What is c 1.5 1 in glasses. What does a cylinder mean in a glasses prescription? Final in vivo examination

Qualitative tasks

1. Using a converging lens, a real image of an object with magnification G1 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 G2 in this case?

2. How to position 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 diopters. 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 the optical center, the 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=F1-F2=(40-15)(cm)=25 cm from the converging 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's apply the thin lens formula https://pandia.ru/text/80/354/images/image009_6.gif" alt="http://ido.tsu.ru/schools/physmat/data/res/optika /pract/text/pic6-4-2.gif" width="87" height="45">, (1)!}

. (2)

From similar triangles AOB And A 1O.B. 1 (fig..gif" alt="http://ido.tsu.ru/schools/physmat/data/res/optika/pract/text/pic6-4-6.gif" width="23" height="47">, откуда !} f 1 = Γ1 d 1.

Similarly for the second position of the object after moving it by l: , where f 2 = (d 1 + l)Γ2.
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 n 2 = 1,7.

Solution:

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

,
Where nl- refractive index of the lens, nav- refractive index of the medium, F- focal length of the lens, R1 And R2- radii of curvature of its surfaces.

If the lens is in the air, then

; (4)
in a medium with a refractive index 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 1ABOUT 1 and ABOUT 2ABOUT 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:

, .
The difference between them according to the condition is equal to

l = f 1 - (-f 2) = .
From where see

Answer: cm.

Task 7. A converging lens produces an image on the screen S´ luminous point S, lying on the main optical axis. A diverging lens was placed between the lens and the screen at a distance d = 20 cm from the screen. By moving the screen away from the diverging lens, a new image was obtained S´´ luminous point S. In this case, the distance of the new screen position from the diverging lens is equal to f= 60 cm.

Determine the focal length F diverging lens and its optical power in diopters.

Solution:

Image S´ (Fig. 11) source S in a collecting lens L 1 is located at the intersection of the beam running along the main optical axis 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 1R 1 converging lens). If you put a diverging lens L 2 then 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 2R 2 diverging lenses L 2.F = 100 cm. Determine the refractive index n 2 liquids if the refractive index of the glass lens n 1 = 1,5.

Answer: .

2. The object is located at a distance of 0.1 m from the front focus of the converging lens, and the screen on which a clear image of the object is obtained is located at a distance of 0.4 m from the rear focus of the lens. Find the focal length F lenses. At what magnification Γ is the object depicted?

Answer: F = √(ab) = 2·10-1 m; Lighting technology and light sources" href="/text/category/svetotehnika_i_istochniki_sveta/" rel="bookmark">a light source so that the rays coming from it, after passing through both lenses, form a beam of rays parallel to the main optical axis? Consider two options.

Answer: cm in front of the first lens;

see behind the second lens.

4. Lens with focal length F= 5 cm tightly inserted into the round hole in the board. Hole diameter D= 3 cm. At a distance d= 15 cm from the lens on its optical axis there is a point source of light. On the other side of the board there is a screen on which a clear image of the source is obtained. What will be the diameter D 1 light circle on the screen if the lens is removed from the hole?

Answer: cm.

5. Construct an image of a point lying on the main optical axis of the collecting lens at a distance less than the focal one. The position of the lens's focal points is specified.

6. A parallel beam of light falls perpendicularly onto a collecting lens, optical power which D 1 = 2.5 diopters. At a distance of 20 cm from it there is a diverging lens with optical power D 2 = -5 dtr. The diameter of the lenses is 5 cm. The screen is located at a distance of 30 cm from the diverging lens E. What is the diameter of the light spot created by the lenses on the screen?

Answer: 2.5 cm.

7. Two converging lenses with optical powers D 1 = 5 diopters and D 2 = 6 diopters spaced apart l= 60 cm apart. Find, using construction in lenses, where the image of an object located at a distance is located d= 40 cm from the first lens, and lateral magnification of the system.

Answer: 1m; 5.

8. The path of the incident and refracted rays in the diverging lens is specified (Fig. 12). Find the main focal points of the lens by construction.

If you have good vision, This is wonderful. But if it so happens that you have been given a prescription for glasses, how to understand it and understand what these numbers, icons, incomprehensible terms and strange abbreviations mean?

