In order to understand common vision
defects, it is helpful to understand how the “normal” eye works. The muscles that control the focal length of
the eye-lens are fully relaxed when the eye is focused on a very distant
object. The muscles contract and shorten the focal length of the eye-lens to
bring nearer objects into focus. The two limits of this range are called the
far-point, which is the distance of an object that is in focus when the muscles
are relaxed, and the near-point, which is the distance at which an object is in
focus when the muscles have shortened the focal length of the eye-lens as much
as possible.
The distance between the eye-lens and the
retina is about 20 mm. When an object is very far away from the eye, the image
is located essentially at the focal point. Therefore the focal length of the
cornea and the eye-lens should be about 20 mm when the muscles of the eye are
relaxed. Since the strength of a lens
is the reciprocal of its focal length in meters, the strength of the cornea and
the eye-lens in this situation is about 1/0.020 = 50 diopters.
When an object is located at the
near-point (the closest point at which an object can be brought into clear
focus on the retina), the focal length of the cornea and the eye-lens must be
changed so that the image is formed on the retina, which is still 20 mm away.
If we take 25 cm as a typical value for the near-point, the algebraic form of
the ray-tracing rules shows that the focal length of the cornea and the
eye-lens must now be about 18.52 mm. The strength of the cornea and the
eye-lens must now be about 1/0.01852 = 54 diopters. Thus the muscles of the eye must provide an accommodation range
of 4 diopters. (This required range is actually independent of the size of the
eye or the focal length of the eye lens when it is focused on a very distant
object. It depends only on the value for the near-point.)
1. myopia or “near-sightedness”
In this condition, the strength of the
cornea and the eye-lens combination is too great even when the muscles of the
eye are completely relaxed. In other words, the focal length of the cornea and
the eye-lens combination is always less than the distance to the retina, so
that images of distant objects are formed in front of the retina even when the
eye is totally relaxed. However, objects that are closer can be brought into
focus. In many situations the focal length of the cornea and the eye-lens is so
short that objects closer than the conventional near point of 25 cm can be
brought into focus, which is why this condition is called “near-sightedness.”
People with this condition can thread needles and read books, but they often cannot
read distant street signs.
Since the problem is that the strength
of the eye-lens and the cornea combination is too great, the solution is to
provide eye glasses (or contact lenses) with negative lenses. The negative lens
weakens the strength of the cornea and the eye lens just enough so that the
resulting focal length when the eye muscles are relaxed matches the distance
back to the retina so that distant images are now in focus. Since the eye glass lenses are negative
lenses, they are thinner in the middle than at the edges. It is easy to identify this kind of eye
glass lenses, since acting by themselves they do not form a real image of an
object at any distance.
2. hyperopia or “far-sightedness”
In this condition, the strength of the
cornea and the eye-lens combination is too weak when the eye muscles are
totally relaxed, so that the image of a distant object is formed behind the retina.
It is usually possible to bring distant objects into clear focus by using the
eye muscles to shorten the focal length of the eye-lens, but this accommodation
is usually not sufficient to bring nearby objects into clear focus. Therefore people with this condition can
focus on distant objects just fine, but cannot focus on an object at the
conventional near point. People with this condition may not be able to focus on
a book unless it is quite far away from the eyes, and they usually cannot
thread a needle or do other close-up work.
The solution is the opposite of the
previous case. The eye glass lenses are positive lenses which strengthen the
cornea and eye lens just enough so that the resulting focal length when the eye
muscles are relaxed matches the distance back to the retina. Since these eye glass lenses are positive
lenses, they are thicker in the middle than at the edges. Acting by themselves
they can form a real image of a distant object at their focal point, so that it
is easy to distinguish between eye glasses for myopia and hyperopia, since the
latter will form a real image of a distant object while the former will not.
3. astigmatism
Astigmatism is the situation in which
the focal length for the cornea and the eye-lens for an object oriented in some
direction is not the same as for another object located in a perpendicular
direction. In other words, the eye cannot bring the vertical and horizontal lines
in a “+” symbol in sharp focus at the same time. (The axes of differing focal
lengths need not be exactly horizontal and vertical.) This condition is often combined with one of the two previous
conditions, but it need not be – it can exist even if the cornea and the eye
lens have the proper average focal length and range of accommodation.
Since the problem is that the cornea
or the eye lens are not symmetrical, the solution is to use eye glasses whose
lenses are not symmetrical in a complementary way. An extreme version of this
is a cylinder lens – a shape that is circular in one direction where it acts as
a normal lens and flat in the other direction where it has no focusing
properties. The strength and direction of the cylinder are designed to
compensate for the asymmetry of the cornea or the eye lens. The curved portion
of the cylinder lens may be positive or negative, depending on the detailed
asymmetry in the eye.
It is easy to recognize eye glasses
designed to deal with astigmatism, since acting by themselves they produce
distorted images of any object. This is because they have different focal
lengths (and therefore different magnifications) in different directions.
Although people with mild hyperopia or myopia can often function without
wearing glasses, people with astigmatism usually must wear glasses all the
time. Otherwise they often get eye strain headaches caused by the eye muscles
trying (and failing) to focus on the vertical and horizontal portions of an
object at the same time.
The cylinder lens may be combined with
an additional positive or negative lens if the person also has hyperopia or
myopia.
4. decreased accommodation or
“presbyopia”
This condition is typical of middle
age. The eye muscles gradually weaken with age, so that the range of accommodation
decreases. People with this condition cannot bring both near objects and far
objects into focus. The weakening of the eye muscles often causes the focal
length of the eye lens to increase as well, so that many people of middle age
tend to become far sighted.
Since the problem is inadequate accommodation,
no single lens can correct it, and people with this problem usually need
bifocals, which are glasses with two different lens strengths: one for near and
one for distant objects. The usual arrangement is that the bottom half of the
lens is the near strength and the top half is the far strength.
5. cataracts
This condition is also common among
older people, although it can happen at any age. The lens of the eye becomes
clouded and partially opaque. The result is that objects at all distances
become blurred. The cloudiness of the
lens often scatters light in all directions, so that people with cataracts are
more easily blinded by bright lights. The lens often becomes yellow as well,
and tends to absorb blue light.
The solution is to replace the lens
with a fixed-focus lens of the correct strength. Since the replacement lens
cannot be deformed, the result is that people with replacement lenses have no
accommodation at all and must wear bifocals (or even trifocals).
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