Geometric optics. Refraction of light in lenses
The simplest case of a centered system, consisting of only two spherical surfaces separating some transparent, highly refractive material from the environment, has a very great importance. Such a system is lens and plays an important role in many optical devices.
A lens is called thin if the distance between the vertices of the spherical surfaces bounding it is small compared to the radii of curvature of the surfaces. For a thin lens, the vertices of the refractive surfaces can be considered to coincide at one point, which is called optical center lenses. Any paraxial ray passing through the optical center point experiences virtually no refraction. Indeed, for such rays, sections of both surfaces of the lens can be considered parallel, so that the ray, passing through them, does not change direction, but only shifts parallel to itself (refraction in a plane-parallel plate), and since the thickness of the lens can be neglected, this shift is negligible and the beam passes practically without refraction. The ray passing through the center is called axis lenses. The one of the axes that passes through the centers of curvature of both surfaces is called main , the rest - side effects .
Depending on the type of instrument, we can choose between refractive error measurement, keratometry, pachymetry and intraocular pressure or aberometry. Otherwise: measurement of diopter and other eye parameters. Definition of refraction.
In the optical sense of refraction, the diopter of the patient is measured. Physical refraction means the bending of a light beam at the boundary of two optical media. The human eye is a system of more such media, but the front and lens are the main factors in the brightness of light. If the light beam breaks over these parts of the eye in the correct length corresponding to the length of the eye, vision becomes sharp, the image is displayed directly on the retina, you do not need glasses or contact lenses.
An expression connecting the position of an object and its image in a lens ( lens formula ) can be derived by considering two successive refractions of rays at each of the interfaces (Fig. 2.8). The first (along the ray) refractive surface gives an image of object A at point C, which, in turn, is the object for the second surface along the ray. The final image of object A in the lens is point B. The expression presented below was obtained under the same restrictions that we introduced for refraction at one spherical interface. Conditions: homocentricity bunches, stigmatization images , paraxiality And rule of signs. The main planes of a thin lens coincide and run perpendicular to the main one optical axis in the optical center, therefore the distances from the object and the image are measured from the optical center of the lens ( A 1 and A 2). We denote the refractive index of the lens n l, the refractive index of the homogeneous medium in which (we assume) the lens is located – n Wed R 1 – radius of curvature of the first spherical refractive surface along the ray path, R 2 radius second. In this case, the lens formula will look like:
(2.12)
The expression allows you to uniquely determine the position of the image if the position of the object is specified. The right side of the equality does not depend on the position of the object and its image and is determined only by the properties of the optical system itself. First parenthesis ( n l – n cp) determines the physical parameters of the system, and (1/ R 1 – 1/R 2) – geometric. By analogy with the formula for a spherical refractive surface, the right side of expression (2.12) is called optical power thin lens:
However, if the refraction of the beam is disproportionate to the length of your eye, you have a refractive or visual defect. Refractive errors include farsightedness, nearsightedness and astigmatism. These visual defects and the values for their correction can be determined by a refractometer or using.
Refraction is determined in two stages: first, the so-called objective refraction, where the patient looks at the refractometer and the device prints the measured dioptres and other parameters. Then subjective refraction, where the measured values are tested directly by testing bristles with glasses in the appropriate parameters on the patient using optics, and according to the patient's reactions, the expert will know when the vision is of good quality.
It is easy to show that the optical power of a thin lens is essentially the sum of the optical powers of its surfaces. Really:
The optical power of the lens is measured in dioptres (diopter). 1 diopter is the optical power of a lens in air having a focal length of 1 meter.
The lens is called collecting (positive ), If D > 0; dispersive (negative ), If D < 0. В случае линзы представленной на рис. 2.9: R 1 > 0, and R 2 < 0, тогда и оптическая сила такой линзыD> 0 if n l > n Wed Thus, the sign of the optical power of a lens is determined by its geometric parameters and the ratio of the refractive indices of the media.
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There are a number of benefits to wearing contact lenses in the summer. Compared to classic glasses, contact lenses provide precise visual correction in the field of view. You can also combine them with sunglasses without purchasing tinted diopter glass. Especially in summer types sports, begging on the beach and relaxation will be appreciated.
A refraction or visual inspection will be performed while you wait. We also offer discounts through health insurance companies, but be careful, your glasses prescription only lasts 90 days. The eye works on the principle of light refraction. It changes the direction of the rays passing through it. A retropic eye, that is, one that does not have any ocular defect, creates an image of observed objects on the retina. If the image occurs outside the retina, then it is an ametropic eye.
