What is c 1.5 1 in glasses. quality tasks. Final examination in vivo

Home Glasses from A to Z Prescription glasses

After examining and performing the necessary diagnostic tests, the doctor may prescribe you to wear glasses. The recipe entry will look something like this:
OD Sph -3.0D, Cyl -1.0Dax 180
OS Sph -3.0D, Cyl -2.0Dax 175
Dp 68 (33.5/34.5)
Let's try to figure out what these strange letters and numbers mean.

OD (oculus dexter) is the designation of the right eye, OS (oculus sinister) - respectively, the left. In some cases, it may be indicated - OU (oculus uterque), which means "both eyes." In ophthalmology, to avoid confusion, it is customary to always indicate the right eye first, then the left.

Sph (sphere) - denotes a spherical lens. These lenses are used to correct nearsightedness (myopia) and farsightedness (hypermetropia).

The number (in our example 3.0) indicates the optical power of the lens, expressed in diopters - D (dioptria). In the case of converging lenses (for hypermetropia), a “+” sign is placed in front of its value, in the case of scattering lenses (for myopia) - “-”; In our example, the “-” sign is used, which indicates the need for correction of myopia.

Cyl (cylinder) - designation of a cylindrical lens. These lenses are used to correct astigmatism. By analogy with a spherical lens, it is easy to guess that 1.0, as in our example, is the optical power.

The value of the cylinder can be negative for correcting myopic (nearsighted) astigmatism and positive for correcting hyperopic (farsighted) astigmatism.

A mandatory parameter of a cylindrical lens is such an indicator as Ax (axis) - the axis of the cylinder. It is measured in degrees from 0 to 180. This is due to the peculiarities of the refraction of light passing through a cylindrical lens. Beams are refracted that are perpendicular to the axis of the cylinder. Axes running parallel do not change their direction. Such properties allow us to "correct" the refraction of light in the specific meridian we need.

Dp (distantio pupillorum) - the distance between the centers of the pupils in millimeters (in brackets it can be indicated for each eye separately).

So, let's summarize this information and read the above recipe. For the right eye, correction of myopia is required, with a lens with a power of 3.0 diopters. Astigmatism correction is also required, with a cylindrical lens with a power of 1.0 diopter and with a cylinder axis of 180 degrees. The left eye has the same correction for myopia as the right eye, but for the correction of astigmatism, a cylindrical lens with a power of 2.0 diopters and an axis of 175 degrees is required. The interpupillary distance is 68 mm.

There are differences in prescriptions for glasses abroad. There, the number of characters is minimized and the recipe looks like this: −2.00 +1.50×80

Table of contents [Show]

Cylinder transposition

It is not uncommon for patients to encounter a phenomenon that is incomprehensible to them. When ordering glasses in the workshop, the receiver can change the parameters of the lenses. For example, a doctor in optics wrote the following prescription:
OD sph - cyl +0.5 ax 180
OS sph - cyl +0.5 ax 0
DP=52mm
In the workshop, an entry like the following may appear on the order form:
OD sph +0.5 cyl −0.5 ax 90
OS sph +0.5 cyl -0.5 ax 90
DP=52mm

Do not worry - this is a normal phenomenon, a purely technical moment without any deception. An astigmatic lens always corresponds to two equivalent records: one with a plus cylinder, and the other with a minus one. The transition from one notation to another is called the transposition of the cylinder. Its principle is as follows:
1. Add the force of the sphere and the cylinder, taking into account the sign, to obtain a new value of the force of the sphere:
In this case, 0+0.5 gives a value of sph +0.5
2. Change the sign of the cylinder force to obtain a new value for the cylinder force:
+0.5 replace + with - and get cyl −0.5
3. Change axis position by 90 degrees:
180 degrees turns into 90, just like 0 turns into 90.

This is how two outwardly different entries can appear, but in fact they mean the same lens parameters for glasses.

The current version of the page so far

not tested

The current version of the page so far

not tested

experienced participants and may differ significantly from

prescription for glasses- a form that contains the data necessary for the correct manufacture or purchase of finished glasses.

Conventions

When issuing a prescription, the following designations are observed:

• OD(lat. oculus dexter) - right eye;
• OS(oculus sinister) - left eye;

In ophthalmology in general and in eyeglass prescriptions in particular, information about the right eye is always indicated first, and then about the left, in order to avoid confusion and errors.

