Qualitative tasks. Glasses prescription and what it says

Visual impairment is already stressful in itself. And the prescription for glasses written out after visiting an ophthalmologist does not help in any way to calm you down. Understanding what is written on the form is quite capable of making our state of mind more calm.

In addition, it usually significantly increases confidence in the doctor who prescribed it.

Most often, a prescription is written on the form shown below.
As you can see, the parameters of the right eye come first, and then the left. This required condition all ophthalmic prescriptions.
Here we will look at all the possible parameters that are entered in the form. But each specific recipe contains only a part of them. Those that concern this patient.

Thus, when prescribing glasses to correct strabismus, most likely there will be no addition correction (near correction). Correction of astigmatism is not always necessary, and, therefore, it will not be indicated.

Designations on the form for glasses of the right and left eyes

In our sample it is written “Right Eye” and “Left Eye”, but often doctors write OD for the right eye and OS for the left eye. Sometimes they write OU - this means both eyes. As already noted, be sure to start with the right eye first, and then the left.

Glasses help you see better using a lens system built into them. In fact, there may be three or even four (with bifocals). But most often only a combination of the two occurs.

Designations on the form for sphere glasses

This is the designation for the optical power of a spherical lens. It is marked “Sph” when writing a recipe by hand. Calculate the lens power in diopters (D or D) with a minimum step of 0.25 D. Here, there may also be two types of lenses:

• scattering - they are marked with a “-” sign before the number, for example -1.75, and are prescribed in the presence of myopia (myopia). If you are prescribed glasses with a “-” symbol, this means that such a person has poor distance vision;
• collecting ones, which are marked with a “+” sign in front of the number, for example + 2, 5, and are prescribed, accordingly, for farsightedness (hyperopia). When writing a prescription with a plus value of lenses, you need to think that the person has difficulties with reading and other similar actions at close range.

If bifocals or progressive glasses are prescribed for presbyopia, then two indicators “top” and “bottom” will be indicated here. But the difference between them should not exceed 3 D.

Symbols on the cylinder glasses form

These are cylindrical lenses designed to help the eye create a single focal system for astigmatism. They are designated “Cyl” when writing a recipe by hand. Here the position of the cylinder axis must be indicated in degrees from 0 to 180. This is due to the fact that light rays passing through the cylinder axis, depending on the degree of refraction, act differently:

• if the ray is perpendicular to the axis, it is refracted;
• if the ray travels parallel, it does not change its direction.

This property of a cylindrical lens allows you to correct astigmatism in the desired meridian and create a single focal system of the eye, which allows you to see objects more clearly. This indicator is indicated on the scale located at the bottom of the table. The indicator is set separately for the right and left eyes.

To determine the value of a cylindrical lens, a special TABO scale is used, which is placed on the frame (it has special notches and looks the same as in the prescription).

Cylindrical lenses for astigmatism correction can be of two types:

• with a minus sign when correcting myopic astigmatism;
• with a plus sign to correct farsighted astigmatism.

Data on the value of cylindrical lenses are indicated in the table with the corresponding sign in diopters. With step values ​​up to 0.25 D.

Symbols on the form for axis glasses

This is a number that shows in which direction the astigmatism is developed; it will be expressed in degrees. Designated as "AH"
If there is no astigmatism, then this column of the form will be blank.
There is usually a gradation within 1, 5 or 10 degrees, but parts of a degree are never written.

Prism on glasses form

This type of lens is used to correct strabismus. This indicator"p.d." or used to indicate the direction of squint. In this case, the base of the triangle indicates the direction of the prism, for example: towards the nose, outwards, etc. It is determined in diopters; the minimum step value must be at least 0.5 D.

It is present in prescriptions for glasses to correct strabismus. But it is not filled out in other forms.

Important! If your glasses prescription contains this icon, try ordering lenses and frames from your doctor. Try to have the fitting done by an ophthalmologist. Here, precise alignment of the pupil and lens is very important for treatment.

