Mathematics of the Human Eye

The Human Eye:

Just what exactly goes on in our eye to produce images? Why can't some people see as well as others? Well my friend, look no further... the answers to your 2 most burning questions are about to come!

First of all, what happens when we see images?

Our eye acts as a simple model of a lens system. The average adult eye is about 25 mm in diameter. As light enters our eye, it is refracted first through the cornea which does about 80% of the refracting. The crystalline lens which is located after the aqueous humour (just under the cornea) approximately contributes the rest. Muscles around the crystyalline lens will contract or expand to adjust to the light rays entering so as to focus them onto the retina, just located at the back of the eye (assuming paraxial light rays). This adjusting process is called accomodation. For people who have no vision problems, all the light rays are focussed onto the retina as it should. Let's call this distance, from where the light enters at the crystalline lens to the retina as f (focal point). For people who don't have 20/20 vision, the light rays entering do not land on the fovea (majority of light rays strike at on the focal plane).

People who can see close up objects but not far-sighted images, they're near-sighted. Why can't they see clearly? Well, the light rays that enter their eye is refracted too much and the focal point is located before the retina.

Whereas, people who cannot see far away but can see close up objects, are far-sighted. This usually occurs in older people because the crystalline lens grows "stiffer", thus impeding it's ability to accomdate so there is less refraction and the focal point is located behind the retina.

To correct both these common vision problems, glasses and contacts redirect the rays so that they may land on the retina.

Nearsighted people need a lens system that will diverge the rays so that as it enters the cornea, it will refract light rays onto the fovea.

Farsighted people need a lens system that will converge the rays so that as it enters the cornea, it will refract light rays onto the fovea.

Astigmatism is also another common vision problem in people these days. When the cornea is irregularly shaped, ie. its' surface is not uniform due to greater thicknesses in certain parts of the cornea, light rays from objects refract all at different rates.