Optics of Myopia (Nearsighted) & Hyperopia (Farsighted)

This article is intended for educational purposes only.

Before we discuss the optics of myopia and hyperopia we should acknowledge the laypersons terms for myopia and hyperopia. Briefly, the uncorrected myope or nearsighted person usually can see up close better than far away, hence the term "nearsighted" makes sense. Unfortunately hyperopia is not as easy to explain. Depending on a person's prescription and ability to focus (basically their age), a farsighted person will either see clearly but have to work harder to see up close or they may see blurry.

Eye Doctors do not use the terms "nearsighted" or "farsighted", they use the optical terms "myopia" and "hyperopia" described below.

Key Words

Cornea: The clear dome of tissue protruding from the white conjunctiva on the front surface of eye that covers the iris and pupil.

Refract: The bending of light (for our use). Refractive error (Pertaining to the eye): Meaning the rays of light entering an eye does not focus on the retina, causing blur.

Correction: Used in terms of eyeglasses or contact lens: To correct a refractive error. The correction is the amount of power, in diopters, needed to bring the rays of light back to focus on the retina.

Optics Background

A diopter (D) is a measurement of the ability of a lens to CONverge or DIverge light. A diopter is equal to the inverse of the distance between the lens and its focal point (1/ Focal length (meters)). If a lens was to focus light coming from optical infinity onto a point 2 meters away this would be a 1/2 diopter lens (1/2D = 2 meters). If the lens were to focus these rays at 50cm. this would be a 2 diopter lens (1/(1/2meters) = 2D). This would be a stronger lens than the first.

The eye's cornea and crystalline lens are both powerful lenses. The cornea accounts for about 43D of convergence power while the lens adds another 20D. If both the lens and the cornea were actually touching each other the total power of the system would be 63D. The actual power of the eye system is only 58.7D because the lens and the cornea are separated by fluids and form a complex optical system.

The average eye is about 24mm. long, with the distance of the crystalline lens to the retina being somewhat less. In an eye with no refractive error the optical system will focus light directly on the retina. If you calculate the focal length of a 58.7D system you will find it is not 24mm but really 17mm. This is because the center of the eye lens system is 17mm away from the retina. The reasons for this are advanced optical principles including thick lens equations, multiple lens equations, differing indexes of refraction etc.

Refractive Error Definition

A refractive error exists when the rays of light do not focus on the retina because:

  1. The eye's optical system is to powerful, overconverging light in front of the retina (myopia/nearsighted).
  2. The eye's system is too weak and under converges light so the focal point lies behind the retina (hyperopia/farsighted).

Myopia (Nearsighted)

From above we see that the eye's optical system needs to be about 59 diopters (D) to converge light onto the retina. If a particular eye system needs 60D to focus light on the retina but actually has 63D then you have a myopic eye. The amount of myopia here is easy to calculate: 63D - 60D = 3D of myopia. The Eye will Over converge light by 3 diopters (diagram 2 below). A subtle steepening in the curvature of the cornea can cause this. Another way to become myopic is for the eyeball to grow too long. A longer eye will need LESS power than a 60D system to focus light on the retina. Highly nearsighted eyes tend to be longer than non near sighted eyes. Unfortunately this "stretching" takes its' toll on the eye by thinning the retina, rendering it more fragile and prone to tearing. This is why your eye care practitioner will recommend dilating pupils often to look at the peripheral retina if you are highly nearsighted.

emmetropia myopia

In the diagrams above we see 2 images. In the first image light enters the eye from optical infinity and focuses on the retina, yielding clear vision (normal vision = "emmetropia"). The second image shows light from optical infinity focusing in front of the retina due to the eye being too powerful. This is myopia. To correct this we put a lens that DIverges light exactly the opposite of what the eye over CONverges light, thereby weakening the eye to exactly the point where light converges on the retina (diagram 3)

corrected myopia

Hyperopia (Farsighted)

Hyperopia

The eye's optical system needs to be about 59 diopters (D) to converge light onto the retina. If a particular eye needs 60D of power to focus light on the retina but actually has 56D then you have a hyperopic eye. The amount of hyperopia here is easy to calculate: 60D - 56D = 4D of hyperopia. A subtle change in the curvature of the cornea can cause this. Another way to become hyperopic is for the eyeball to not grow long enough for the eyes optical system. In this example, a shorter eye will need MORE power than a 60D system to focus light on the retina, and if the system is 60D or less, the eye will be hyperopic. An eye will become more farsighted if the cornea becomes flatter. This is what refractive surgery does; it flattens a very curved cornea to make it less nearsighted. Highly farsighted eyes tend to be shorter than non-farsighted eyes. Because of this, farsighted eyes sometimes have a small or narrow drainage systems near the iris, and are more likely to close off, causing a form of glaucoma that needs urgent attention. This is why some farsighted eyes cannot be dilated safely.

In the first diagram below light enters the eye from optical infinity and focuses on the retina, yielding clear vision (normal vision = "emmetropia"). The second diagram shows light from optical infinity focusing in back of the retina due to the eye being too weak. This is hyperopia. To correct this we put a lens that CONverges light, thereby strengthening the (weak) eye to exactly the point where light converges on the retina, as shown in the bottom diagram.

emmetropia hyperopia corrected hyperopia

The crystalline lens of the eye can also use effort to temporarily "correct" hyperopia. A hyperopic person will see well IF they have the ability to focus "through" their refractive error. This depends on how high the hyperopia is AND how old the person is. As we age we lose the ability to use the crystalline lens the change focus, a process called presbyopia. Presbyopia is not the same phenomena as hyperopia, but it does affect a person's ability to compensate for hyperopia.

For this reason, a 20 year old +2.00 hyperope may see 20/20 at distance with a little effort or strain by using the crystalline lens to converge the light rays back onto the retina, similar to what the a plus lens would do. A 50 year old +2.00 hyperope with little ability to use their crystalline lens to change focus would see about 20/80 (very poorly).

Therefore, a farsighted person does not necessarily see well at far. It depends on how farsighted they are and how old they are.

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