Reasons for receiving points

Additions are usually added here. Among them will be:
ADD – or reading supplement. Used with bifocal glasses.

Interpupillary distance

When selecting points, this indicator plays a very important role. The correction lens must be located opposite the pupil. This is the only way the eye will get necessary correction, and not an additional load. An incorrectly placed lens will require additional eye strain, which can cause headaches, eye fatigue, and sometimes...

The distance between the pupils is measured in millimeters. Can range from 40 to 70. Sometimes measured for each eye separately.

Important! Interpupillary distance (Dp) is not always indicated in the prescription. Therefore, he can be asked to indicate to order glasses that are more comfortable to use.

In our example form it is indicated below under the TAVO scale.

Assigning points on the form

The lowest part of the prescription will be the prescription of glasses. Usually the doctor explains exactly how to wear glasses. But the recipe also indicates this. So, the designations will indicate the following:

1. emphasized “For distance” (or Dist) - this type of glasses is worn all the time without taking it off. It is designed to correct myopia. Sometimes it is used for driving a car or watching TV;
2. “For work” (or Near) is highlighted – this type of glasses corrects presbyopia and will allow you to work at the computer, read, and sew without problems. They are used periodically and should not be worn all the time;
3. designated “For constant wear” (or Inter) – they are used to correct variable vision. As a rule, they use transition (bifocal) lenses.

How to read a recipe?

Now let's try to read the written prescription for glasses:

We see that the right eye has poor distance vision - 5.0 D, while there is astigmatism -0.5 D. with an axis degree of 50. The left eye also sees poorly, but astigmatism does not appear.

Glasses will need to be worn at all times. The distance between the pupils is 64 mm.

Prescription for contacts or glasses?

There is a difference between these two recipes. Since glasses are located at some distance from the eyes, lenses are also selected as vision correction. Lenses actually create a single optical system with the eye. Here the correction system will differ from glasses.

Therefore, for lenses and glasses they always prescribe different recipes with different data and on different forms. And you can't order glasses with a prescription for lenses. Exactly the same as vice versa - lenses with prescription glasses.

Many have encountered incomprehensible symbols written by doctors

When passing ophthalmological examination, we often receive a lot of results, but it is extremely difficult to understand what is written.

Blame it all complex ophthalmic language, incomprehensible abbreviations and designations. So that you can understand at least a little about all these symbols, we will guide you small excursion on the basics of ophthalmology.

Of course, we all understand that a letter, icon or stick carries certain information, which helps to correctly diagnose, prescribe effective treatment and avoid further deterioration. Undoubtedly, professionals are well versed in all these subtleties, but it would be nice for you to understand the meaning of such abbreviations.

SPH - what is the diagnosis?

If you find in your test sheet this characteristic and you have no idea about vision sph, what it means, then our information will be very useful for you. So, SPH characterizes presence of astigmatism: i.e. V different parts The eyes rays are refracted at certain angles (different), which brings significant discomfort to the patient.

The Sph value usually suggests the presence of astigmatism

There are several types of astigmatism that can be targeted for such diagnoses:

• myopia;
• farsightedness;
• mixed astigmatism.

The concept itself "sph vision" practically never occurs without accompanying digital indicators. For example, sph +2.5 means that for the patient and as corrective means, it is necessary to select a dioptre of +2.5. If the number is minus (-3), then the person has progressive.

Usually, the bottom line describes astigmatism level in relation to the pupil. If you abstract a little from the numbers and remember what it looks like human eye, then it becomes clear that the cornea has a spherical shape, which can be divided into 4 equal parts.

So, astigmatism indicates to the level of deflection where the beam is refracted. For example, the luminous flux should fall directly on the conventional horizon, but the bar moves and turns out to be higher/lower than the desired indicator.

Special complex diagnostic measures will help calculate the level of deviation and select a rational accompanying glass that will optimally complement the diopter and bring visual acuity closer to unity.

