35mm equivalentfocal length calculator

Angle of View is the angle subtended at the image of the eye by the mirror. It is defined in terms of the image size and the effective focal length,

Focal lengthto angle of viewcalculator

nimage space is the refractive index of the medium in which the image is formed, and R2 is the radius of curvature of surface 2.

If we consider the object at infinity, the image will be formed at the principal focus of the lens. So put u=∞ and v=f in the above equation and can be rewritten as,

FOV andfocal length

In such a lens where the power depends on the thickness of the lens, the effective focal length cannot be taken as the sum of individual foci of the two surfaces. So, we define Effective Focal Length as the reciprocal of the effective power of the lens, showing the thickness dependence of the lens.

In the case of a thick lens, the optical power of the surfaces depends on the refractive index of the lens. Thus the power output of both surfaces will be different.

Correction for myopia takes a “minus” lens which is a spherical lens that takes the natural “near” focal point of the eye and moves it out to infinity so that the eye can see off at a distance. The lenses look normal for the most part. However, as the amount of myopia increases, lenses can become rather thick and make the eyes look small. Also, images through the lenses may seem small to those wearing myopic correction. Much of these effects can be greatly helped or reduced with proper grinding and fitting of glasses.

Considering the refraction at the spherical surfaces we can derive an equation for the image formation. The basic concept is that the image formed by the first refracting surface acts as a virtual object for the second refracting surface. By applying the Gauss Formula which is a geometrical method to describe the behavior of light, we can write,

For example, if a patient has good distance vision with little or no distance correction needed, then reading glasses may be all that is required. They are simple to use and require little adjustment. However “full-view” readers will cause blurred distance vision since they are designed only for reading activities. With them on, reading the newspaper will be heavenly, but the TV news will be blurry unless you take them off. In this case, “half-glasses” readers (“granny-glasses”) which sit low on the nose will allow one to read while looking down through the lenses, and will also allow distance vision when looking up over the frame. Many people, however, do not like the cosmetic aspect of half-glasses.

Close vision is impaired, with some impairment of distance vision, as well. The eye is too short or the cornea too flat. Therefore light rays are not yet in focus when they reach the retina, so images appear blurry. Unlike myopia (nearsightedness), hyperopia (farsightedness) is usually well tolerated during younger years and generally doesn’t become a problem which requires correction until later on in adult years. Some children however are very sensitive to hyperopia and can develop a form of strabismus called accomodative esotropia commonly seen by age 18 months to 2 years old. This form of strabismus is often correctable with glasses.

Since the thickness is non-negligible, the Effective Power is not just simply the sum of the individual powers, but it depends on the thickness of the lens. The equation for the effective power of a lens is given by the Gullstrand Equation as,

Consider the image formation by a spherical mirror. Figure shows a concave mirror with a radius of curvature R. The center of curvature of the surface is at C and the vertex of the mirror is at P. The line OP is the optic axis. Point O is an object lying on the optic axis and we assume that the distance OP is greater than R.

Focal Point is the point to which a set of rays parallel to the principal axis is set to converge (in the case of a convex lens) or appear to diverge (in the case of a concave lens).

NEARSIGHTEDNESS (MYOPIA): Distance vision is impaired when the eye is too long or the cornea too steep. This causes light to focus before it reaches the retina. Close objects look clear (hence “nearsighted”), but distant objects appear blurry.

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Myopia is extremely common and is the most common form of refractive error in children. It is common for myopia to progress during adolescent years and finally taper off in the early to mid-20’s. Depending upon the degree of myopia, regular exams are usually in order. Most cases of myopia are mild and are uncommonly associated with other eye problems. High myopia however can have associated problems usually due to the eye becoming very elongated. When this happens, intraocular structures such as the retina can become thin and will need monitoring on a periodic basis for hole formation or tears. Other problems such as macular degeneration, retinal detachment, and glaucoma can develop with high myopia.