• ou(oculus uterque) - both eyes - when prescribing identical lenses, there is no need to designate a lens for each eye, you can put the corresponding designation (OU);
• D.P. or D.P.(distantia pupillaris) or RMC - the distance between the centers of the pupils in millimeters;

The distance is measured with a millimeter ruler from the outer edge of the cornea of ​​one eye to the inner edge of the cornea of ​​the other eye. When installing the ruler, the patient should look exactly into the pupil of the researcher's left eye with his right eye and vice versa, into the pupil of his right eye with his left eye. For distance, the distance is 2 mm more than for near.

• Sph(sphaera) - sphere - optical power of the lens, expressed in diopters (denoted D or diopter) needed to correct the refractive error.
  • For myopia (myopia), divergent lenses are used - there is a “-” sign in front of the numerical value. Often above the minus sign in Latin is written "concave".
  • For farsightedness (hypermetropia), converging lenses are used - there is a “+” sign - in Latin they are denoted by “convex”.
• cyl(cylindrus) - cylinder - the optical power of the lenses used to correct astigmatism.

This anomaly is corrected by cylindrical lenses. In this case, the position of the axis of the cylinder must be indicated Ax(axis - axis) in degrees from 0 to 180. This is due to the peculiarities of the refraction of light passing through a cylindrical lens:

• rays traveling perpendicular to the axis of the cylinder are refracted;
• rays traveling parallel to the axis do not change their direction.

Such properties allow you to "correct" the refraction of light in the desired specific meridian. The value of the cylinder is

• minus - to correct myopic (myopic) astigmatism;
• plus - for the correction of hyperopic (far-sighted) astigmatism.

The value of a cylinder is a value equal to the difference between the refractive indices in the two meridians and its sign can be reversed if necessary. To do this, the rules of transposition are applied: the sign of the cylinder is reversed, 90 ° should be subtracted or added to the axis so that the number is from 0 ° to 180 °, the sphere index is calculated by adding the cylinder index to it. For example: sph -1.0 cyl +1.0 ax 100 = cyl -1.0 ax 10 sph +6.0 cyl -2.0 ax 80 = sph +4.0 cyl +2.0 ax 170 Meridians are determined by applying a special scale to the front surface of the eye. Usually such a scale is built into the trial frame used for determining visual acuity and fitting glasses, and is called the scale, or system, TABO.

• Add(additio - addition) - addition - "near addition" - this is the difference in diopters between the zones for distance vision and for working at close range in the manufacture of bifocal and progressive glasses for presbyopia correction.

The maximum value of addition does not exceed +3.0D.

• Prisma - prism - the power of a prismatic lens, measured in prismatic diopters: p.d. or a triangle icon (if the recipe is written by hand). Prismatic lenses are used to correct strabismus. When prescribing prismatic lenses, depending on the type of strabismus, it is indicated in which direction the base of the prism is facing - with the base up, down, inward (toward the nose), outward (to the temple).

The optical power of spherical and cylindrical lenses, as well as additions, are indicated in diopters with a maximum refinement of up to 0.25 (D or diopter.).

Prismatic diopters are rounded to half values ​​- 0.5 p.d.

Eyeglass prescription examples

OD sph -1.5 cyl -1.0 ax 90 (or sph -1.5 -1.0 x 90) OS sph -3.0

Recipe means:

• for the right eye, a spherical diverging lens (for the correction of myopia) with a power of -1.5D is required, there is astigmatism, which is corrected by a lens with a power of -1.0D (minus cylindrical), while the axis of the cylinder, that is, the inactive meridian, is located along the axis of 90 degrees;
• for the left eye, a spherical diverging lens with a power of -3.0D was assigned (for the correction of myopia).

OU sph -2.0 +1.5 add

Recipe means:

• Bifocal lenses were prescribed for both eyes with a distance zone of -2.0D and a “near gain” of +1.5D.

see also

• Determination of visual acuity

Links

• prescription for glasses

Right/Left Eye (OD/OS)

It is important to correctly enter your prescription values ​​for the right and left eyes. Very often these parameters have different values ​​for one and the other eye. As a rule, in the prescription of an ophthalmologist, they write "OD", "Right", or simply "P." - for the right eye; a, "OS" "Left" or simply "L." - for the left eye ... shortening these words by abbreviation.

Sphere (sph.)

The sphere setting gives the basic diopter power needed by your eyeglass lenses. As a rule, in the prescription of an ophthalmologist, they write "Sph", "Sphere" or simply "S" - "Sph." - shortened by abbreviation. This value is preceded by a "+" sign when you are farsighted, or a "-" sign if you are nearsighted. In some cases, the prescription for glasses does not put any sign - then, by default, it means "+" diopters. If you are not sure what “sphere” value you should enter in your spectacle lens order, please call our consultant opticians on 8 800 777 5929. Our friendly team of experienced opticians are happy to help you choose the right spectacles.

Cylinder

When you have "astigmatism", the cornea of ​​your eye is deformed. The round shape of the cornea actually becomes oval. This can happen both vertically and horizontally. With astigmatism, clear vision in some directions disappears. Astigmatic eyeglass lenses can correct vision with different diopters in horizontal or vertical lines.

In the case of “astigmatism”, the “cylinder” parameter is included in the prescription for spectacle lenses, which compensates for this distortion. The meaning of "cylinder" can be found in your eyeglass prescription. Basically it is written as "Cyl", "S.", "Cyl." shortening the word "Cylinder" in an abbreviation. This value is also preceded by a "+" or "-" sign, be careful when ordering.

The "Cylinder" parameter is always accompanied by another value - "Axis" - read about this below.

If you are unsure which “cylinder” you should enter on your spectacle lens order, please call our Consultant Opticians on 8 800 777 5929. Our friendly team of experienced opticians are happy to help you select the right spectacles.

Axis (Ax)

This is the value of the axis of inclination of the "cylinder" indicated in degrees. It describes the orientation of the "cylinder" in the eyeglass frame opening. For accurate correction of astigmatism, it is necessary to carefully follow the doctor's prescription indicated in the prescription.

This parameter is always between 0° and 180°. Basically, it is written as "Ax", "Axis", "Axis", shortening the word "Axis" in an abbreviation. If you are not sure what value of "axis" you should enter in your spectacle lens order, please call our consultant opticians on 8 800 777 5929. Our friendly team of experienced opticians are happy to help you choose the right spectacles.

Addition (ADD)

The Add parameter describes the amount of diopter required in addition to "distant vision" so that you can see clearly at "close" distances, such as when reading or working on a computer, without changing your glasses. This value is available for "progressive lenses", which simultaneously correct vision at three distances "far" + "middle distance" + "near".

This value only appears when bifocal or progressive lenses are selected and can be found in your eyeglass prescription. Sometimes, this parameter is written as "add" or "ADD". In addition, often, this value is recorded once for both eyes (right and left).

If you are not sure what value to enter in the "add" field, please call our consultant opticians on 8 800 777 5929. Our friendly team of experienced opticians are happy to help you choose the right glasses.

Intercenter pupillary distance of the RC (PD)

“'RC' is the location of your eyes in the frame. The ophthalmologist in the prescription indicates how far from the bridge of the nose or the center of the nose the right and left eyes are located separately, in millimeters. In this case, this parameter will be in the range of 25–40 millimeters. If the doctor combined this value for both eyes together, then the value of "RC" usually varies between 50-80 millimeters.

If your prescription says the average value of "RC", you divide this number by two (in half) and enter the result in the field of the right and left eyes. For example, "RC" 63 mm is indicated: it turns out that this parameter will be 31.5 mm for the right and left eyes.

The value of "RC" can be found in your eyeglass prescription. Basically, it is written as "RC", "PD", "DP", shortening the phrase "center distance" in an abbreviation.

Visual impairment is stressful in itself. And the prescription for glasses written out after visiting an ophthalmologist does not contribute to calming. Understanding what is written on the form is quite capable of making the state of our psyche more calm.

In addition, it usually greatly increases the credibility of the doctor who prescribed it.

Most often, a prescription is written out on the form shown below.
As you can see, the parameters of the right eye go first, and then the left. This is a prerequisite for all ophthalmic prescriptions.
Here we will consider all the possible parameters that are entered in the form. But in each specific recipe, only a part of them is present. Those that relate to this patient.