In Fig. 2.10 presents lenses of various configurations. If n l > n cf, then lenses numbered 1, 2, 3 are positive, and lenses numbered 4, 5, 6 are negative, if n l< n Wed, then vice versa.
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Considering a thin lens located in a homogeneous medium, we can introduce the quantities
, (2.14)
We distinguish between these ametropias. Myopia hypermetropia. . This is an ocular defect where distant objects perceive blur to the observer. The distance indicated by the myopia is shorter the less myopic. The cause is a disproportion in the length of the eye and a fracture of its optical apparatus. A clear image is created in front of the retina, and a blurry image is created by the retina. Myopia is corrected using minus spectacle lenses using so-called diffusers. This lens is stronger at the edges than in the middle.
The higher the myopia, the stronger the lens. This defect is most often caused by various curvatures of the cornea. Rays penetrating the eye do not create one focus, but two perpendicular axes at different distances. Astigmatism can be combined with other eye defects. Astigmatism is corrected with toric spectacle lenses.
determining the positions of the main focal points of this optical system. They are obtained by analogy with the focal lengths of a spherical refractive surface and, as can be seen, have different signs. Thus, the focal points lie on opposite sides of the lens (the first focal point is in front of the lens, the second focal point is behind the lens along the ray), but are equal in absolute value. Therefore, sometimes, using physics jargon, they talk about the “focus” of a lens (one focal length).
This is an ocular defect when the observer has difficulty seeing not only near, but also at a distance. In most cases, it is capable of focusing remotely, but it only depends on the use of its own placement. This leads to significant eye strain and fatigue. The hypermetropic eye is too short and the sharp image is formed behind the retina and the retina is blurred. Hypermetropia is often accompanied by saliva, which must be quickly removed to prevent dullness. Hypermetropicorygia with plush glasses with so-called muffs.
An example of constructing an image in a thin lens is shown in Fig. 2.11. Here the converging (positive) lens constructs a real, inverted and reduced image y¢ subject y. The linear (transverse) magnification given by a thin lens is calculated in exactly the same way as for a single surface:
These lenses are stronger in the center than at the edge. The higher the diopter error, the stronger the lens. With advancing age, the elasticity of the lens opens up. This significantly reduces the possibility of its placement. External speech is difficult to read and work nearby. If you have short arms while reading, this is a symptom that starts with presbyopia.
Vision is our most important goal because it provides us with more than 80% of the information. Visual development is a very complex process that goes through several stages. This process is influenced by fractures of the cornea and lens, the depth of the anterior chamber and the eye's anterior length. These are the values that determine the refraction of the eye.
. (2.15)
Similar to the above, we find that for inverted real images the increase is negative, and for direct imaginary ones V > 0.
The magnitude and sign of linear magnification for the same lens depend on the location of the object. If the object is located behind double focus converging lens (Fig. 2.12a), then its image turns out to be real, inverted and reduced.
The refraction of the eyes changes throughout life, especially in the first months and years of a child's development, and remains unchanged even after the end of body growth for about 20 years. These are physiological changes, they progress slowly, and any sudden change may indicate a painful cause.
The refraction of the eye expresses the relationship between the length of the eye and the optical power of its fragile surroundings. If the parallel rays entering the eye after refraction converge on the retina, we call this condition as emetropia, but if the parallel rays after fracture converge outside the retina, we call this condition as ametropia. Then the ametropic eye has some refractive errors.
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If the object is at the point of double focus, then the image becomes equal, remaining real and inverted (Fig. 2.12b). As the object further approaches the lens, the image gradually moves away, increasing in size, and when the object reaches the front focal plane, it is transferred to infinity (Fig. 2.12c, d).
The location of an object between the focus and the lens leads to the formation of an imaginary, direct, enlarged image (the case of a magnifying glass or magnifying glass, Fig. 2.12e).
Therefore, refractive error is a condition where there is an imbalance between the eye's fracture and its length. The defects are predominantly axial, where the anterior length of the eye is shorter or longer due to a fracture in the optical medium. There are fewer curvature refractive defects when the curvature of the refractive surfaces is too small or too large. There are also index defects, where the higher refractive index of the lens causes myopia and the lower refractive index hyperopia. Refractive defects can be divided into small and large.
A negative (scattering) lens is characterized by significantly less variability in the images formed: for any position of the object, the image is virtual, straight and reduced (Fig. 2.12e).
If there is an optical system consisting of several thin lenses placed together in a homogeneous medium ( n cp), then to determine the focal length of such a system you can use the expression
Small refractive errors are corrected on their own; through our own efforts, this activity is unintentional. This constant effort can lead to difficulties that we call asthenopic problems. The cause of these problems is not only the refractive error, but also the constant efforts to correct it.
Asthenopic problems: visual - they appear with blurred, foggy or even double vision, especially when tired or in poor light - appear with redness of the eye, soreness, foreign body sensation, burning, abnormal - manifest as headache.
, (2.16)
Where D syst is defined as the sum of the optical powers of each lens separately, calculated for the environment in which the system itself is located.
Light refraction- change in the direction of propagation of optical radiation (light) as it passes through the interface between two media.
Small refractive errors are corrected only in the case of asthenopic problems, and after correction these problems disappear. Large refractive errors cannot be corrected with increased effort and decreased visual acuity, so these defects must be corrected with a correction device such as glasses or contact lenses.
Lens selection - after surgery without glasses
If you want to remove your glasses and don't mind your reading glasses, you can choose between monofocal intraocular lenses. There is a whole range on the market, they are spherical and aspherical, with blue filters and without these filters. Aspherical lenses with a blue filter are great for the driver. These lenses are very well tolerated and adapt quickly. If you don't want to use glasses for most activities, you'll need to choose a multifocal lens. There are two options on the market - bifocal and trifocal lenses.
Laws of light refraction:
1) The incident ray, the refracted ray and the perpendicular, restored to the point of incidence to the interface between two media, lie in the same plane .
2) The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant value for a given pair of media. This constant is called the refractive index n 21 of the second medium relative to the first:
These lenses have focus at distance, near and even at mid-distance. The last three years have been trifocal lenses - they have three defined flashes - at distance, near and the all-important mid-range. They are still the most expensive, but the experience with them is excellent. If you have astigmatism, it is not a problem to solve this defect with a so-called toric lens. Both monofocal toric and multifocal toric lenses are available in the market. Our experience shows that astigmatism with an intraocular lens is very beneficial, resulting in significantly sharper vision.
The relative refractive index of two media is equal to the ratio of their absolute refractive indices n 21 =n 2 /n 1
The absolute refractive index of a medium is the value n, equal to the ratio of the speed c of electromagnetic waves in a vacuum to their phase speed v in the medium n=c/v
3) A ray of light incident on the interface between two media perpendicular to the surface passes into the other medium without being refracted.
Lens calculations are a little more complicated. The lens is made to order - it's about 1 month to wait for delivery before surgery. Each glass is carefully selected and handcrafted according to the wishes and needs of the client. With an individual approach, we exclude mass production.
It has been a long time since the first glasses saw the light of day in the world. A little before someone saw the beauty of the world with their first glasses. Since then, the first acquaintance at a meeting between two people is not just eyes, but also glasses. Only then do we evaluate dresses and shoes. Each of these brands is a concept of fashion, tradition, design, materials and innovation. We are honored to collaborate with them.
4) Incident and refracted rays are reversible: if the incident ray is directed along the path of the refracted ray, then the refracted ray will follow the path of the incident ray.
Total internal reflection- reflection of light at the interface of two transparent substances, not accompanied by refraction. Total internal reflection occurs when a beam of light is incident on a surface separating a given medium from another, optically less dense medium, when the angle of incidence is greater than the limiting angle of refraction.
Correct correction phase
Their more than twenty years of professional experience and continuous education make them the absolute leader in Czech optometry. At this stage, we clarify the values measured by the device and adapt them to the subjective sensations of the client. By optimizing, we achieve the correct depth of field and natural color perception of the resulting image. Diagnosis of binocular vision. In many cases, the rays of light do not reach the eye from the best point of view and the extraocular muscles make a correction that is not natural. This aggravates distance estimation, reaction speed and, therefore, the overall concentration of the body.
- Objective determination of refraction using an autorefractometer.
- The result is indicative only and cannot be used for scoring purposes.
- Analysis and modulation of subtle deviations by subjective methods.
Path of rays in the lens.
A lens is a transparent body bounded by two spherical surfaces. If the thickness itself
lens is small compared to the radii of curvature of spherical surfaces, then the lens is called thin.
Lenses are either converging or diverging. Collecting(positive) lenses are lenses that convert a beam of parallel rays into a converging one. Scattering(negative) lenses are lenses that convert a beam of parallel rays into a divergent one. Lenses whose centers are thicker than the edges are converging, and those whose edges are thicker are diverging.
