PH 332 – September 29 class

Some introductory remarks:The book we are using not going to use

was written as long ago as in 1986. That’s OK,the 1986 status of the basic theory of light isstill valid! Progress has been made, of course,but rather in the advanced theory. We will talkabout those new developments later, in thefinal part of this course. But for now, the bookis perfectly OK.

However, I am not 100% entusiastic abouthow things are presented in Chapter 1. Theemphasis is almost exclusively on the wavetheory of light (WTL). Photon theory of light is not even mentioned. It may leave the impression that WTL is the only, or at least the “dominant” present lighttheory. In fact, it is not so! Therefore, I wantto add “my own story” to the book material.

A brief history of the theory of light

The XVII-century scientist already knew some important properties of light: (a)propagation along straight lines, (b) the laws of reflection and refraction,

(c) the effect of diffraction.

A Dutch scientist (or “philosopher”, as they called them at that time), Christian Huygens, noticed that waves on water exhibit the verysame phenomena. Based on that analogy, he assumed that light had a wave-like nature, and he constructed the firstearly version of the WTL.

But the great Isaac Newton did not like the idea – he believed that light wasactually a stream of tiny particles. He was also able to explain all the effects listed above on the grounds of his theory. Therefore, it was not possible todecide which one was correct.

Newton’s authority in the scientific communitywas so great that his theory was widelyaccepted, and the Huygen’s theorywas almost forgotten over the 100+ years that followed.

However,....

At the very beginning of the XIX-thCentury, everything was turned up-side down! Or, using a more elegant expression, a major “paradigm shift”happened.

It was all due to the famous experiment of Thomas Young who observed that if light passes through a a system of two narrow parallel slits, it forms a pattern of bright anddark “stripes” on a screen placed behind the slits.

Such an effect could only be explained onthe grounds of the Huygens’ wave theory.

Huygens was vindicated, and the Newton’stheory was “pronounceddead”.

Over most of the XIX-th century scientistscollected experimental facts that providedmore and more support for the wave-likenature of light. But still it was not clear what was “oscillating”In such waves.

And then, around 1860, there came a real revolutionary theoretical achievement – James Clark Maxwell presented a set of equations “unifying” the electric and mag-netic fields. The equations led to the pre-diction of the existence of electromagneticwaves.

The speed of such waves deducedfrom Maxwell’s theory appeared to be very close to the speed of light that had been determined earlier from Astronomical observations, and from“terrestrial” experiments conducted in France by Fizeau and Fresnel.

km/s 000,300c

So, the nature of light was almost explained – only one “piece of the puzzle” was still missing. Namely, there was still no “hard evidence” that the predictions emerging from Maxwell’s Equations were indeed correct, and the hypothetical “elec-tromagnetical waves” really exist, and they are not just a “mathema-Tical illusion”.

The breakthrough came in 1886, when aGerman scientist, Heinrich HERTZ, built an apparatus that, according to the Max-well’s theory, should have generated elec-Tromagnetic waves – and he convincinglydemonstrated that the waves were indeedproduced. It was believed to be the final Victory of the Wave Theory of Light.

But MOTHER NATURE, as it turns out, has a perverse sense of humor! Because one year later, in 1887, the very sameHeinrich Hertz discovered a strange phenomenon that we call now the “photoelectric effect” (PE).

The photoelectric effect is a process whereby light falling on a surface of metal knocks electrons out of the surface. The WTL gives no explana-tion for it! The origin of PE became amajor riddle for the physicists at the end of the XIX-th century.

The riddle was solved in 1905 by Albert Einstein (it was what he got his Nobel Prize for). Almost exactly 100 years afterthe Newton’s “corpuscular” theory of light was “killed” by the Thomas Young’s experiments.

What Einstein did? He sort of “brought Newton’s theory back to life”. Heproved that light consists of particle-like “quanta” – we call them now “photons”.

But what about the wave theory of light?!!! Were all those experimental facts

supporting the WTL phony?

No, they were 100% authentic!

Then, which theory is the “good one”? The answer may be somewhat surprising:

Both are!

How comes?! Well, as we see it now, light has a dual nature. In some phenomena it behaves like a wave – and in some other phenomena itclearly exhibits particle-like properties.

It may seem as something completely counterintuitive – therefore, we will need to spend more time to discuss this peculiar “duality”. But we will do that later, not now.

Another thing that is not in the book, but may be interesting.

The book tells us about the Michelson’s measurement of the speed oflight c, in which he used a rotating octagonal mirror. But the very first “on-Earth” measurement of c was made by H. Fizeau in 1849 in Paris.Fizeau used a simpler method, with a rotating “toothwheel”. I will ex-plain how it works, with the help of the picture below.

Another addition, now about waves:

As you already know fro the book, a wave,in general, is characterized by three para-meters: the wavelength , the frequency ,and the amplitude A (i.e., the maximum displacement in the y direction).

Can we describe the wave using a mathematical expression? Yes, it’scalled a “wave equation” and has the form:

txAtxy

22

sin),(