So, when prescribing glasses for the correction of strabismus, most likely there will be no correction of addition (near correction). Correction of astigmatism is not always needed, and, therefore, it will not be indicated.

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

In our sample, “Right Eye” and “Left Eye” are written like that, but often doctors write to designate the right eye as OD, and the left as OS. Sometimes they write OU - it means both eyes. As already noted, the right eye must be first, and only then the left.

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

Designations on the form for glasses of the sphere

This is the optical power of a spherical lens. Her marking "Sph" when writing a recipe by hand. Calculate the lens power in diopters (Dopter or D) with a minimum step of 0.25 D. Here, there can also be two kinds of lenses:

• scattering - they are marked with a “-” sign in front of a number, for example -1.75, and are prescribed in the presence of myopia (myopia). If glasses with the “-” sign were prescribed, then this means that such a person does not see well into the distance;
• collecting, which are marked with a “+” sign in front of a number, for example + 2, 5, and are prescribed, respectively, for farsightedness (hypermetropia). When writing a prescription with a plus lens value, one should think that the person is having difficulty reading and other similar activities at close range.

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

Designations on the form for glasses of the cylinder

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 the rays of light passing through the axis of the cylinder, depending on the degree of refraction, act differently:

• if the beam is perpendicular to the axis, it is refracted;
• if the ray goes 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, which is located at the bottom of the table. The indicator is separately set for the right and left eyes.

To determine the value of a cylindrical lens, a special TAVO scale is used, which is worn on the frame during the examination of vision (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 meaning of cylindrical lenses are indicated in the table with the corresponding sign in diopters. With a step value up to 0.25 diopters.

Designations on the blank for axis points

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

Prism on spectacle blank

This type of lens is used to correct strabismus. This p.d. or used to indicate the direction of strabismus. 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 diopters.

It is present in prescription glasses for the correction of strabismus. But it is not filled in other forms.

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

Reasons for earning points

Additions are usually added here. Among them will be:
ADD - or Reading Addendum. Used with bifocals.

Interpupillary distance

When selecting points, this indicator plays a very important role. The corrective lens must always be opposite the pupil. Only in this way the eye will receive the desired correction, and not an additional load. An incorrectly positioned lens will require additional eye strain, which can cause headaches, eye fatigue, and sometimes double vision.

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

Important! Interpupillary distance (Dp) is not always indicated in the prescription. Therefore, it can be asked to specify in order to order glasses more convenient to use.

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

Assignment of points on the form

The lowest in the recipe will be the appointment of points. Usually the doctor will explain exactly how to wear glasses. But the recipe says so too. So, the designations will indicate the following:

1. underlined "For the distance" (or Dist) - this type of glasses is worn all the time, without taking off. It is designed to correct myopia. It is sometimes credited for driving a car or watching TV;
2. highlighted "For work" (or Near) - this type of glasses corrects presbyopia and allows you to work without problems at the computer, read, sew. They are used intermittently and should not be worn all the time;
3. marked "For permanent wear" (or Inter) - they are used to correct variable vision. As a rule, they use transitional (bifocal) lenses.

How to read a recipe?

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

We see that the right eye sees poorly into the distance - 5.0 diopters, while there is astigmatism -0.5 diopters. 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.

A prescription for lenses or glasses?

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

Therefore, for lenses and glasses, different prescriptions are always written out with different data and on different forms. And you can't order prescription glasses for lenses. Exactly, as well as vice versa - prescription lenses for glasses.

Topic. Solving problems on the topic "Lenses. Building images in a thin lens. Lens formula".

Target:

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

Lesson progress

Before starting the task, it is necessary to repeat the definitions of the main and secondary optical axes of the lens, focus, focal plane, the properties of the main rays when building images in thin lenses, the thin lens formula (collecting and scattering), determining the optical power of the lens, lens magnification.

For the lesson, students are offered several calculation tasks with an explanation of their solution and tasks for independent work.

Qualitative tasks

1. Using a converging lens, a real image of the object was obtained on the screen with magnification Г 1 . Without changing the position of the lens, the object and the screen were swapped. What will be the increase in Г 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 a lens change if its temperature rises?
5. The doctor's prescription says: +1.5 D. Decipher what kind of glasses these are and for which eyes?