You can buy all types of lenses. Reduced When using refractive index material, the lens becomes thinner and lighter. The problem is that under the beautiful sunglasses you must wear contact lenses because you cannot see through them. Self-coloring Their coloring constantly adapts to lighting conditions. Polarization will prevent unwanted flashes of light reflected on sports glasses sports glasses sand special lenses with diopters, appropriate filters and colors. These lenses will have the same parameters as the original. The room turns pale in the darkness. . All spectacle lenses.
A straight line passing through the centers of curvature O1 and O2 of spherical surfaces is called main optical axis of the lens. In the case of thin lenses, we can approximately assume that the main optical axis intersects with the lens at one point, which is usually called optical center of the lens O. The light beam passes through the optical center of the lens without deviating from its original direction. All straight lines passing through the optical center are called secondary optical axes.
If a beam of rays parallel to the main optical axis is directed at a lens, then after passing through the lens the rays (or their continuation) will converge at one point F, which is called the main focus of the lens. A thin lens has two main foci, located symmetrically on the main optical axis relative to the lens. Converging lenses have real foci, while diverging lenses have imaginary foci. Beams of rays parallel to one of the secondary optical axes, after passing through the lens, are also focused at point F", which is located at the intersection of the secondary axis with the focal plane Ф, that is, the plane perpendicular to the main optical axis and passing through the main focus. Distance between the optical center lenses O and the main focus F is called the focal length. It is denoted by the same letter F. For a converging lens, F > 0 is considered, for a diverging lens, F< 0.
The reciprocal of D focal length, is called the optical power of the lens. The SI unit of optical power is the diopter (dopter).
Path of rays in lenses
The main property of lenses is the ability to produce images of objects. Images can be upright or inverted, real or imaginary, enlarged or reduced.
The position of the image and its character can be determined using geometric constructions. To do this, they use the properties of some standard rays (remarkable rays), the course of which is known. These are rays passing through the optical center or one of the focal points of the lens, as well as rays parallel to the main or one of the secondary optical axes. Constructing an image in a thin lens:
1. A ray parallel to the main optical axis passes through the main focus point.
2. A beam parallel to the secondary optical axis passes through the secondary focus (a point on the secondary optical axis).
3. The beam passing through the optical center of the lens is not refracted.
4. Real image - intersection of rays. Virtual image - intersection of continuations of rays
Converging lens
1. If the subject is located behind a double focus.
To construct an image of an object, you need to shoot two rays. The first ray passes from the top point of the object parallel to the main optical axis. At the lens, the ray is refracted and passes through the focal point. The second ray must be directed from the top point of the object through the optical center of the lens; it will pass through without refraction. At the intersection of two rays we place point A’. This will be the image of the top point of the object. The image of the lower point of the object is constructed in the same way. As a result of the construction, a reduced, inverted, real image is obtained.
2.If the subject is located at the double focus point.
To construct, you need to use two beams. The first ray passes from the top point of the object parallel to the main optical axis. At the lens, the ray is refracted and passes through the focal point. The second ray must be directed from the top point of the object through the optical center of the lens; it will pass through the lens without being refracted. At the intersection of two rays we place point A1. This will be the image of the top point of the object. The image of the lower point of the object is constructed in the same way. As a result of the construction, an image is obtained whose height coincides with the height of the object. The image is upside down and real
3. If the object is located in the space between focus and double focus
To construct, you need to use two beams. The first ray passes from the top point of the object parallel to the main optical axis. At the lens, the ray is refracted and passes through the focal point. The second beam must be directed from the top point of the object through the optical center of the lens. It passes through the lens without being refracted. At the intersection of two rays we place point A’. This will be the image of the top point of the object. The image of the lower point of the object is constructed in the same way. The result of the construction is an enlarged, inverted, real image
diverging lens
The object is placed in front of the diverging lens.
To construct, you need to use two beams. The first ray passes from the top point of the object parallel to the main optical axis. At the lens, the ray is refracted in such a way that the continuation of this ray goes into focus. And the second ray, which passes through the optical center, intersects the continuation of the first ray at point A’ - this will be the image of the upper point of the object. The image of the lower point of the object is constructed in the same way. The result is a direct, reduced, virtual image. When moving an object relative to a diverging lens, a direct, reduced, virtual image is always obtained. When moving an object relative to a diverging lens, a direct, reduced, virtual image is always obtained.
The position of the image and its nature (real or imaginary) can also be calculated using
thin lens formulas. If the distance from the object to the lens is denoted by d, and the distance from the lens to the image by f, then the formula for a thin lens can be written as:
The quantities d and f also obey a certain sign rule: d > 0 and f > 0 – for real objects
(that is, real light sources, and not extensions of rays converging behind the lens) and images; d< 0 и f < 0 – для мнимых источников и изображений.
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