In the case of a mirror, where the mirror-to-object distance is comparable to the focal length, we need to consider the magnification factor, hence the effective focal length can be written as,

If the object is taken at a very large distance from the mirror (u=∞), then the incoming rays are almost parallel, then the above equation becomes,

Focal length is the distance between the focal point and the optical center of a lens. It is the measure of the ability of a lens to converge or diverge a ray of light. The plane perpendicular to the principal axis of the lens and passing through its focal point is known as the focal plane.

The ray from O at the angle α with the axis strikes the mirror at Q and is reflected. The incident and reflected rays make equal angle θ with the normal CQ (law of reflection). A second ray from O, passing through C strikes the mirror normally and is reflected back on itself. The two reflected rays intersect at I forming a real image of O.

Thin Lens are those lenses whose thickness can be neglected when compared to the lengths of the radii of curvature of its two refracting surfaces, and to the distances of the objects and images from it.

The point at which the incident parallel rays converge is called the focal point and the distance from the vertex to the focal point is called the focal length denoted by f. So focal length is the image distance when the object is at infinity. Thus, v = f and f = R/2

Unlike “regular” astigmatism, “irregular” astigmatism is usually due to diseases processes of the cornea in which the corneal surface itself is irregular or warped. This type of astigmatism cannot be neutralized with glasses. Rigid contact lenses can be helpful, and as a last resort, replacement of the cornea itself (corneal transplant) can be done. Causes of irregular corneal astigmatism can include chemical burns, corneal scars, corneal injuries, and corneal diseases such as keratoconus.

Numerical Aperturecalculator

Also, contact lenses are an option. (Click on to Common Glasses Problems and Solutions for helpful suggestions about problems you may be having with your glasses.)

Consider a thin convex lens XY with an optical center at C. Let the refractive index of the lens µ2 and that of the surrounding medium be µ1. The centers of curvature of the two refracting surfaces of the lens are C1 and C2 and let the corresponding radii of curvature be R1 and R2 respectively. Consider a point object 'O' placed on the principal axis of the lens.

Equivalentfocal length calculator

Unlike myopia or hyperopia where there is only ONE abnormal focal point, in astigmatism, there are at least 2 abnormal focal points (called “regular astigmatism) which do not focus properly on the retina. In cases where there are more than 2 abnormal focal points, the astigmatism becomes irregular.

Power of a lens is the measure of its ability to produce convergence of a parallel beam of light. A convex lens has a converging effect and thus its power is taken as positive, but a concave lens produces divergence and so its power is taken as negative. The unit in which the power of a lens is measured is called Dioptre. Mathematically,

A ray of light OA strikes the first surface at A and is refracted in the direction 'BI1'. This ray is further refracted by the second surface in the direction of 'BI' and meets the ray which passes undeviated through the principal axis at 'I'. So, the final image is formed at 'I' after the refraction by the two surfaces of the lens.

Correction for presbyopia requires careful thought to minimize the adjustment period and to smooth the transition, especially if bifocals are going to be used. The decision to transition into bifocals will depend upon a variety of circumstances including lifestyle, nature of work, refractive error, and other factors.

Correction for astigmatismIn requires a lens that can neutralize both focal points. This type of lens is called a spherocylinder lens as opposed to lenses for myopia or hyperopia called spherical lenses. To the naked eye, a spherocylinder lens looks no different than any other type of lens. Going into astigmatic correction for the first time, however, can require some time to adjust, especially for older adults. Also for those experienced with astigmatic correction, a change in the amount of correction or the orientation of the lens can cause adjustment difficulties. Images at first may seem somewhat slanted, and walking or reading may create the sensation of going “uphill.” With properly fitted glasses, these effects usually disappear with time although at times, the astigmatic correction may need to be adjusted.

Generally, people who have worn glasses for years adjust to bifocals rapidly. Those who use bifocals just for reading may have a difficult time wearing them while moving about. No matter what form of bifocal, there is usually adjustment that a newcomer experiences. Difficult activities include stepping off curbs, going up or down stairs, and walking in general. Certain types of bifocals may be better suited to certain types of work, and bifocal segments can be located either below (which is the norm), or even in the top part of the lens which is sometimes required by postal clerks, carpenters, electricians, or others who do work overhead.