Examples of solving computational problems

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

Solution:

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

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

Let's get through S and S´ straight line (side axis) to the intersection with the main optical axis NN at the point FROM. Dot FROM determines the position of the optical center of the lens, located perpendicular to the axis NN. Rays passing through the optical center FROM, are not refracted. Ray SA, parallel NN, is refracted and goes through the focus F and picture S´, and through S´ the beam continues SA. This means that the image S´ in the lens is imaginary. Subject S located between the optical center and the focus of the lens. The lens is converging.

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

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

Case 3 Subject S and its image lie on opposite sides of the main optical axis NN(Fig. 4).

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

Task 2. On fig. 5 shows a beam AB passed through a diverging lens. Plot the path of the incident beam if the position of the lens foci is known.

Solution:

Let's continue the beam AB before crossing the focal plane RR at the point F´ and draw a side axis OO through F and FROM(Fig. 6).

Beam going along side axis OO, will pass without changing its direction, the beam DA, parallel OO, is refracted in the direction AB so that its continuation goes through the point F´.

Task 3. On a converging lens with a focal length F 1 = 40 cm a parallel beam of rays falls. Where to place a diverging lens with a focal length F 2 \u003d 15 cm, so that the beam of rays after passing through two lenses remains parallel?

Solution: By condition, the 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 beam AB(Fig. 7), incident on a diverging lens, passes through its focus F 2 , and according to the construction rule in a diverging lens, the refracted beam BD will be parallel to the main optical axis NN, therefore parallel to the beam EA. From fig. 7 shows that the divergent lens should be placed at a distance d=F 1 -F 2 =(40-15)(cm)=25 cm from the converging lens.

Answer: at a distance of 25 cm from the converging 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 was moved aside. l\u003d 1.5 cm further from the lens and, moving the screen, again got a sharp image of the flame 10 cm high. Determine the main focal length F lenses and the optical power of the lens in diopters.

Solution: We apply the thin lens formula , where d is the 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 OB 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 to 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

.
Optical power of the lens

Answer: , diopter

Task 5. Biconvex lens made of refractive index glass n= 1.6, has a focal length F 0 = 10 cm in air ( n 0 = 1). What will be the focal length F 1 of this lens, if it is placed in a transparent medium with a refractive index n 1 = 1.5? Determine 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 is the refractive index of the lens, n sr is the refractive index of the medium, F is the focal length of the lens, R1 and R2 are the 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 can be expressed from (4):

.
Let us substitute the obtained 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 converging 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 some distance from each other. It is known that if the lenses are interchanged, then the actual image of the Moon given by this system will shift by l\u003d 20 cm. Find the focal length of each of the lenses.

Solution:

Let us consider the case when parallel beams 1 and 2 are incident on a diverging lens (Fig. 9).

After refraction, their extensions intersect at a point S, which is the focus of the diverging lens. Dot S is the "subject" for the converging lens. Its image in the converging lens will be obtained according to the construction rules: rays 1 and 2, incident on the converging lens, after refraction, pass through the intersection points of the corresponding side 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 converging lens. Let us apply the formula for a converging lens

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

Now let the rays fall on a converging lens (Fig. 10). Parallel rays 1 and 2, after refraction, will converge at a point S(focus of a converging lens). Falling on a diverging lens, the rays are refracted in the diverging lens so that the continuation of these rays pass through the points of intersection To 1 and To 2 corresponding side axles O 1 O 1 and O 2 O 2 with focal plane RR diverging lens. Image S´ is located at the point of intersection of the extensions of the outgoing beams 1 and 2 with the main optical axis NN on distance f 2 from a 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 SA after refraction going in the direction AS´ according to the construction rules (through the point To 1 crossing of the secondary optical axis OO, parallel to the incident beam SA, 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 divergent lens) in the direction KS´´. Continuation KS´´ passes through the point To 2 intersections of the secondary optical axis 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 subject S´, f- distance from the lens L 2 to image S´´.

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

Optical power of the lens diopter

Answer: see, diopter.

