Optics: Index Refraction: Eyeglasses

Eyeglasses are an example of the usefulness of refractive index that most people are familiar with. Although contact lenses are slowly making glasses less public and more the thing that gets you safely from the bathroom to the bed at night, everyone knows someone who wears glasses.

If it weren't for the index of refraction of materials being different, we couldn't make eyeglasses. This is because the difference in the index of refraction leads to a bending of light at the interface between materials, known as refraction. How much the light bends depends on the ratio of the two mismatched indices, and is encapsulated in a fundamental law of optics called Snell's Law*.

This is useful because it allows us to make converging and diverging lenses. A converging lens is one that brings all incoming light to a tight focus; a magnifying lens is an example of a double converging lens, as any child who used one to light small fires can tell you. A diverging lens takes incoming light and spreads it out, rather than bringing to to a focus. This makes them useful for correcting short sightedness.



If a person is short sighted, it means that their eyes focus light too quickly. Instead of focusing the image of whatever they are looking at on the retina, where it should, it focuses the image somewhere in the the middle of the eye, in the jelly bit, and so only a blurred and distorted image ends up at the retina.

With a diverging lens in front of the eye, we can change the effective focal length of the system and move the image from somewhere in the middle of the eyeball to the retina where it should be. This works because focal lengths (where the lens focuses) combine in a specific way, namely as the sum of their inverses, so we can tune to focal length of a system of lenses.

An example might help illustrate this. The average human eye is 2.5 cm (about an inch) in diameter. Let's say there is a person who's eye focuses 0.5 cm short of the retina. They go to an old school optician to get corrective lenses to push the focal length of their eye from 2 cm to 2.5 cm.

First, the optician needs to find the focal length of the lens that will create the effective focal length of 2.5 cm. Once he has that, he can use the Lensmaker's Equation to help determine the shape and material of the lens. Ideally, you want the lens to be as thin as possible, both for the comfort of the wearer and for reducing aberrations. One way to do this is to use a high index material, like some plastics instead of glass. The higher the index, the more the light bends at the interfaces, meaning you don't need as much curvature of your surfaces and you don't need as much thickness. The rising use of polycarbonate plastics in place of glass is one reason you don't see as many 'coke bottle' glasses anymore.

So, if you wear glasses or ever plan on getting old, be thankful that so many transparent materials have a significantly different index of refraction than air. Not only do we get to correct our vision because of this fact, we don't have to have super strong noses.

~PhysicsGal

NEXT TIME: Ninja Fish!


*Technically, Willebrord Snellius (Snell) was the last in a long line of people to discover this relationship, but was the first to put it in a nice mathematical form and was born after the invention of the printing press. He never published his paper, and so got posthumous recognition.