1. The lens
Although the lenses of the eye are not
simple spherical lenses, they are thicker in the center than at the edges.
Therefore, they are positive and converging, and form a real, inverted image on
the retina – the optically sensitive screen that is located at the back of the
eye. The image on the retina is formed by two lenses – the cornea, which is a
converging lens whose focal length is fixed, and the eye-lens, which is a
positive lens whose focal length can be varied by changing its shape. The focal length of the combination varies
among different people, but is typically about 20 mm.
The optical strength of the cornea is
much greater than the strength of the eye-lens, and most of the focusing of the
lens combination in humans is due to this part of the optical system. The focal
length of the cornea depends on its internal index of refraction and on the
fact that the material in front of it is air. The focal length is therefore very
different when the cornea is in water, since the refraction at the front
surface of the cornea is much less in this situation. (This is why it is easier to see underwater when you are wearing
goggles, since the goggles produce an air space in front of the cornea.) Fish
and other animals that see in the water therefore have eyes whose lenses are
much more curved and bulging than human eyes. In all cases, the index of
refraction of the lens material is much closer to the index of refraction of
water, so that a lens of the same shape has a much smaller optical strength.
Lenses that must operate in water are therefore much more curved than a lens of
equivalent focal length designed to work in air.
Neither surface of the eye-lens is exposed to air,
and its focal length is determined by its index of refraction and by the
indices of refraction of the materials that surround it. The index of
refraction of the eye-lens is not homogeneous but is smallest at the surface
and increases somewhat with depth.
The eye focuses on objects at
different distances by changing the focal length of the eye lens. This change
is realized by changing its shape – decreasing its radius of curvature (and
therefore shortening its focal length) as the object comes closer to the eye.
The range over which this works varies among different people, but is typically
from infinity to the near point, which is about 25 cm (10 inches) for
most people. This variation in the focal length of the eye-lens is called accommodation,
and this ability to vary the focal length of the eye-lens decreases slowly with
age. Since the eye is focused on distant objects when the muscles are relaxed,
the decreases in the strength of the muscles and in the flexibility of the lens
with age generally means that people lose the ability to focus on nearby
objects as they grow older. They therefore often tend to become far-sighted
as a result.
2. The iris and the pupil
The iris is a circular diaphragm, and
its color is what we call the color of a person’s eyes. The color of the iris
has no role in the optical characteristics of the eye. The central opening of
the iris is called the pupil. The diameter of the opening changes in response
to changes in the ambient light level. It
varies by about a factor of 4 in people: from about 2 mm in diameter in
bright light to about 8 mm in diameter in the dark. The variation is much
larger among nocturnal animals, such as cats. The f/number of the human eye therefore
varies from about f/2.5 (20/8) in dim light to about f/10 (20/2) in bright
light. The variation in ambient light level is much larger than this factor of
about 16 in light-gathering ability, and the eye uses other mechanisms to
adjust to changes in the intensity of the ambient light. However, the increase
in f/number as the ambient light increases is important in increasing the depth
of field of the optical system, and it is one of the reasons that it is easier
to read and do other tasks that require precise focusing when the light is
brighter. As we have discussed previously, many other optical aberrations are also
smaller at larger f/numbers, since the paraxial-ray approximation is more
accurate in this case.
The largest residual aberration is
usually chromatic aberration, which is due to the variation in the index of
refraction of the eye lenses with wavelength. When the ambient intensity is
high, the use of the cones to process the image tends to minimize this problem
by selectively ignoring the blue and violet portions of the image, where the
chromatic aberration is the largest, and concentrating instead on the yellow and green portions, which
are at the center of the visible spectrum. However, objects illuminated with
light containing lots of violet and yellow (or ultra-violet and blue) can
appear fuzzy because the images in the two different colors cannot be brought
to a sharp focus simultaneously.
3. The retina
The retina is the optically-sensitive
portion of the eye. It is the screen on which images are formed, and is
connected to the brain via the optic nerve. The retina is composed of about 130
million sensors called rods and cones. The rods are more sensitive to low light
levels, whereas the cones operate at higher light levels and are also
responsible for color vision.
The cones are concentrated at the fovea, a point
near the optical axis of the eye. Since this point is close to the optical axis
of the eye, the various lens aberrations are smallest here, and the image
quality is therefore best at this point. In addition, the density of cones is
very high in this region, and the resolution of the eye is therefore greatest
when the image falls on this area.
The rods predominate at other places on the retina,
especially at the edges, which have mostly rods and few cones. The rods are
most sensitive to low light levels, but cannot distinguish color. Therefore
perception of color gets poorer as the ambient light level decreases. Since
there are more rods on the periphery of your retina than at the center,
peripheral vision tends to be more sensitive at lower levels of ambient light.
The image quality is poorer, however,
both because of the lower density of rods in these regions and because
the aberrations are relatively larger this far from the optical axis.
The sensitivity of both the rods and the cones can
be adjusted in response to changes in ambient light intensity, and this is one
of the ways the eye adjusts its sensitivity. These changes are much larger than
the change in effective f/number produced by changes in the size of the pupil. This
effect is called adaptation. It is a relatively slow process – the change
in the sensitivity of the retina to a sharp change in ambient light intensity
typically takes 15 or 20 minutes.
In addition to being more sensitive at lower levels
of ambient light, the rods are also more sensitive to blue light than to red
light. If an object is illuminated with only red light, the rods will tend to
see the scene as “dark” and will increase their sensitivity as a result, while
the cones will tend to see the scene as lighter and will become active because
of that. This trick is often used in illuminating the instrument panel of a car
at night and in movie theatres. In both cases, the goal is to provide the best features of night vision
using the rods and day vision using the cones simultaneously.
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