Mathematics of Human Vision and Corrective Lenses

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It is a daily ritual...wake up, eat, shower, contacts, class. I do this every morning, however I have never stopped to think, "Why?"

No, not "Why am I going to class so early?" but "Why do I need these contacts?" With this project I will attempt to explain the basics of vision and corrective lenses, as I, myself, finally learn the reason for sticking my finger in my eye every morning.

Basic Eye Anatomy

The cornea is responsible for protecting the eye and for refracting incoming light rays.

The pupil is merely an opening that allows light to enter into the eye. Its black color is attributed to the fact that light is not able to exit the eye through the pupil.

The iris acts to control the size of the pupil. In bright light, the iris is dilated in such a way as to reduce the size of the pupil and limit the amount of entering light. In dim light, the iris adjusts its size as to maximize the size of the pupil and increase the amount of incoming light.

The crystalline lens is a fibrous, jelly-like material that serves to fine tune the vision process by adjusting its shape and therefore the focal length of the system.

The ciliary muscles relax and contract to change the shape of the lens.

The retina contains rods and cones which detect the intensity and frequency of incoming light and, in turn, send nerve impulses to the brain.

Behind the Eye

The four main components of the eye that are responsible for producing an image are the cornea, lens, ciliary muscles and retina. Incoming light rays first encounter the cornea. The bulging shape of the cornea causes it to refract light similar to a convex lens. Because of the great difference in optical density between the air and the corneal material and because of the shape of the cornea, most of the refraction to incoming light rays takes place here. Light rays then pass through the pupil, and then onto the lens. A small amount of additional refraction takes place here as the light rays are "fine tuned" so that they focus on the retina.

This is a representation of the eye's lens system. This eye has no eye condition, such as nearsightedness or farsightedness, and the lens is drawn in its relaxed position. The light rays are focused appropriately on the retina. The thickness of the cornea is 0.449 mm, the distance from the cornea to the lens is 2.

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