Week 12: Lenses and Mirrors 407
objects (at “infinity” compared to the size of the eye) are automatically in focus (as a
real image cast upon) on the retina. Given a distance from the cornea to the retina of
roughly 2.5 cm, this means that the strength of the lens of a normaleye is approximately
1
0. 025 = 40.00d. When viewing less distant objects, accomodationshortensthe focal
length to bring them into focus on the retina.The focal length of a relaxedfarsightedeye isbehindthe retina (too long, strength less
than 40.00d) and is corrected with aconverginglens to make up the difference. If one
expresses strength in diopters, one can simply add a converging lens with a strength in
diopters to the strength of the the eye to get the “right strength” to make the combination
focus distant objects on the retina with the eye’s lens relaxed. Note that a hyperopic
personcansee in focus all the way out to infinity, but they have to use accommodation
to shorten their lens’s “too long” relaxed focal length see even distant objects, which can
lead to eye fatigue and headaches.The focal length of a relaxednearsightedeye is infrontof the retina (too short, strength
greater than 40.00d) and is corrected with adiverginglens to takeawaysome of its
strength. A myopic individual simply cannot see distant objects in focus without a
corrective lens because accommodation cannotincreasethe focal length of the eye’s lens,
it can only further decrease it.Accommodation can shorten the focal length only so far, which limitshow close an object
can be and still be focused on the retina. The nearest point one canbring an object to
the eye and still bring it into focus on the retina is called thenear pointof the eye and is
also thedistance of most distinct vision, representedxnp. In most adults, this distance
is around 25 cm (less for small children, longer for the elderly).A nearsighted person’s lensalreadyhas too short a focal length to be able to focus distant
objects on the retina, and accommodation only shortens the focal length still farther.
A nearsighted person cannot see anything clearly at distancesgreaterthan some point,
called thefar pointfor that person’s eyes. A nearsighted person is one for whom the far
pointxfpis less than infinity.A common aberration of human eyes is a condition calledastigmatism. Astigmatism
is what happens when the eye’s lens is no cylindrically symmetric. That is, the focal
length of the lens in the horizontal plane is not the same as the focallength in the vertical
plane. One can then bring things into focus in one dimension with accommodation, but
only at the expense of blurring them in the other. The solution is to wear lenses that
are astigmatic in the opposite direction to add up to neutral (or to person’s otherwise
necessary correction).As a person’s eyes age, their ability to focus changes. People with once normal vision
can become nearsighted or farsighted. After the age of roughly 50 a new condition often
emerges – that ofpresbyopism. The collagen of the lens hardens over time. Its flexibility
decreases, making it more difficult for the eye to accommodate andincreasing the near
point. This kind of “farsightedness” can occur even for nearsighted individuals. The
solution is to correct with “reading glasses” – positive lenses that permit a presbyopic
individual to read at normal distances. They can be combined into “bifocals” – reading
glasses for short distances plus diverging lenses to correct myopiaat long distances – for
people with the latter condition.