OD and OS and other abbreviations

OD and OS are short for the Latin terms " oculus dexter" And " oculus sinister", translated meaning right and left eye, respectively. Sometimes only the abbreviation OU is found - this is an abbreviation for “ oculus uterque", which translates as "both eyes".

These designations are traditionally used by ophthalmologists and optometrists when writing prescriptions for glasses, contact lenses or eye drops.

In ophthalmology in general and in prescriptions for glasses in particular, information about the right eye is always indicated first, and then about the left. This makes it easier to avoid confusion and mistakes.

There may be other abbreviations in your glasses prescription. For example:

Sph (sphere) - “sphere” - means the optical power of the lens, expressed in diopters, necessary to correct your myopia, farsightedness or presbyopia. If there is a “-” sign in front of the numerical value, this means that you have nearsightedness, scientifically called myopia, which, as is known, is corrected by minus diverging lenses.

Often above the minus sign in Latin it is written “ concave" If there is a “+” sign, and you have been prescribed distance glasses, it means you have longsightedness, or hypermetropia, and you need plus, converging lenses, designated “ convex» .

Cyl (Cylinder) - “cylinder” - indicates the optical power of lenses used to correct astigmatism. Astigmatism is spoken of when the surface of the cornea is uneven, non-spherical, and refraction occurs stronger in one of the meridians than in others. This anomaly is corrected by cylindrical lenses. In this case, the position of the cylinder axis must be indicated ( Axis, abbreviated as Ax) in degrees from 0 to 180.

This is due to the characteristics of the refraction of light passing through a cylindrical lens. Rays going perpendicular to the axis of the cylinder are refracted. And axes running parallel do not change their direction. Such properties allow us to “correct” the refraction of light in the specific meridian we need.

The cylinder value can be minus - to correct myopic (nearsighted) astigmatism, or positive - to correct hypermetropic (farsighted) astigmatism.

The trial frame is used to determine visual acuity and select glasses

The meridians are determined by applying a special scale to the front surface of the eye. Typically, such a scale is built into the trial frame used to determine visual acuity and select glasses, and is called a scale, or system, TABO.

Add – addition – the so-called “near increase” 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 the correction of presbyopia. Those. if you need lenses +1.0 Dptr for distance vision, and +2.5 Dptr for near vision, then the addition will be +1.5 Dptr. Maximum value addition does not exceed +3.0 D.

Prism is the power of a prismatic lens, measured in prismatic diopters. (p.d. or 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 - base up, down, inward (toward the nose), outward (towards the temple).

The optical power of spherical and cylindrical lenses, as well as additions, is indicated in diopters with a maximum refinement of up to 0.25 D. (e.g. 0.75 D, 1.25 D, etc.) Prismatic diopters are rounded to half values -0.5 p.d.

Dp (distancia pupilorum) or RC is the distance between the centers of the pupils in millimeters. For distance it is, as a rule, 2 mm more than for near.

Example of a prescription for glasses

By saving your glasses prescription, you can compare the results later.

OD sph-1.5 cyl -1.0 ax 90 (sph-1.5 - 1.0 x 90)
OS sph -2.0

This prescription means that the right eye requires spherical correction of myopia with a -1.5 D lens; there is astigmatism, which is corrected with a minus cylindrical lens of 1.0 D, while the axis of the cylinder, i.e. inactive meridian, located along an axis of 90 degrees. For the left eye, spherical correction with a minus lens of 2.0 D was prescribed.

OU sph +1.0 +1.5 add

In this case, bifocal lenses with a distance zone of +1.0 D and a near increase of +1.5 D were prescribed for both eyes.

Contact lens prescription

Why can't I use my glasses prescription to buy contact lenses? Prescriptions for glasses and contact lenses are slightly different.

A contact lens, unlike glasses, fits directly onto the cornea and is built into the optical system eyes

First, your contact lens prescription must specify the base curvature and diameter of the lenses. Secondly, the contact lens is placed directly on the cornea, forming a single optical system with the eye, unlike glasses, which are separated from the cornea at a certain distance (on average 12mm).

Therefore, for myopia, it is necessary to slightly reduce the power of contact lenses, and for farsightedness, increase it.

If you have been fitted for glasses or contact lenses, you must be given a prescription. Save it. The next time you have your eyesight checked, you can compare the results. In addition, regardless of the place of examination, having a prescription in hand, you can order glasses or contact lenses in any salon you like.