Therefore, seeing vision sph cyl ax and the corresponding figure, there is no need to be scared and perplexed, because this is absolutely normal indicators. For example, if your doctor prescribed you prescription for glasses/lenses, then he is simply obliged to indicate the appropriate parameters, only taking into account which corrective measures will be correctly selected.

There are situations when they try to place dozens of indicators on one small piece of paper with tests, which further confuses and misleads patients.

Watch gymnastics to restore vision in this video: Link

Correct selection of glasses

Only a doctor can help you choose the right glasses, and only after an examination.

If you had to deal with this set of numbers and letters: SPH -1.75 CYL -0.25 (AX120A), then we will try to provide you with a short answer about each of the indicators.

Since we have already talked about SPH and CYL, let’s delve into the essence of the add-on vision "sph cyl ax" what is it and how to treat it.

Index ax represents useful addition, aimed at specifying the angle of the visual cylinder, which is responsible for the correct refraction of light fluxes. I would like to note that AX can fluctuate from 0 to 180 degrees, which will help make a diagnosis faster and more correctly.

As a rule, if the examination is carried out on both eyes, then indicators will be different. There is an opinion that one eye always sees worse, and accordingly, the indicators in one will be significantly higher than in the other.

By the way, if you were able to write down all types of vision characteristics in one line, then we can assume that in medical center there is modern equipment.

Similar detailed eye diagnostics important for correct selection glasses, because many people spend the whole day wearing glasses, and do not use them only for moments of intense visual activity.

For more clear example and a rational understanding of all these concepts, let's look at one prescription with which the patient goes to the optician for the appropriate purchase.

Most people require custom glasses

So, OD sph +2.5 cyl +0.5 ax 90:

• As we can see, the patient suffers from farsightedness (since +),
• astigmatism level by 0.5 (an additional correction diopter is selected), which is set at an angle of 90 degrees.

Of course, upon arrival at the optician, you Once again will check to make sure the initial diagnostics are correct and will be launched mechanism for creating individual glasses.

If the difference in diopters is large, then to restore vision, you need to buy exclusively complex glasses: lenses in the right/left eye can be radically different and even have plus and minus diopters.

Understanding what your doctor wrote in your glasses prescription is as easy as shelling pears! After reading the article, in a few minutes you will know what “sphere”, “addition”, “cylinder”, “axis” and “prism” are and what OD, OS, OU, DP, SPH, ADD, CYL, AXIS and P.D. You will easily understand any prescription and figure out what is wrong with your eyes and what optics modern medicine can help you with.

We receive approximately 90% of information about the world around us through vision. This active use the eyes very often lead to the fact that sooner or later problems arise with them, for which we are forced to consult a doctor. After the examination get a prescription for glasses and, naturally, there is a desire to read and understand it. It seems very challenging task. But in fact, it’s quite simple to figure it out if you know for what vision problems glasses are prescribed and what the letters and numbers in the prescription mean.

What are the types of vision problems and what types of glasses are there?

Points are usually issued in the following cases:.

Depending on the disease and visual defect, they can be used the following types of glasses:

• for myopia, farsightedness and presbyopia, spherical (stigmatic) glasses are prescribed;
• for astigmatism - cylindrical (astigmatic);
• with strabismus - prismatic.

There are also multifocal glasses (bifocal and progressive) and combined glasses (bifocal astigmatic and prismatic astigmatic). Bifocals have two optical areas: the upper one is used for distance vision, and the lower one is used for near vision, for example, when reading. If there is no obvious boundary between the focal areas, and the transition is smooth, then such glasses are progressive. Prismatic glasses are used for stabismus (squint).

Basic concepts and notations: OD, OS, OU, and DP

In medicine Latin terminology adopted. A prescription from an ophthalmologist or ophthalmologist is no exception.

Optical power: SPH, CYL and PD

Optical power is indicated in diopters(in recipes denoted D, D or diopter) and characterizes the refractive power of the lens, the degree of deflection of rays passing through it. The optical power of spherical lenses is indicated by SPH, cylindrical - CYL, prismatic - PD or, if the form is filled out by hand, by a triangle icon.

