Accord between different laws of Nature that seemed incompatible

To broaden our knowledge of the world, we use different methods that rarely lead us to the same truths.

Certain fundamental truths of Philosophy can be illustrated by geometric arguments or algebraic proofs.

An example is in the laws governing light, whether:

• moving through a uniform medium, or
• being reflected from an opaque surface, or
• changing direction upon entering another transparent medium.

These laws are fundamental to the science of optics and colors.

The ancient Greeks knew the laws that govern the propagation of light in a uniform medium and upon its reflection.

However, the law governing the refraction of light as it passes from one transparent medium to another was unknown until the last century.

• Snell discovered it
• Descartes tried to explain it
• Fermat criticized his explanation.

Since then, many great geometers have researched the problem.

Although no one has yet found a way of harmonizing the law of refraction with more fundamental laws that Nature must obey.

Here are the laws that govern light.

Law 1: light moves in a straight line in a uniform medium.

This is the same for both light and material bodies; they both move in a straight line, as long as they are not deflected by an outside force.

Law 2: When light encounters a medium it cannot penetrate, it is reflected and the angle of reflection equals the angle of incidence.

In other words, upon reflection, light makes an angle with the surface that is equal to the angle at which the light encountered the surface.

This law is also the same as that governing the reflection of an elastic ball from an impenetrable surface.

Mechanics shows that such a ball is reflected from such a surface so that its angle of reflection equals its angle of incidence, as observed for light.

Law 3: When light passes from one medium to another, it is bent. The sine of the angle of refraction always has the same ratio to the sine of the angle of incidence.

For example, if a ray of light passes from air to water, it is bent so that the sine of the angle of refraction is 3/4 of the sine of the angle of incidence, regardless of what the angle of incidence is.

But this law requires an explanation.

The passage of light from one medium to another exhibits behavior that is totally different from a ball moving through different media.

Every explanation of refraction has some problems that have not yet been overcome.

The explanations of the reflection and refraction of light are of 3 classes.

1. One class seeks to derive the behavior of light from purely mechanical laws, i.e., the basic laws governing the motion of material objects.

This is Descartes and his followers.

They modeled the reflection of light as the motion of a ball that, encountering an impenetrable surface, rebounds to the same side from which it came.

Similarly, they modeled the refraction of light as a ball that, encountering a penetrable surface, continues to progress, albeit with a changed direction.

Descartes’ explanations of refraction are imperfect. But he still deserves credit for trying to derive the laws of light from the simplest mechanical laws.*

2. Another class augments the mechanical laws with an attraction between light and matter, or something that produces an equivalent effect.

Several mathematicians have noted gaps in Descartes’ logic and have sought an improved explanation.

Newton despaired of deriving the law of refraction from those governing the motion of a ball when it passes between two media of different resistance.

So he proposed an attraction between light and matter that increases proportionally to the amount of matter present, which was able to account for refraction exactly and rigorously.

Mr. Clairaut has laid out the failings of the Cartesian theory. He subscribes to the attraction theory between light and matter.

He proposes that an “atmosphere” surrounding the matter causes the apparent force of attraction. He derives the law of refraction with the clarity that is typical of all the subjects he has researched.

3. Another class use purely metaphysical principles, i.e., from laws to which Nature herself seems subjugated by a superior Intelligence that always produces an effect in the simplest possible manner.

Fermat was the first to recognize the failings of Descartes’ explanation.

He also despaired of explaining the refraction law from purely mechanical laws governing balls encountering obstacles or passing through a resistant medium.

However, he also did not resort to “atmospheres” surrounding material bodies or other forms of attraction between light and matter, although he was certainly aware of the attraction theory and found it tolerable.

Rather, Fermat sought to explain refraction using a totally different and purely metaphysical principle.