Where nlens is the refractive index of the lens, nobject space is the refractive index of the medium in which the object is kept and R1 is the radius of curvature of surface 1.

In regular astigmatism, the cornea and or lens surfaces of the eye are not perfectly round, but rather elliptically shaped like perhaps a football with a flatter curve to it and a steeper curve. This type of curvature of the cornea and/or lens causes light to focus on more than one point in the eye. These two points of focus can lie anywhere in relation to the retina (either both in front of the retina, both in back of the retina, one in front and one behind, etc.).

Mirror is any surface that redirects light rays, thereby forming an image of the object. They may be plane or curved. Image formation by mirrors involves only the law of reflection.

Hyperfocal distancecalculator

Your ophthalmologist will be able to direct you on what is best for you. Remember too that how well you see will also depend upon the quality of workmanship of the glasses. Please click to Common Glasses Problems and Solutions for a discussion on problems you may be having with your glasses and how to remedy them.

Fortunately with modern day frames, proper fitting, and smaller lenses, reading glasses can be very versatile AND attractive. These frames will allow one to wear the glasses in normal position when doing computer work, or in a low position to read while preserving their distance vision.

Angle of View is the angular measure of how much of the area can be captured by the lens. It is defined in terms of the image size and the effective focal length,

For those who need distant correction, who have the need for safety glasses, or who do not like reading glasses, bifocal glasses are necessary. Bifocals allow one to focus both at a distance and at near, and come as either a “line” (traditional) bifocal or a “no-line” style. While most patients now are preferring a “no-line” design, each has its advantages and disadvantages depending upon many factors.

Lens thicknesscalculator

Optical Center is a point on the principal axis for which the rays passing through it are not deviated by the lens. Any ray passing through the optic center emerges in a direction parallel to the incident ray, i.e. the ray emerges undeviated.

Thick lens is a physically large lens whose spherical surfaces are separated by a distance. In other words, it is a lens whose thickness cannot be neglected when compared to its focal length.

In the case of a thin lens, where the lens-to-object distance is comparable to the focal length, we need to take into account the magnification factor, so we can write the effective focal length as,

Correction for hyperopia requires a “plus” lens which will help light rays “converge” upon the retinal surface properly. Some people are concerned that large amounts of hyperopic correction make the eyes look large as though they are magnified. With proper grinding and fitting of glasses, these unwanted effects can be reduced greatly. Contact lenses for many are an excellent choice. See Optical Services.

From the figure, the light leaving the first surface would form an image I1 if the second surface was absent. With the second surface, I1 becomes a virtual object for the second surface and it forms an image at I, which is the final image. The equation for the final image formation can be written using the Gauss formula. Here we take u = v and R = R2, thus we get,

Uncorrected astigmatism impairs both distance and near vision. Depending on the degree of astigmatism, objects may appear distorted.

The ratio of dimensions of the final image formed by an optical system to the corresponding dimension of the object is defined as the magnification. Here the object and image have different sizes and they have opposite orientations. Then from the figure, we can write,

Image formation in a lens takes place by the refraction of light at its two bounding surfaces. Each surface of the lens acts as an image-forming component and contributes to the final image formed by the lens.

The first surface XAY forms a real point-image I1. So in the above equation, v can be replaced by v1 and R by R1. Using sign convention, the distances measured to the left of the principal axis is negative. So, here u is negative and the above equation can be rewritten as,

When young, the lens of the eye is soft and flexible, allowing people to see objects both close and far away. After the age of 40, the lens of the eye becomes more rigid, making it more difficult for the lens to change its shape, or accommodate, to do close work such as reading, doing needlepoint, playing the piano, or doing computer work. This condition is known as presbyopia and is the reason reading glasses or bifocals are necessary at some point after age forty.