The “+” sign and the Latin word “convex” (convex lens) mean farsightedness, the “-” sign and the word “concave” ( concave lens) - myopia.

CYL and AXIS: correction of astigmatism

For vision correction in case of impaired correct form cornea or lens (astigmatism), glasses with cylindrical lenses are used. The recipe contains:

• The optical power of a cylindrical lens (CYL) and the farsightedness sign “+” for hyperopic astigmatism or the myopia sign “-” for myopic astigmatism.
• AXIS or AX - cylinder axis angle in the range from 0 to 180°.

PD and Prism Base Direction: Strabismus Correction

To correct stabilism, they are used glasses with prismatic lenses, for which the following parameters are specified:

• Prismatic lens power (PD or triangle icon).
• Orientation of the base of the prism: outward (toward the temple) or inward (toward the nose), up or down.

Bifocals and progressive glasses: addition (ADD)

This section is devoted to more complex, from an optical point of view, glasses with several focuses (multifocal) and their main characteristic - addition. As already mentioned, multifocal glasses include glasses with two focuses, for near and distance, (bifocals) and progressive glasses with a gradient (smooth) change in focal length.

Addition (ADD) or, as professionals say, “near gain” is the difference in optical power between near vision and distance vision. For example, if to correct the clarity of perception of objects at long distances, glass with an optical power of +1.0D should be used, and for close distances +1.5D, then the addition will be +0.5D.

It should be kept in mind that the addition value cannot exceed +3.0D.

Examples

Now we have everything necessary information to decipher any glasses prescription. We know how eyes are designated and the distance between them; what is SPH, CYL and cylinder axis angle; PD and direction of the base of the pyramid. We've covered addition and multi-trick points. Now we can correctly understand what diagnosis has been made and what optics are recommended.

Example 1

• Addition (ADD) is indicated, so lenses must be bifocal or progressive. Farsightedness of both eyes (OU) is the same and its value is +1.5D (SPH) for long distances and +2.5D for loved ones (SPH+ADD).
• Distance between pupils (DP) - 61 mm.

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OD, OS and other abbreviations

Abbreviations OD and OS - short names Latin terminology“oculus dexter”, “oculus sinister”, which translated means “right eye” and “left eye”. The abbreviation OU is also often found, from the abbreviation “oculus uterque”, which means “both eyes”.

This is the professional terminology of ophthalmologists and optometrists, used when filling out a prescription for any type of glasses or eye drops.

Please note that in ophthalmology, all information about the right eye is always indicated first, and then about the left eye. This is how doctors insure themselves against confusion and mistakes. Therefore, your recipe will say exactly that. In addition, it will also contain other abbreviations. Eg:

Sph (sphere), which translates as “sphere” and indicates the optical power of the lens, which is expressed in diopters. It is the power of the lens that plays the main role in correction, either. Moreover, when a “-” sign is indicated in front of the numerical value, this means that you are myopic. Myopia, or scientifically, is corrected by diverging minus lenses. Sometimes you can see the Latin “concave” above the minus sign.

If there is a “+” in front of the numerical value, then you are farsighted, and your glasses are for distance. Farsightedness, or farsightedness, is corrected with plus converging lenses, otherwise designated “convex”.

The concept of Cyl (Cylinder) - “cylinder” will indicate the optical power of the lenses that are used for correction. Astigmatism is an uneven, non-spherical surface in which refraction in one of its meridians occurs somewhat stronger than in the others. This anomaly can be corrected with cylindrical lenses. In this case, the recipe must indicate the position of the cylinder axis (from the Latin Axis or Ax), which is expressed in the degree range 0 - 180. This is due to the peculiarity of the refraction of light passing through a cylindrical lens. Moreover, only rays traveling strictly perpendicular to the cylinder axis are refracted. Rays running parallel to it do not change their direction. These properties make it possible to “correct” the refraction of light in a specific “offending” meridian.

