1. PH 332 – September 20 class Some introductory remarks:
The book we are using not going to use
was written as long ago as in That’s OK,
the 1986 status of the basic theory of light is
still valid! Progress has been made, of course,
but rather in the advanced theory. We will talk
about those new developments later, in the
final part of this course. But for now, the book
is perfectly OK.

2. However, I am not 100% entusiastic about
how things are presented in Chapter 1. The
emphasis is almost exclusively on the wave
theory 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 light
theory. In fact, it is not so! Therefore, I want
to add “my own story” to the book material.

3. A brief history of the theory of light
The XVII-century scientist already knew
some important properties of light:
propagation along straight lines,
(b) the laws of reflection and refraction,
(c) the effect of diffraction.

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

5. But the great Isaac Newton
did not like the idea – he
believed that light was
actually 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 to
decide which one was correct.

6. Newton’s authority in the scientific community
was so great that his theory was widely
accepted, and the Huygen’s theory
was almost forgotten over the
100+ years that followed.

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

9. 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 and
dark “stripes” on a
screen placed behind
the slits.

11. Such an effect could only be explained on
the grounds of the Huygens’ wave theory.
Huygens was vindicated,
and the Newton’s
theory was “pronounced
dead”.

12. Over most of the XIX-th century scientists
collected experimental facts that provided
more and more support for the wave-like
nature of light.
But still it was not clear what was “oscillating”
in such waves.

13. 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 electromagnetic
waves.

14. The speed of such waves deduced
from 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.

15. 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”.

16. The breakthrough came in 1886, when a
German scientist, Heinrich HERTZ, built
an apparatus that, according to the Max-
well’s theory, should have generated elec-
tromagnetic waves – and he convincingly
demonstrated that the waves were indeed
produced. It was believed to be the final
Victory of the Wave Theory of Light.

17. But MOTHER NATURE, as it turns out, has a perverse sense
of humor! Because one year later, in 1887, the very same
Heinrich 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 a
major riddle for the physicists at the end of the XIX-th century.

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

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

20. No, they were 100% authentic!
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!

21. 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 it
clearly 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.

22. Another thing that is not in the book, but may be interesting.
The book tells us about the Michelson’s measurement of the speed of
light 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.

23. 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’s
called a “wave equation” and has the form: