

Biconcave lens.

Now we will consider a completely different lens, limited by two concave spherical surfaces (Fig. 4). Such a lens is called biconcave. Just as above, we will trace the course of two rays, guided by the law of refraction.

The beam leaving the point and going along the main optical axis is not refracted - after all, the main optical axis, being the axis of symmetry of the lens, is perpendicular to both spherical surfaces.

Beam parallel to the main optical axis, after the first refraction, begins to move away from it (since when passing from air to glass), and after the second refraction, it moves away from the main optical axis even more (since when passing from glass to air).

A biconcave lens converts a parallel beam of light into a divergent beam ( fig. 5) and is therefore called scattering.

Spherical aberration is also observed here: the continuations of the diverging rays do not intersect at one point. We see that the farther the incident beam is from the main optical axis, the closer to the lens the continuation of the refracted beam crosses the main optical axis.

As in the case of a biconvex lens, spherical aberration will be almost imperceptible for a narrow paraxial beam (Fig. 6). The continuations of the rays diverging from the lens intersect at approximately one point - at focus lenses .

If such a divergent beam enters our eye, then we will see a luminous point behind the lens! Why? Recall how an image appears in flat mirror: our brain has the ability to continue diverging rays until they intersect and create the illusion of a luminous object at the intersection (the so-called imaginary image). It is precisely such a virtual image located at the focus of the lens that we will see in this case.

Types of converging and diverging lenses.

We considered two lenses: a biconvex lens, which is converging, and a biconcave lens, which is divergent. There are other examples of converging and diverging lenses.

A complete set of converging lenses is shown in Fig. 7.

In addition to the biconvex lens we know, here are: plano-convex a lens in which one of the surfaces is flat, and concave-convex a lens that combines concave and convex boundary surfaces. Note that in a concave-convex lens, the convex surface is more curved (its radius of curvature is smaller); therefore, the converging effect of the convex refractive surface outweighs the scattering effect of the concave surface, and the lens as a whole is converging.

All possible diffusing lenses are shown in Fig. eight .

Along with the biconcave lens, we see plano-concave(one of the surfaces of which is flat) and convex-concave lens. The concave surface of a convex-concave lens is curved to a greater extent, so that the scattering effect of the concave boundary prevails over the converging effect of the convex boundary, and the lens as a whole is divergent.

Try to build the path of rays yourself in those types of lenses that we have not considered, and make sure that they are really converging or diffusing. This is great exercise, and there is nothing complicated in it - exactly the same constructions that we did above!

Lesson Objectives: formation of ideas about the structure of the eye and the mechanisms of the optical system of the eye; elucidation of the conditionality of the structure of the optical system of the eye by the laws of physics; developing the ability to analyze the studied phenomena; developing a caring attitude towards one's own health and the health of others.

Equipment: table "Organ of vision", model "Human eye"; light-collecting lens, lens with large curvature, lens with small curvature, light source, task cards; on the students' tables: a light-collecting lens, a light-diffusing lens, a screen with a slot, a light source, a screen.

DURING THE CLASSES

Biology teacher. A person has a system of orientation in the surrounding world - sensory system, which helps not only to navigate, but also to adapt to changing environmental conditions. In the previous lesson, you began to get acquainted with the structure of the organ of vision. Let's take a look at this stuff. To do this, you must complete the task on the card and answer the questions.

Review questions

Why does a person need vision?
What organ performs this function?
- Where is the eye located?
Name the membranes of the eye and their functions.
Name the parts of the eye that protect it from injury.

There is a table on the board Organ of vision”, on the teacher's table - a model of the “Human Eye”. After collecting the cards with the answers of the students, the biology teacher checks their completion, together with the students, naming and showing the parts of the eye on the model and poster.

Students are given a second card.

Biology teacher. Based on knowledge anatomical structure eyes, name which parts of the eye can perform an optical function.

(Students, referring to the model of the eye, come to the conclusion that the optical system of the eye consists of the cornea, lens, vitreous body and retina.)

Physics teacher. Which optical device reminds you of a lens?

Students. Biconvex lens.

Physics teacher. What types of lenses do you still know, and what are their properties?

Students. A biconvex lens is a converging lens, i.e. Rays passing through a lens converge at a single point called the focus. A biconcave lens is a diverging lens, the rays passing through the lens are scattered in such a way that the continuation of the rays is collected in an imaginary focus.

(Physics teacher draws(rice. one) on the board, and students in the notebook, the path of rays in the collecting and scattering lens.)

Rice. 1. Ray path in converging and diverging lenses (F - focus)

Physics teacher. What will the image look like if the object is beyond twice the focal length of the converging lens?

(Students draw the path of rays in their notebooks in this case (Fig. 2) and make sure that the image is reduced, real, inverted.)

Rice. 2. Image construction in a converging lens

Frontal experiment

On each table, students have a converging and divergent lens, a current source, an electric light bulb on a stand, a screen with a slot in the shape of the letter G, and a screen.

The physics teacher invites students to choose a biconvex, i.e. converging lens and verify experimentally that the converging lens gives an inverted image. Students assemble the installation (Fig. 3) and, moving the lens relative to the screen, achieve a clear image of the inverted letter G.

(Students are convinced by experience that the image is real inverted and is obtained clearly on the screen only at a certain location of the screen relative to the lens..)

Rice. 3. Installation scheme for demonstrating the path of rays in a converging lens

Biology teacher. Since the lens, cornea and vitreous body- this is a converging lens, then the optical system of the eye gives an inverted reduced image, and we should see the world upside down. What allows you to see things upside down?

Students. Normal, and not inverted, vision of objects is due to their repeated “turning over” in the cortical section of the visual analyzer.

Biology teacher. We see objects well at different distances. This is due to the muscles that attach to the lens and, by contracting, regulate its curvature.

Physics teacher. Let us consider experimentally how the properties of a lens change depending on its curvature. The smaller the radius of curvature, the smaller focal length, - such lenses are called short-focus lenses, lenses with a small curvature, i.e. with big radius of curvature, are called long-focus (Fig. 4).

Rice. 4. Changing the properties of a lens depending on its curvature

Biology teacher. When viewing nearby objects, the lens has a reduced radius of curvature and acts as a short focus lens. When viewing distant objects, the lens has an increased radius of curvature and acts as a telephoto lens. In both cases, this is necessary to ensure that the image is always focused on the retina. The ability to clearly see objects at different distances due to a change in the curvature of the lens is called accommodation (students write the definition in a notebook).

There are deviations in the structure of the eye or in the work of the lens.

With myopia, the image is focused in front of the retina due to excessive curvature of the lens or elongation of the axis of the eye. With farsightedness, the image is focused behind the retina due to insufficient curvature of the lens or a shortened axis of the eye.

Physics teacher. Which lenses are needed to correct nearsightedness and which lenses are needed to correct farsightedness?

Students. Nearsightedness is a diverging lens, farsightedness is a converging lens.

(The teacher of physics, by demonstrating experience, experimentally proves the validity of the conclusions of students.)

Biology teacher. There is another deviation from the norm in the operation of the optical system human eye is astigmatism. Astigmatism is the impossibility of convergence of all rays at one point, at one focus. This is due to deviations in the curvature of the cornea from the spherical. Cylindrical lenses are used to correct astigmatism.

findings

Students, together with a biology teacher, formulate the basic rules of visual hygiene:

- protect the eyes from mechanical influences;
– read in a well-lit room;
- hold the book at a certain distance (33–35 cm) from the eyes;
- the light should fall on the left;
- you can’t lean close to the book, because this can lead to the development of myopia;
- you can not read in a moving vehicle, because. due to the instability of the position of the book, the focal length changes all the time, which leads to a change in the curvature of the lens, a decrease in its elasticity, as a result of which the ciliary muscle weakens and vision is impaired.

biconvex lens

Plano-convex lens

Characteristics of thin lenses

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

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

To build optical devices with corrected optical aberration (primarily chromatic, due to 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 media with a relatively high refractive index (see immersion microscope, immersion liquids).

Types of lenses:
Gathering:
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 meniscus and can be collective (thickens towards the middle) or scattering (thickens towards the edges). The meniscus, whose surface radii are equal, has optical power, zero(used for dispersion correction or as a cover lens). So, the lenses of myopic glasses are usually negative menisci.

A distinctive property of a converging lens is the ability to collect rays incident on its surface at one point located on the other side of the lens.

The main elements of the lens: NN - the main optical axis - a straight line passing through the centers of the spherical surfaces limiting the lens; O - optical center - a point that, for biconvex or biconcave (with the same surface radii) lenses, is located on the optical axis inside the lens (in its center).
Note. The path of the rays is shown as in an idealized (flat) lens, without indicating refraction at the real phase boundary. Additionally, a somewhat exaggerated image of a biconvex lens is shown.

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

If light from a very distant source falls on the lens, the rays of which can be represented as traveling in a parallel beam, then upon exiting the lens, the rays will be refracted at a larger angle and the 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 main focus F ', and the distance from the center of the lens to the main focus - the main focal length.

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

Apparent focus of a diverging lens

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

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

Imaging with a thin converging lens

When describing the characteristics of lenses, the principle of constructing an image of a luminous point at the focus of the lens was considered. Rays incident on the lens from the left pass through its back focus, and rays incident from the right pass through the front focus. It should be noted that in divergent lenses, on the contrary, the back focus is located in front of the lens, and the front one is behind.

Building a lens image of objects that have certain form and dimensions, is obtained as follows: let's say the line AB is an object located at some distance from the lens, much greater than its focal length. From each point of the object through the lens, an uncountable number of rays will pass, of which, for clarity, the figure schematically shows the course of only three rays.

The three rays emanating from point A will pass through the lens and intersect at their respective vanishing points on A 1 B 1 to form an image. The resulting image is valid and upside down.

In this case, the image was obtained in conjugate focus in some focal plane FF, somewhat distant from the main focal plane F'F', passing parallel to it through the main focus.

If the object is at an infinite distance from the lens, then its image is obtained in the back focus of the lens F ' valid, upside down and reduced to a similar point.

If an object is close to the lens and is at a distance greater than twice the focal length of the lens, then its image will be valid, upside down and reduced and will be located behind the main focus on the segment between it and the double focal length.

If an object is placed at twice the focal length of the lens, then the resulting image is on the other side of the lens at twice the focal length from it. The image is obtained valid, upside down and equal in size subject.

If an object is placed between the front focus and double focal length, then the image will be taken beyond double focal length and will be valid, upside down and enlarged.

If the object is in the plane of the front main focus of the lens, then the rays, having passed through the lens, will go in parallel, and the image can only be obtained at infinity.

If an object is placed at a distance less than the main focal length, then the rays will leave the lens in a divergent beam, without intersecting anywhere. This results in an image imaginary, direct and enlarged, i.e., in this case, the lens works like a magnifying glass.

It is easy to see that when an object approaches from infinity to the front focus of the lens, the image moves away from the back focus, and when the object reaches the front focus plane, it turns out to be in infinity from it.

This pattern has great importance in practice various kinds photographic work, therefore, to determine the relationship between the distance from the object to the lens and from the lens to the image plane, it is necessary to know the main lens formula.

Thin Lens Formula

The distances from the point of the object to the center of the lens and from the point of the image to the center of the lens are called conjugate focal lengths.

These quantities are dependent on each other and are determined by a formula called formula thin lens :

where is the distance from the lens to the object; - distance from the lens to the image; is the main focal length of the lens. In the case of a thick lens, the formula remains unchanged with the only difference that the distances are measured not from the center of the lens, but from the main planes.

To find one or another unknown quantity with two known ones, the following equations are used:

It should be noted that the signs of the quantities u , v , f are selected based on the following considerations - for a real image from actual subject in a converging lens - all these quantities are positive. If the image is imaginary - the distance to it is taken negative, if the object is imaginary - the distance to it is negative, if the lens is divergent - the focal length is negative.

Image Scale

Image scale () is the ratio of the linear dimensions of the image to the corresponding linear dimensions of the object. This ratio can be indirectly expressed as a fraction , where is the distance from the lens to the image; is the distance from the lens to the object.

Here there is a reduction factor, i.e. a number showing how many times the linear dimensions of the image are less than the actual linear dimensions of the object.

In the practice of calculations, it is much more convenient to express this ratio in terms of or , where is the focal length of the lens.

Calculation of the focal length and optical power of the lens

The lenses are symmetrical, that is, they have the same focal length regardless of the direction of the light - left or right, which, however, does not apply to other characteristics, such as aberrations, the magnitude of which depends on which side of the lens is turned towards the light.

Multiple Lens Combination (Centered System)

Lenses can be combined with each other to build complex optical systems. The optical power of a system of two lenses can be found as simple sum optical powers of each lens (provided that both lenses can be considered thin and they are located close to each other on the same axis):

If the lenses are located at some distance from each other and their axes coincide (a system of an arbitrary number of lenses with this property is called a centered system), then their total optical power can be found with a sufficient degree of accuracy from the following expression:

where is the distance between the principal planes of the lenses.

Disadvantages of a simple lens

In modern photographic equipment, high demands are placed on image quality.

The image given by a simple lens, due to a number of shortcomings, does not meet these requirements. Elimination of most of the shortcomings is achieved by appropriate selection of a number of lenses in a centered optical system - objective. Images taken with simple lenses have various drawbacks. The disadvantages of optical systems are called aberrations, which are divided into the following types:

Geometric aberrations
Diffractive aberration (this aberration is caused by other elements of the optical system, and has nothing to do with the lens itself).

Lenses with special properties

Organic polymer lenses

Contact lenses

quartz lenses

Quartz glass - remelted pure silica with minor (about 0.01%) additions of Al 2 O 3 , CaO and MgO. It is characterized by high thermal stability and inertness to many chemicals except hydrofluoric acid.

The refraction of light is widely used in various optical instruments: cameras, binoculars, telescopes, microscopes. . . An indispensable and most essential part of such devices is the lens.

A lens is an optically transparent homogeneous body bounded on both sides by two spherical (or one spherical and one flat) surfaces.

Lenses are usually made of glass or special transparent plastics. Speaking about the material of the lens, we will call it glass, this does not play a special role.

4.4.1 biconvex lens

Consider first a lens bounded on both sides by two convex spherical surfaces (Fig. 4.16). Such a lens is called a biconvex lens. Our task now is to understand the course of rays in this lens.

Rice. 4.16. Refraction in a biconvex lens

The simplest situation is with a beam traveling along the main optical axis of the lens symmetry axis. On fig. 4.16 this ray leaves the point A0 . The main optical axis is perpendicular to both spherical surfaces, so this beam passes through the lens without being refracted.

Now let's take a beam AB, running parallel to the main optical axis. At the point B of the beam incident on the lens, the normal MN to the lens surface is drawn; since the beam passes from air to optically denser glass, the angle of refraction CBN is smaller than the angle of incidence ABM. Therefore, the refracted ray BC approaches the main optical axis.

At the point C of the beam exit from the lens, a normal P Q is also drawn. The beam passes into optically less dense air, so the angle of refraction QCD is greater than the angle of incidence P CB; the beam is again refracted towards the main optical axis and crosses it at point D.

Thus, any ray parallel to the main optical axis, after refraction in the lens, approaches the main optical axis and crosses it. On fig. 4.17 shows the refraction pattern of a sufficiently wide light beam parallel to the main optical axis.

Rice. 4.17. Spherical aberration in a biconvex lens

As you can see, a wide beam of light is not focused by the lens: the farther the incident beam is from the main optical axis, the closer to the lens it crosses the main optical axis after refraction. This phenomenon is called spherical aberration and refers to the shortcomings of lenses, because we still would like the lens to reduce a parallel beam of rays to one point5.

A very acceptable focusing can be achieved by using a narrow light beam passing near the main optical axis. Then the spherical aberration is almost imperceptible look at fig. 4.18.

Rice. 4.18. Focusing a narrow beam with a converging lens

It is clearly seen that a narrow beam parallel to the main optical axis, after passing through the lens, is collected at approximately one point F. For this reason, our lens is called

collecting.

5 Precise focusing of a wide beam is indeed possible, but for this the lens surface must have a more complex shape rather than a spherical one. Grinding such lenses is time-consuming and impractical. It's easier to make spherical lenses and deal with the emerging spherical aberration.

By the way, the aberration is called spherical precisely because it arises as a result of replacing an optimally focusing complex non-spherical lens with a simple spherical one.

Point F is called the focus of the lens. In general, a lens has two foci located on the main optical axis to the right and left of the lens. The distances from the foci to the lens are not necessarily equal to each other, but we will always deal with situations where the foci are located symmetrically with respect to the lens.

4.4.2 Biconcave lens

Now we will consider a completely different lens, bounded by two concave spherical surfaces (Fig. 4.19). Such a lens is called a biconcave lens. Just as above, we will trace the course of two rays, guided by the law of refraction.

Rice. 4.19. Refraction in a biconcave lens

The beam leaving the point A0 and going along the main optical axis is not refracted because the main optical axis, being the axis of symmetry of the lens, is perpendicular to both spherical surfaces.

Ray AB, parallel to the main optical axis, after the first refraction begins to move away from it (because when passing from air to glass \CBN< \ABM), а после второго преломления удаляется от главной оптической оси ещё сильнее (так как при переходе из стекла в воздух \QCD >\PCB). A biconcave lens converts a parallel beam of light into a divergent beam (Fig. 4.20) and is therefore called a diverging one.

Rice. 4.20. Spherical aberration in a biconcave lens

As in the case of a biconvex lens, spherical aberration will be almost imperceptible for a narrow paraxial beam (Fig. 4.21). The extensions of the rays diverging from the lens intersect at approximately one point at the focus of the lens F.

Rice. 4.21. Refraction of a narrow beam in a diverging lens

If such a divergent beam enters our eye, then we will see a luminous point behind the lens! Why? Remember how an image appears in a flat mirror: our brain has the ability to continue diverging rays until they intersect and create the illusion of a luminous object at the intersection (the so-called imaginary image). It is precisely such a virtual image located at the focus of the lens that we will see in this case.

In addition to the biconvex lens known to us, here are shown: a plano-convex lens, in which one of the surfaces is flat, and a concave-convex lens, combining concave and convex boundary surfaces. Note that in a concave-convex lens, the convex surface is more curved (its radius of curvature is smaller); therefore, the converging effect of the convex refractive surface outweighs the scattering effect of the concave surface, and the lens as a whole is converging.

All possible diffusing lenses are shown in Fig. 4.23.

Rice. 4.23. Divergent lenses

Along with a biconcave lens, we see a plano-concave (one of the surfaces of which is flat) and a convex-concave lens. The concave surface of a convex-concave lens is curved to a greater extent, so that the scattering effect of the concave boundary prevails over the converging effect of the convex boundary, and the lens as a whole is divergent.

Try to build the path of rays yourself in those types of lenses that we have not considered, and make sure that they are really converging or diffusing. This is a great exercise, and there is nothing difficult in it exactly the same constructions that we did above!