Cylinder values ​​can be either: or negative, i.e. designed to correct myopic astigmatism (for myopia), or plus ones - to correct hypermetropic astigmatism (for farsightedness).

Meridians are determined by applying them to the front surface of one of the eyes special scale. As a rule, such a scale is built into the frame sample, which is used for measuring and further selecting glasses. This scale, like the entire system, is called TABO.

Addition - Add - “addition for near”, a term denoting the difference in diopters that exists between the zones of distance vision and near vision, which is necessary in the manufacture of bifocal or progressive glasses intended for correction. That is, when you need +1.0D lenses to improve distance visual acuity, and +2.5D for near vision, the addition will be +1.5 D. In this case, the maximum addition value cannot exceed +3.0D.

Prism or prismatic lens power. This value is measured in prismatic diopters (that is, p.d. or triangle symbol when the recipe is written by hand). These lenses are used for correction, and when prescribed, depending on its type, they indicate which direction the base of the prism is facing: up, down, outwards (towards the temple), inwards (towards the nose).

The optical power of spherical or cylindrical lenses, as well as the addition value, is indicated in diopters, using a maximum refinement of up to 0.25D. Prismatic diopters may be rounded to their half values ​​(e.g. -0.5p.d.)

The distance between the centers of the pupils (RC) - Dp (distancia pupilorum) - value measured in millimeters. It is noteworthy that for near it is 2 mm less than for distance. In recipes it can also be referred to as Dpp.

Prescription for glasses

OD sph-2.5 cyl -0.5 ax 90 (sph-2.5 - 0.5 x 45)

This recipe can be deciphered as follows:

For the right eye, spherical correction of myopia is indicated, using a -2.5D lens,

There is astigmatism, corrected by a minus cylindrical lens - 0.5D,

The cylinder axis is an inactive meridian, located along the 45o axis,

For the left eye, spherical correction is indicated using a 3.0D minus lens.

DP – interpupillary distance 64 mm.

OU sph +2.0 +0.5 add

Prescription for glasses and contact lenses

Sometimes people ask, can a glasses prescription be used to make contact lenses? The answer is clear - it’s impossible.

In the preparation of prescriptions, both for glasses and contact lenses have their own characteristics. The contact lens prescription must specify the base curvature as well as the diameter of the lenses. A contact lens is placed directly on the cornea and forms an almost single optical system with the eye; glasses lenses, on the contrary, are located at a certain distance from the cornea (up to 12 mm). Therefore, in case of myopia, the power of contact lenses is slightly reduced, and in case of farsightedness, it is increased.

When choosing glasses or contact lenses, a prescription must be given to you. Be sure to save it and the next time you have your eyes checked, you can compare the results. In addition, if you have a prescription, you can order contact lenses or glasses at any optical shop you like, regardless of the location of the examination.

Subject. Solving problems on the topic "Lens. Constructing images in a thin lens. Lens formula."

Target:

• - consider examples of solving problems using the formula thin lens, properties of the main rays and rules for constructing images in a thin lens, in a system of two lenses.

Progress of the lesson

Before starting the task, it is necessary to repeat the definitions of the main and secondary optical axes of the lens, focus, focal plane, properties of the main rays when constructing images in thin lenses, the formula of a thin lens (converging and diverging), determination of the optical power of the lens, and magnification of the lens.

To conduct the lesson, students are offered several calculation problems with an explanation of their solution and problems for independent work.

Qualitative tasks

1. Using a converging lens, a real image of an object with magnification G 1 is obtained on the screen. Without changing the position of the lens, we swapped the object and the screen. What will be the increase in G 2 in this case?
2. How to arrange two converging lenses with focal lengths F 1 and F 2 so that a parallel beam of light, passing through them, remains parallel?
3. Explain why, in order to get a clear image of an object, a nearsighted person usually squints his eyes?
4. How will the focal length of the lens change if its temperature increases?
5. The doctor's prescription says: +1.5 D. Decipher what kind of glasses these are and for which eyes?

Examples of solving calculation problems

Task 1. The main optical axis of the lens is specified NN, source position S and his images S´. Find by construction the position of the optical center of the lens WITH and its focuses for three cases (Fig. 1).

Solution:

To find the position of the optical center WITH lens and its focal points F we use the basic properties of the lens and rays passing through optical center, focal points of the lens or parallel to the main optical axis of the lens.

Case 1. Item S and its image are located on one side of the main optical axis NN(Fig. 2).

Let's walk you through S And S´ straight line (side axis) until it intersects with the main optical axis NN at the point WITH. Dot WITH determines the position of the optical center of the lens, located perpendicular to the axis NN. Rays passing through the optical center WITH, are not refracted. Ray S.A., parallel NN, refracts and goes through the focus F and image S´, and through S´ the beam continues S.A.. This means that the image S´ in the lens is imaginary. Item S located between the optical center and the focal point of the lens. The lens is converging.

Case 2. Let's walk you through S And S´ secondary axis until it intersects with the main optical axis NN at the point WITH- optical center of the lens (Fig. 3).

Ray S.A., parallel NN, refracting, goes through the focus F and image S´, and through S´ the beam continues S.A.. This means that the image is imaginary, and the lens, as can be seen from the construction, is scattering.

Case 3. Item S and his image lie on different sides from the main optical axis NN(Fig. 4).

Connecting S And S´, we find the position of the optical center of the lens and the position of the lens. Ray S.A., parallel NN, is refracted through the focus F goes to the point S´. The beam passes through the optical center without refraction.

Task 2. In Fig. 5 shows a beam AB passed through a diverging lens. Construct the path of the incident ray if the position of the focal points of the lens is known.

Solution:

Let's continue the beam AB to intersection with the focal plane RR at the point F´ and draw the secondary axis OO through F And WITH(Fig. 6).

Beam along the side axis OO, will pass without changing its direction, the ray D.A., parallel OO, refracted in the direction AB so that its continuation goes through the point F´.

Task 3. On a converging lens with focal length F 1 = 40 cm a parallel beam of rays falls. Where should a diverging lens with focal length be placed? F 2 = 15 cm so that the beam of rays remains parallel after passing through two lenses?

Solution: According to the condition, a beam of incident rays EA parallel to the main optical axis NN, after refraction in the lenses it should remain so. This is possible if the diverging lens is positioned so that the rear focal points of the lenses F 1 and F 2 matched. Then the continuation of the ray AB(Fig. 7), incident on a diverging lens, passes through its focus F 2, and according to the rule of construction in a diverging lens, the refracted ray BD will be parallel to the main optical axis NN, therefore, parallel to the ray EA. From Fig. 7 it can be seen that the diverging lens should be placed at a distance d=F 1 -F 2 =(40-15)(cm)=25 cm from the collecting lens.

Answer: at a distance of 25 cm from the collecting lens.

Task 4. The height of the candle flame is 5 cm. The lens gives an image of this flame 15 cm high on the screen. Without touching the lens, the candle is moved to l= 1.5 cm further from the lens and, moving the screen, again obtained a sharp image of a flame 10 cm high. Determine the main focal length F lenses and the optical power of the lens in diopters.

Solution: Let us apply the thin lens formula, where d- distance from the object to the lens, f- distance from the lens to the image, for two positions of the object:

. (2)

From similar triangles AOB And A 1 O.B. 1 (Fig. 8) the transverse magnification of the lens will be equal to = , whence f 1 = Γ 1 d 1 .

Similarly for the second position of the object after moving it by l: , where f 2 = (d 1 + l)Γ 2 .
Substituting f 1 and f 2 in (1) and (2), we get:

. (3)
From the system of equations (3), excluding d 1, we find

.
Lens power

Answer: , diopters

Task 5. A biconvex lens made of refractive index glass n= 1.6, has a focal length F 0 = 10 cm in air ( n 0 = 1). What is the focal length? F 1 of this lens if placed in a transparent medium with a refractive index n 1 = 1.5? Determine the focal length F 2 of this lens in a medium with a refractive index n 2 = 1,7.

