### Re: What causes the reflection of light?

Area: Physics
Posted By: Adrian Popa, Staff Optical/Microwave Physics
Date: Mon May 5 14:51:07 1997
Area of science: Physics
ID: 862338456.Ph
Message:
```Greetings:

My discussion of reflection is based on the the late Nobel Laureate,
Professor Richard P. Feynman's lectures at the California Institute of
Technology and I will try and paraphrase Professor Feynman's conclusions
here without including the difficult mathematics. I have included some
quotations from the lectures and you can also find the mathematical
derivations  in the following reference:

Richard P. Feynman, Robert B. Leighton, Matthew Sands,
The Feynman Lectures on Physics, Addison-Wesley 1964.
Volume 2, Chapter 32, Refractive Index of Dense Materials
Volume 2, Chapter 33, Reflection from Surfaces

When an electromagnetic field  ( e.g.. Radio, microwave, infrared or light)
from a distant source (S) is incident on a thin sheet of glass  we often
use Snell's Law to describe the reflection and refraction that takes place
as the waves pass through the glass. In these calculations we use the index
of refraction (n) of the material at the frequency of the wave source. The
refractive index is a measure of the velocity of light in the material (v)
relative to the velocity of light in a vacuum (c) such that v = c/n.
However, for completeness, n is in reality a complex number consisting of a
real and an imaginary component.

I'll label the real component of n, N(r) and I'll label the imaginary
component of n, N(i). N(r) is the "apparent" velocity of the wave in the
glass and N(i) is a measure of attenuation (absorption) in the glass and
describes an exponential decay of the amplitude of the light wave as it
passes through the glass. In many optically transparent materials such as
glass N(i) is very small and we neglect it.

Also, we tend to think of materials as opaque or transparent because they
behave that way in the region of the spectrum we are using, be it microwaves
or light; however, opaque materials can change into transparent materials
in some regions of the spectrum and vice versa (e.g. color filters). For
example we consider copper and other metals to be opaque at radio, microwave
, infrared and optical wavelengths yet copper does become transparent to
light in very thin layers (solar window coatings) and at X-ray wavelengths.
Some metals such as Li, Na, K and Rb become transparent in the ultraviolet
wavelengths. The point of this discussion is that general equations of
matter must include  the behavior of materials throughout the
electromagnetic spectrum from radio waves through X-rays which in turn
makes these equations very complex and difficult to comprehend in a physical
sense. However, I feel Professor Feynman had a super ability to provide
both a mathematical and a physical view of a problem.

Professor Feynman writes: "We have said that light goes slower in water than
in air, and slower, slightly , in air than in vacuum. This effect is
described as the index of refraction (n). How does this come  about? Let's
use the following physical statements.

(a) That the total electric field in any physical circumstance can always
be represented by the sum of the fields from all of the charges in the
universe.

(b) That the field from a single charge is given by its acceleration
evaluated with a retardation at the speed c, always (for the radiation field)."

REFLECTION FROM GLASS
If an external light source is incident on a thin sheet of glass we would
say that the light in the glass is retarded at the speed c/N(r). Professor
Feynman then writes:  "That, however is not right, and we have to understand
why it is not. It is approximately true that light or any electrical wave
does appear to travel at a speed c/n through a material whose index of
refraction is n, but the fields are still produced by the motions of all
the charges - including the charges moving in the material - and with these
basic contributions of the field traveling at the ultimate velocity c.
Our problem is to understand how apparently slower velocity comes about.
Why should there be charges moving in the glass? We know that all material
consists of atoms which contain electrons. When the electric field of the
source acts on these atoms it drives the electrons up and down, because it
exerts a force on the electrons. And moving  electrons generate a field
- they constitute new radiators. These new radiators are related to the
source S, because they are driven by the field of the source.  This means
that the field is not the same as the one that was there before the glass
was there, but is modified in such a way that the field inside the glass
appears to be moving at a different speed. These charges also radiate waves
back toward the source. This backward going field is the one we see
reflected from the surfaces of transparent materials. It does not come
from just the surface. The backward radiation comes from every
where in the interior , but it turns out that the total
effect is equivalent to a reflection from the surface."

REFLECTION FROM METAL
"In metals some of the electrons have no binding force holding them to a
particular atom; it is these free electrons which are responsible for the
conductivity. There are other electrons which are bound - however; there
influence is usually swamped by the effects of the conduction electrons."
The motions of these free electrons travel with a velocity derived from
the average field from the source but they follow a jagged path from
collision to collision. One result of the free electrons is that : " The
real and imaginary parts of n have the same magnitude".

This is true for Feynman's  low - frequency approximation , where the metal
is opaque to light, which is derived in his lecture.

"With such a large imaginary part to n, the wave is rapidly attenuated in
the metal." The distance in which the amplitude of the wave decreases by a
factor of 1/3 is called the skin depth  and a calculation shows that for
copper the penetration of the wave is a small fraction of a wavelength.

While a wavelength of light is about 500 nanometers in length the atomic
spacing in a metal is about one half of a nanometer. Thus a wavelength is
1000 atoms long and a plane area of one square wavelength has 1 million
atoms.  Thus even with less than a wavelength penetration, there are
countless numbers of atoms and electrons to excite and reradiate energy
near the metals surface!

The rapid exponential decay near the metal's surface causes both a rapid
decrease in the amplitude of the wave and a large phase shift in the
excitation and reradiation from the free electrons. This 180 degree phase
shift in a very small distance is required because a metallic surface should
short out the voltage of a field hitting the surface.  For this case
Maxwell's wave equations require that the reflected field should be equal
in magnitude to the incident wave only 180 degrees out of phase with the
incident wave, so that the vector sum of the voltages of the incomming wave
and the outgoing waveat the surface is zero (an effective short circuit).

It is often difficult to realize that a fixed zero field plane can be
composed of two large amplitude waves, traveling in opposite directions;
yet this happens in many areas in physics including musical instruments,
radio antennas as well as in optics. I have shown this interference effect
graphically in my response to the following question:

Physics : Re: When waves collide, do both kinds of interference occur?
Adrian Popa, Staff Optical/Microwave Physics, Tue Jan 21 11:42:59 1997

Professor Feynman then concludes: "Metals do not reflect 100%, but many do
reflect visible light very well. In other words the imaginary part of their
indexes is very large. But we have seen that a large imaginary part of the
index means a strong absorption. So there is a general rule that if any
material gets to be  a very good absorber at any frequency, the waves are
strongly reflected at the surface and very little gets inside to be absorbed
." " We want to emphasize that the amplitude of a surface reflection is not
a property of the material as in the index of refraction. It is a surface
property, one that depends precisely on how the surface is made." Thus,
polishing, coatings, films and surface corrosion are all part of the
surface and must be considered in the calculations.

```

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