# The wave model of light

#### Prerequisites

Back in the 17th century, when Newton was making great strides in understanding the nature of light with his model of light as small, very fast moving particles, a Dutch competitor, Christian Huygens, had another idea: light was an oscillation, like sound or water waves. Unfortunately for Huygens, his model was more complicated than Newton's to calculate with, it didn't do any better than Newton's model (for anything that could be measured — at the time), and besides, Newton had the star billing. Not much attention was paid to Huygens' model (though it had its advocates) until a fateful competition more than 100 years later.

## Young's experiment and the French Academy Prize

At the end of the 18th century (1799), an English scientist, Thomas Young, began reviving Huygens' wave model. His two slit experiment, published in 1803 (discussed briefly below and discussed in more detail in the page, Two slit interference) was very hard for the particle model to explain. More people became interested in the wave model and, in 1817, the French Academy of Sciences, proposed a competition for papers on the theory of light.

Most of the academy members supported the particle model and hoped to kill the wave theory once and for all. But French physicist, August Fresnel, presented a paper with a detailed wave theory that permitted calculations to be done. The academy members pounced. Some noticed right away that his theory predicted a  strange result. If a point source of light were blocked by a perfect circular disk it would produce a circular shadow — but Fresnel's version of the wave theory predicted that there should be a bright spot at the center of the shadow. (To see why — after you have read through the pages on the wave theory and understanding interference, go to the page on Arago's bright spot.)

Of course, you have already figured out what happened. Despite the scoffers in the academy, one of them decided the experiment had to be tried. To almost everyone's surprise, the spot was indeed found to be there. This was enough to convince most scientists that the wave theory had to be right and Fresnel was awarded the prize. The wave theory was assumed to be correct — until a century later, when Einstein came along and things became a lot more complicated!

## Young's two-slit interference

From our study of the ray model and our understanding of the patterns of light and shadow, if we set up the situation shown at the right, with a tiny (point source) bulb, a mask with a small slot cut out of it, and a screen on which to observe the transmitted light, we expect (in the ray model) to see a bright spot that has the shape of the slot in the mask. We can easily see this by taking a spray of rays from the bulb in all directions. Those that are not blocked by the mask will just go straight through, painting a copy of the slot in the mask in light on the screen, as shown.

But now what would happen if we made the slot on the screen narrower? Surprisingly, once the slot gets pretty narrow (less than a mm), we begin to notice that there is light outside the shadow. In fact, as the slot gets narrower, the spot on the screen begins to spread out! What's happening?

The particle modelers suggested that perhaps as the slot got narrower, that the particles of light were scattering off the edges of the slit. (WARNING: This is NOT what is happening here!) But Thomas Young came up with another, even more perplexing experiment: one with two slits.

Young's experiment is shown in the figure at the left.  When the slits are narrow, what happens? What the particle theory predicts is that the pattern observed for the two slits will be the sums of the patterns that were observed for the individual slits, shifted a bit. After all, in the particle model, all that can matter is the total number of particles received and scattering from a point on the screen.

But what happens is something very different. The actual pattern for one and two slits (taken with a laser source, not a yellow bulb) looks like the figures below.

There are some places where adding more light by opening another slit makes the result darker, not brighter.

This really is a fatal flaw in the particle model. If the intensity is the total number of light particles, there is no way that adding more light (from a second source) can make anything darker. This suggests:

Light must somehow be both positive and negative and that two sources of light can cancel each other — at least in some localized spots.

This was a serious challenge to the particle model and the central spot result was the final nail in the coffin. The wave theory won. (At least for a century.)

In the follow-on pages, we'll explore how Huygens created a model that described this phenomenon, and how Maxwell unified Huygens with electricity and magnetism.

Joe Redish 4/23/12 and 7/3/19

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