Solution:

The optical power of a thin lens is determined by the formula

,
Where n l- refractive index of the lens, n avg- refractive index of the medium, F- focal length of the lens, R 1 And R 2- radii of curvature of its surfaces.

If the lens is in the air, then

; (4)
n 1:

; (5)
in a medium with a refractive index n :

. (6)
For determining F 1 and F 2 we express from (4):

.
Let's substitute the resulting value into (5) and (6). Then we get

cm,

cm.
The sign "-" means that in a medium with a refractive index greater than that of the lens (in an optically denser medium), the collecting lens becomes divergent.

Answer: cm, cm.

Task 6. The system consists of two lenses with identical focal lengths. One of the lenses is converging, the other is diverging. The lenses are located on the same axis at a certain distance from each other. It is known that if the lenses are swapped, the actual image of the Moon given by this system will shift by l= 20 cm Find the focal length of each lens.

Solution:

Let's consider the case when parallel rays 1 and 2 fall on a diverging lens (Fig. 9).

After refraction, their continuations intersect at the point S, which is the focus of the diverging lens. Dot S is the “subject” for a converging lens. We obtain its image in a collecting lens according to the construction rules: rays 1 and 2 incident on the collecting lens, after refraction, pass through the intersection points of the corresponding secondary optical axes OO And O´O´ with focal plane RR converging lens and intersect at a point S´ on the main optical axis NN, on distance f 1 from the collecting lens. Let us apply the formula for a converging lens

, (7)
Where d 1 = F + a.

Let the rays now fall on a collecting lens (Fig. 10). Parallel rays 1 and 2 after refraction will converge at a point S(focus of the collecting lens). Falling on a diverging lens, the rays are refracted in the diverging lens so that the continuations of these rays pass through the intersection points TO 1 and TO 2 corresponding side axes ABOUT 1 ABOUT 1 and ABOUT 2 ABOUT 2 with focal plane RR diverging lens. Image S´ is located at the intersection point of the extensions of emerging rays 1 and 2 with the main optical axis NN on distance f 2 from the diverging lens.
For diverging lens

, (8)
Where d 2 = a - F.
From (7) and (8) we express f 1 and - f 2:NN and beam S.A. after refraction going in the direction AS´ according to the rules of construction (through the point TO 1 intersection of secondary optical axis OO, parallel to the incident beam S.A., with focal plane R 1 R 1 converging lens). If you put a diverging lens L 2, then the beam AS´ changes direction at a point TO, refracting (according to the construction rule in a diverging lens) in the direction KS´´. Continuation KS´´ passes through the point TO 2 secondary optical axis intersections 0 ´ 0 ´ with focal plane R 2 R 2 diverging lenses L 2 .

According to the formula for a diverging lens

,
Where d- distance from the lens L 2 to item S´, f- distance from the lens L 2 to image S´´.

From here cm.
The "-" sign indicates that the lens is diverging.

Lens power diopter

Answer: cm, diopters

Tasks for independent work

1. Kasyanov V.A. Physics. 11th grade: Educational. for general education institutions. - 2nd ed., additional. - M.: Bustard, 2004. - P. 281-306.
2. Elementary textbook of physics / Ed. G.S. Landsberg. - T. 3. - M.: Fizmatlit, 2000 and previous editions.
3. Butikov E.I., Kondratiev A.S. Physics. T. 2. Electrodynamics. Optics. - M.: Fizmatlit: Laboratory of basic knowledge; St. Petersburg: Nevsky dialect, 2001. - pp. 308-334.
4. Belolipetsky S.N., Erkovich O.S., Kazakovtseva V.A. and others. Problem book in physics. - M.: Fizmatlit, 2005. - P. 215-237.
5. Bukhovtsev B.B., Krivchenkov V.D., Myakishev G.Ya., Saraeva I.M. Tasks for elementary physics. - M.: Fizmatlit, 2000 and previous editions.