Dear visitors of the Proglaza portal! On our website you have the opportunity buy a device for vision treatment "Sidorenko's glasses" right now!

The Proglaza.ru website cooperates with the manufacturer of a device for vision treatment under special conditions; so we are pleased to offer you "Sidorenko glasses" at a reduced price !

Order your Sidorenko Glasses device by filling out.

OD, OS and other abbreviations

The abbreviations OD and OS are short terms for the Latin terminology “oculus dexter”, “oculus sinister”, which 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 - corrective hypermetropic astigmatism(for farsightedness).

The 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 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.

Prescriptions for both 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 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.

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

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?
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?
Explain why, in order to get a clear image of an object, a nearsighted person usually squints his eyes?
How will the focal length of the lens change if its temperature increases?
The doctor's prescription says: +1.5 D. Decipher what kind of glasses these are and for which eyes?

Examples of solving calculation problems

Solution:

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

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).

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

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´.

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

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

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.

Solution:

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

, (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

Kasyanov V.A. Physics. 11th grade: Educational. for general education institutions. - 2nd ed., additional. - M.: Bustard, 2004. - P. 281-306.
Elementary textbook of physics / Ed. G.S. Landsberg. - T. 3. - M.: Fizmatlit, 2000 and previous editions.
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.
Belolipetsky S.N., Erkovich O.S., Kazakovtseva V.A. and others. Problem book in physics. - M.: Fizmatlit, 2005. - P. 215-237.
Bukhovtsev B.B., Krivchenkov V.D., Myakishev G.Ya., Saraeva I.M. Problems in elementary physics. - M.: Fizmatlit, 2000 and previous editions.

Home Glasses from A to Z Recipe for glasses

After inspection and carrying out the necessary diagnostic studies Your doctor may prescribe you to wear glasses. The recipe entry will look something like this:
OD Sph −3.0D, Cyl −1.0D ax 180
OS Sph −3.0D, Cyl −2.0D ax 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) is the left eye, respectively. 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 dioptres - D (dioptria). In the case of collective lenses (for hyperopia), a “+” sign is placed in front of its value, in the case of diverging lenses (for myopia) - “-”; In our example, the “-” sign is used, which indicates the need to correct myopia.

Cyl (cylinder) - designation of a cylindrical lens. These lenses are used to correct astigmatism. By analogy with spherical lens it is not difficult to guess that 1.0, as in our example, is optical power.

The cylinder value can be minus to correct myopic (nearsighted) astigmatism and positive to correct hypermetropic (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 characteristics of the refraction of light passing through a cylindrical lens. Rays going perpendicular to the axis of the cylinder are refracted. And 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 (can be indicated in brackets for each eye separately).

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

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

Contents [Show]

Cylinder transposition

There are often cases when patients are faced with a phenomenon that is incomprehensible to them. When ordering glasses from a workshop, the customer can change the lens parameters. For example, an optician wrote the following prescription:
OD sph - cyl +0.5 ax 180
OS sph - cyl +0.5 ax 0
DP=52mm
In the workshop, the following entry 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

Don't worry - it's normal phenomenon, a purely technical point without any deception. An astigmatic lens always corresponds to two equivalent entries: one with a plus cylinder, and the other with a minus cylinder. The transition from one record to another is called cylinder transposition. 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 for 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 of the cylinder force:
+0.5 replace + with - and get cyl −0.5
3. Change the position of the axis by 90 degrees:
180 degrees turns into 90, just like 0 turns into 90.

This is how two externally can appear different entries, but essentially meaning the same parameters of lenses for glasses.

Current version of the page so far

not checked

Current version of the page so far

not checked

experienced participants and may differ significantly from

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

Legend

When writing a prescription, observe the following notations:

O.D.(lat. oculus dexter) - right eye;
OS(oculus sinister) - left eye;

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

OU(oculus uterque) - both eyes - when prescribing identical lenses, there is no need to designate the lens for each eye; you can put the appropriate 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 must look exactly into the pupil of the examiner'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 greater than for near.