Tasks for independent work

1. Kasyanov V.A. Physics. Grade 11: Textbook. for general education institutions. - 2nd ed., supplement. - M.: Bustard, 2004. - S. 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. - S. 308-334.
4. Belolipetsky S.N., Erkovich O.S., Kazakovtseva V.A. etc. Problem book in physics. - M.: Fizmatlit, 2005. - S. 215-237.
5. Bukhovtsev B.B., Krivchenkov V.D., Myakishev G.Ya., Saraeva I.M. Problems in elementary physics. - M.: Fizmatlit, 2000 and previous editions.

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OD, OS and other abbreviations

The abbreviations OD and OS are short names for the Latin terminology "oculus dexter", "oculus sinister", which means "right eye" and "left eye" in translation. 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 issuing a prescription for any type of glasses or eye drops.

Note that in ophthalmology, all information about the right eye is always indicated first, and then about the left eye. So doctors are insured against confusion and errors. Therefore, in your recipe it will be written that way. In addition, there will be other abbreviations in it. For example:

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 the correction, either. Moreover, when a “-” sign is indicated in front of the numerical value, this means that you are short-sighted. Myopia, or in a scientific way, is corrected by scattering minus lenses. Sometimes you can see the Latin "concave" above the minus sign.

If there is a “+” before the numerical value, then you are farsighted, and your points are for the distance. Farsightedness, or , is corrected with plus convex lenses, otherwise referred to as "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, the refraction in one of its meridians is somewhat stronger than in the others. This anomaly can be corrected with cylindrical lenses. At the same time, the position of the cylinder axis (from the Latin Axis or Ax) must be indicated in the recipe, 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 that travel strictly perpendicular to the axis of the cylinder 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 "guilty" meridian.

The values ​​of the cylinder can be: or minus, i.e. designed to correct myopic astigmatism (with myopia), or plus - correcting hyperopic astigmatism (with farsightedness).

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

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

Prism or the power of a prismatic lens. This value is measured in prismatic diopters (i.e. p.d. or the triangle icon when a recipe is written by hand). These lenses are used for correction, and when prescribed, depending on its type, they indicate in which direction the base of the prism turns: up, down, outward (toward the temple), inward (toward the nose).

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

The distance between the centers of the pupils (RC) - Dp (distancia pupilorum) - a 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.

eyeglass prescription

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

This recipe can be deciphered as follows:

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

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

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

Spherical correction is shown for the left eye using a 3.0D minus lens.

DP - interpupillary distance 64 mm.

OU sph +2.0 +0.5 add

Prescription glasses and contact lenses

Sometimes people ask whether it is possible to use a prescription for glasses to make contact lenses? The answer is unambiguous - it is impossible.

In the design of prescriptions, both glasses and contact lenses have their own characteristics. A prescription for contact lenses must state the base curvature as well as the diameter of the lenses. A contact lens is worn 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, with myopia, the power of contact lenses is slightly reduced, with farsightedness, they are increased.

When choosing glasses or contact lenses, a prescription must be given to the hands. Be sure to save it and the next time you check your eyesight, you can compare the results. In addition, having a prescription, you can order contact lenses or glasses in any optics salon that you like, regardless of the place where the examination took place.

If this is the first time you have received a written prescription for glasses, then most likely you will not understand what all the symbols indicated in it mean. Even users of glasses with experience do not always clearly understand what is written in it. Read this note and you will have a clear idea of ​​what all these letters and numbers mean.

There is a certain order in which all prescriptions for spectacle correction are written. They may differ in design, the order of placement of the symbols used, but if you learn the general scheme, then it will not be difficult to understand any recipe.

What symbols are presented in a standard prescription for corrective glasses?

Traditionally, all prescriptions for glasses, as well as contact lenses, begin with icons OD andOS- these are abbreviations for the Latin terms "oculus dexter" (right eye) and "oculus sinister", (left eye). In the case of assigning the same correction for the right and left eyes, the designation can be indicated ou is an abbreviation for the Latin term "oculus uterque" (both eyes). Instead of OD, some prescriptions have R or Right for the right eye, and L or Left for the left.

If the icon for a particular eye is followed by the designation Plano, 0.00, then this means that you do not need optical correction for this eye.
Also, in the recipe for a quantitative description of the selected correction, there will be symbols - SPH,cyl,AXIS,ADDITION(ADD).
SPH- indicates the optical power of the lens in diopters, necessary to correct nearsightedness or farsightedness. The “-” sign means that you need negative power lenses to correct myopia, “+” means you need positive power lenses to correct farsightedness.
CYL (CYLINDER) - the numbers given after this designation show the diopter correction you need in the presence of astigmatism. Clear vision with astigmatism is achieved by using cylindrical lenses. In the presence of astigmatism and the need to correct also myopia or hyperopia, negative or positive spectacle lenses with a cylindrical component are used. Often such lenses are called simply astigmatic. The value of the cylinder can be negative - to correct myopic (nearsighted) astigmatism, or positive - to correct hyperopic (farsighted) astigmatism.
AX (AXIS) - the numbers after this designation indicate the position of the axis of the cylinder in degrees from 0 to 180. This designation should be present in the prescription only if astigmatism correction is required.
ADDITION(ADD)- near addition or correction - the amount of lens power in diopters added to your distance prescription if you need glasses for clear vision when reading or working at close range. As a rule, Add- indicates the difference in diopter between the optical power in the distance and near zones in the manufacture of bifocals and progressive glasses for the correction of presbyopia. Add always has a sign (+) and in most cases does not exceed 3 diopters. If you need lenses of -2.0 diopters for distance vision, and -0.5 diopters for near vision, then the addition will be +1.5 diopters.
In some cases, the amount of addition may not be specified in the prescription for progressive lenses, but then it will have two values ​​of the selected correction - for distance and for near. For example, for distance - OD: SPH -4.50 diopters, OS: SPH -3.00 diopters, and for near (for reading) OD: SPH -2.50 diopters OS: SPH -1.00 diopters. The value of addition in this case will be equal to +2.00.dptr. The value of addition for the right and left eyes should usually be the same.
is the power of a prismatic lens, which is indicated in prismatic diopters, denoted by Fdpt or p.d. or a triangle icon if an ophthalmologist or optometrist fills out a prescription by hand. Typically, prismatic lenses are used to correct strabismus. When assigning them, it is necessary to indicate in which direction the base of the prism (Base) is facing - base up (base up), down (base down), to the nose (base in), to the temple base out).
In the prescription, the optical power of the lenses is indicated in 0.25 diopters - for example, 3.75 diopters, 0.25 diopters, etc. Prismatic diopters are rounded to half values ​​-0.5 p.d.
PD(pupil distance) or Dp(distancia pupilorum) or RC- the distance between the centers of the pupils in millimeters, for example 64 mm, 72 mm. When ordering individual, progressive and complex lenses PD should be indicated monocularly for each eye, eg OD- 31 mm, OS- 33 mm. In some cases, the PD values ​​​​for distance and for near are indicated separately, and the PD for distance is greater than for near. The correct PD value is very important for the installation of complex lenses in the frame, so the specialist should determine its exact value, and not write its value into the prescription from your words.
Consider examples of correction descriptions in a prescription for eyeglasses:
1.OD sph-3.5 cyl -1.5ax 80 (sph-1.5 - 1.0 x 90)
OS sph-4,.0
This means that for the right eye, the spherical correction of myopia with a lens of -3.5 D is selected, but there is also astigmatism, which is corrected with a negative cylindrical lens of 1.0 D, and the axis of the cylinder is located at an angle of 80 degrees. For the left eye, a spherical correction with a negative lens of 4.0 diopters was selected.
2. OU: sph +1.5 add +2.0 - in this recipe each eye is assigned a power for distance +1.05 diopters and add +2.0 diopters.
Some prescriptions indicate data from additional measurements that are carried out when selecting individual single-vision or progressive lenses - the height of the center of the pupil for each eye, the vertex distance (distance from the cornea to the lens), the pantoscopic angle of the frame, the angle of the frame and others. To optimize the thickness of the lenses, the shape of the light aperture of the selected frame can be drawn directly in the prescription, as well as the designations used for the selected optical coating - hardening, anti-reflective, multifunctional, and also the color you want to color the spectacle lenses.

Please note that a printout obtained by measuring on an autorefractometer cannot be used as a recipe for making glasses. Based on the data obtained with this device, it is possible to determine the objective refraction and evaluate the direction of the axis of the cylinder in astigmatism. The final "subjective" correction is selected by a specialist - an ophthalmologist or an optometrist based on various diagnostic tests.