Sphere 0 5 right eye what does it mean. Which eye is designated OD in a glasses prescription and which is designated OS. Symbols on the cylinder glasses form
If this is your first time receiving a prescription for glasses, then most likely you will not understand what all the symbols indicated in it mean. Even experienced glasses users 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. They may differ in design, the order in which the symbols are used, but if you understand the general scheme, then it will not be difficult to understand any recipe.
What designations are presented in a standard prescription for corrective glasses?
Traditionally, all prescriptions for glasses, as well as contact lenses start with icons OD andOS are abbreviations of the Latin terms “oculus dexter” (right eye) and “oculus sinister” (left eye). If the same correction is prescribed for the right and left eyes, the designation may be indicated OU is an abbreviation of the Latin term "oculus uterque" (both eyes). Instead of OD, some recipes have the designation R or Right for the right eye, and L or Left for the left eye.If the icon for a particular eye is followed by Plano, 0.00, it means that you do not need optical correction for that eye.
Also in the recipe, when quantitatively describing the selected correction, the following symbols will be present: SPH,C.Y.L.AXISADDITION (ADD).
SPH- indicates the optical power of the lens in diopters necessary to correct myopia or farsightedness. The “-” icon means that you need negative power lenses to correct myopia, “+” - you need positive power lenses to correct farsightedness.
CYL (CYLINDER) - the numbers given after this designation show the correction you need in diopters in the presence of astigmatism. Clarity of vision with astigmatism is achieved by using cylindrical lenses. If there is astigmatism and it is necessary to correct myopia or farsightedness, negative or positive spectacle lenses with a cylindrical component are used. Often such lenses are simply called astigmatic. The cylinder value can be minus - to correct myopic (nearsighted) astigmatism, or positive - to correct hypermetropic (farsighted) astigmatism.
AX (AXIS) - the numbers after this designation indicate the position of the cylinder axis in degrees from 0 to 180. This designation should be present in the prescription only if astigmatism correction is necessary.
ADDITION (ADD)- addition or correction for near - the amount of optical power of the lens in diopters added to your prescription for distance if you need glasses for clear vision when reading or working on close range. As a rule, Add- shows the difference in diopters between optical power in areas for distance vision and for work at close range in the manufacture of bifocal and progressive glasses for the correction of presbyopia. Add always has a (+) sign and in the vast majority of 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 indicated 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 D, OS: SPH -3.00 D, and for near (for reading) OD: SPH -2.50 D OS: SPH -1.00 D. The amount of addition in this case will be equal to +2.00 diopters. The addition value for the right and left eyes should generally be the same.
is the power of a prismatic lens, which is indicated in prismatic diopters designated Pdptr or p.d. or a triangle icon if the eye doctor or optometrist is filling out the 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 is facing (Base) - base up (base up), down (base down), towards the nose (base in), towards the temple base out).
In the prescription, the optical power of the lenses is indicated in gradations of 0.25 diopters - for example, 3.75 diopters, 0.25 diopters, etc. Prismatic diopters are rounded to half values -0.5 p.d.
P.D.(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 P.D. should be indicated monocularly for each eye, for example OD - 31 mm, OS - 33 mm. In some cases, the PD values for distance and near are indicated separately, and the PD for distance is greater than for near. The correct PD value is very important for installing complex lenses into frames, so its exact value should be determined by a specialist, and not written into the prescription from your words.
Let's look at examples of descriptions of corrections in a glasses prescription:
1. OD sph-3.5 cyl -1.5 ax 80 (sph-1.5 - 1.0 x 90)
OS sph -4,.0
This means that the right eye has a spherical myopia correction with a -3.5 D lens, but there is also astigmatism, which is corrected with a negative cylindrical lens of 1.0 D, and the cylinder axis is located at an angle of 80 degrees. For the left eye, a spherical correction with a negative lens was selected - 4.0 diopters.
2. OU: sph +1.5 add +2.0 - in this recipe, an optical power for distance of +1.05 diopters and an addition of +2.0 diopters are assigned for each eye.
Some prescriptions indicate data on 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 (the distance from the cornea to the lens), the pantoscopic angle of the frame, the bend angle of the frame, and others. To optimize the thickness of the lenses, the shape of the light field of the selected frame can be drawn directly in the recipe, as well as the designations used for the selected optical coating - hardening, anti-reflection, multifunctional - and also the desired color color can be indicated spectacle lenses.
Please note that a printout obtained from measurements on an autorefractometer cannot be used as a prescription for making glasses. Based on the data obtained with this device, it is possible to determine the objective refraction and estimate the direction of the cylinder axis in case of astigmatism. The final “subjective” correction is selected by a specialist - an ophthalmologist or optometrist based on various diagnostic tests.
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.
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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 ones - to correct 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.
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. Such active use of the eyes very often leads 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 (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. Optical power 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) mean 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:
- Optical power of a cylindrical lens (CYL) and the sign of hyperopia "+" for hyperopic astigmatism or the sign of myopia “-” with 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 (towards 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 close distances (SPH+ADD).
- Distance between pupils (DP) - 61 mm.
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 side 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, the optical power of 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 collecting lenses with optical forces 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.