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

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

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

Such properties make it possible to “correct” the refraction of light in the desired specific meridian. The cylinder value is

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

The value of the cylinder is a value equal to the difference between the refractive indexes in two meridians and its sign can be reversed if necessary. To do this, transposition rules are applied: the sign of the cylinder is changed to the opposite, 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 170Meridians are determined by applying a special scale to the front surface of the eye. Typically, such a scale is built into the trial frame used to determine visual acuity and select glasses, and is called a scale, or system, TABO.

Add(additio - addition) - addition - “near increase” 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 the correction of presbyopia.

The maximum addition value 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 - base up, down, inward (towards the nose), outward (towards 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.

Glass 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 is required (to correct myopia) with a power of −1.5D; 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 an axis of 90 degrees;
A spherical diverging lens with a power of −3.0D was prescribed for the left eye (to correct myopia).

OU sph -2.0 +1.5 add

Recipe means:

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

Right/Left Eye (OD/OS)

It is important to enter your prescription values correctly for the right and left eyes. Very often these parameters have different meanings 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; ah, “OS” “Left” or just “L.” - for the left eye... abbreviating these words by abbreviation.

Sphere (sph.)

The "sphere" setting gives the basic diopter power needed for your glasses lenses. As a rule, in an ophthalmologist’s prescription they write “Sph”, “Sphere” or simply “S” - “Sph.” - abbreviated by abbreviation. This value is preceded by a “+” sign if you are farsighted, or a “-” sign if you are nearsighted. In some cases, the prescription for glasses does not include any sign - then, by default, this means “+” dioptres. If you are unsure what "sphere" value you should enter in your order for spectacle lenses, 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.

Cylinder (Cyl.)

When you have “astigmatism,” the cornea of your eye is misshapen. Round form The cornea actually becomes oval. This can happen both vertically and horizontally. With astigmatism, clear vision in some directions disappears. Astigmatic lenses for glasses can correct vision with different diopters in horizontal or vertical lines.

In the case of “astigmatism,” the prescription for spectacle lenses includes the “cylinder” parameter, which compensates for this distortion. The meaning of "cylinder" can be found in your eyeglass prescription. It is mainly written as "Cyl", "S.", "Cyl." abbreviating the word "Cylinder". 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 further.

If you are unsure which "cylinder" value you should enter in your eyeglass lens order, please call our consultant opticians on 8 800 777 5929. Our friendly team of experienced opticians are happy to assist you in choosing the right glasses.

Axis (Ax)

This is the value of the tilt axis of the “cylinder” indicated in degrees. It describes the orientation of the “cylinder” in the opening of the eyeglass frame. To accurately correct astigmatism, you must carefully follow the doctor's instructions indicated in the prescription.

This parameter is always between 0° and 180°. It is mainly written as “Ax”, “Axis”, “Axis”, abbreviating the word “Axis” by abbreviation. If you are unsure what axis 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 assist you in choosing the right glasses.

Addition (ADD)

The Addition setting describes the strength of dioptres required in addition to "distance vision" so that you can see clearly at "near distances" such as reading or working on a computer - without changing your glasses. This value is found in “progressive lenses”, which simultaneously correct vision at three distances: “distance” + “medium distance” + “near”.

This value only appears when choosing bifocal or progressive lenses and can be found in your glasses 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 unsure what value to enter in the add field, please call our optical consultants on 8 800 777 5929. Our friendly team of experienced opticians are happy to help you choose the right glasses.

Center-to-center pupil distance RC (PD)

“RC” is the position of your eyes in the frame. In the prescription, the ophthalmologist indicates at what distance 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 combines this value for both eyes together, the “RC” value usually varies between 50-80 millimeters.

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

The RC value can be found in your glasses prescription. Basically, it is written as “RC”, “PD”, “DP”, abbreviating the phrase “distance of centers” in an abbreviation.

What is c 1.5 1 in glasses. What does a cylinder mean in a glasses prescription? Final in vivo examination

OD and OS and other abbreviations

Example of a prescription for glasses

Contact lens prescription

OD, OS and other abbreviations

Prescription for glasses

Prescription for glasses and contact lenses

Cylinder transposition

Legend

Glass prescription examples

see also

Links

Right/Left Eye (OD/OS)

Sphere (sph.)

Cylinder (Cyl.)

Axis (Ax)

Addition (ADD)

Center-to-center pupil distance RC (PD)