Link: The Physics Classroom: Refraction and the Ray Model of Light Lesson 6 - The Eye
The simplest model of the human eye is a single lens with an adjustable focal
length that forms an image on the retina, or the light-sensitive bed of nerves
which lines the back of the eyeball. The eye is either relaxed (in its normal
state in which rays from infinity are focused on the retina), or it is
accommodating (adjusting the focal length by flexing the eye muscles to image
The near point of a human eye, defined to be s = 25 cm, is the shortest object distance that a typical eye is able to accommodate, or to image onto the retina.
In a nearsighted eye, the cornea is too steeply curved for the length of the
eye, causing light rays from distant objects to focus in front of the retina. Distant objects appear blurred or fuzzy because the light rays are not in focus
by the time they reach the retina. The eye is able to form images on the retina
for objects that are closer than the eye's far point.
Myopia can be accommodated for through the use of a negative lens that will cause the light rays to diverge. The power of the lens is chosen by matching the lens' focal point with the eye's far point.
In contrast to myopia, hyperopia occurs when the eye is too short for the
power of its optical components. In hyperopia, the cornea is not steep
enough and light rays hit the retina before they come into focus. In the
case of hyperopia, light from distant objects is focused to a point behind the
A positive lens can be used to correct for farsightedness.
When making and selling eyeglasses, people prefer to speak of the lens power
P, measured in diopters D, instead of the focal length f. If you want to buy
eyeglasses, you need to know the power of the lenses. Focal length and power of
a lens are related to each other.
D = 1/f(m)
D = diopters, f = lens focal length (in meters), and a "+" sign indicates a converging lens and a "-" sign indicates a diverging lens.
For two thin lenses in contact, 1/f = 1/f1 + 1/f2, and therefore power is P = Pthin(1) + Pthin(2), i.e. the powers of thin lenses in contact add algebraically.
What is the power of a normal human eye in diopter when focusing
on an object at the near point of the eye? Assume the lens to retina
distance is 2 cm.
P = 1/f = 1/xo + 1/xi.
The object is at the near point, xo - 25 cm = 0.25 m. The image is on the retina, xi = 2 cm = 0.02 m.
P = 1/0.25 m + 1/0.02 m = 54/m = 54 D.