Optical Density and Light Speed
Refraction is the bending of the path of a light wave as
it passes from one material to another material. The refraction occurs at the
boundary and is caused by a change in the speed of the light wave upon crossing the boundary.
The tendency of a ray of light to bend one direction or another is dependent
upon whether the light wave speeds up or slows down upon crossing the boundary.
Because a major focus of our study will be upon the direction of bending, it
will be important to understand the factors that affect the speed at which a
light wave is transported through a medium.
Light
Propagation Through a Medium
The mechanism by which a light wave is transported through a
medium occurs in a manner that is similar to the way that any other wave is
transported - by particle-to-particle interaction. In Unit 10 of
The Physics Classroom Tutorial, the particle-to-particle
interaction mechanism by which a mechanical wave transports energy was
discussed in detail. In Unit 12 of The Physics Classroom Tutorial, the mechanism of energy transport by an electromagnetic wave was
briefly discussed. Here we will look at this method in more detail.
An electromagnetic wave (i.e., a light wave) is produced by a
vibrating electric charge. As the wave moves through the vacuum of empty space,
it travels at a speed of c (3 x 108 m/s). This
value is the speed of light in a vacuum. When the wave impinges upon a particle
of matter, the energy is absorbed and sets electrons within the atoms into
vibrational motion. If the frequency of the electromagnetic wave does not match
the resonant frequency of vibration of the electron, then the energy is reemitted in the form of an electromagnetic wave.
This new electromagnetic wave has the same frequency as the original wave and
it too will travel at a speed of c through the empty space between atoms. The
newly emitted light wave continues to move through the interatomic space until
it impinges upon a neighboring particle.
The energy is absorbed by this new particle and sets the electrons of its atoms
into vibration motion. And once more, if there is no match between the
frequency of the electromagnetic wave and the resonant frequency of the
electron, the energy is reemitted in the form of a new electromagnetic wave.
The cycle of absorption and reemission continues as the energy is transported
from particle to particle through the bulk of a medium. Every photon (bundle of
electromagnetic energy) travels between the interatomic void at a speed of c; yet time delay involved in the process of being absorbed and reemitted
by the atoms of the material lowers the net speed of transport from one end of
the medium to the other. Subsequently, the net speed of an electromagnetic wave
in any medium is somewhat less than its speed in a vacuum - c (3 x 108 m/s).
Optical
Density and the Index of Refraction
Like any wave, the speed of a light wave is dependent upon
the properties of the medium. In the case of an electromagnetic wave, the speed
of the wave depends upon the optical density of that
material. The optical density of a medium is not the same as its physical
density. The physical density of a material refers to the mass/volume ratio.
The optical density of a material relates to the sluggish tendency of the atoms
of a material to maintain the absorbed energy of an electromagnetic wave in the
form of vibrating electrons before reemitting it as a new electromagnetic
disturbance. The more optically dense that a material is, the slower that a
wave will move through the material.
One indicator of the optical density of a
material is the index of refraction value of the material. Index of refraction values
(represented by the symbol n) are numerical
index values that are expressed relative to the speed of light in a vacuum. The
index of refraction value of a material is a number that indicates the number
of times slower that a light wave would be in that material than it is in a
vacuum. A vacuum is given an n value of 1.0000. The n values of
other materials are found from the following equation:
The table below lists index of refraction
values for a variety of medium. The materials listed at the top of the table
are those through which light travels fastest; these are the least optically
dense materials. The materials listed at the bottom of the table are those
through which light travels slowest; these are the most optically dense
materials. So as the index of refraction value increases, the optical density
increases, and the speed of light in that material decreases.
|
Material |
Index of Refraction |
|
|
Vacuum |
1.0000 |
<--lowest optical density |
|
Air |
1.0003 |
|
|
Ice |
1.31 |
|
|
Water |
1.333 |
|
|
Ethyl Alcohol |
1.36 |
|
|
Plexiglas |
1.51 |
|
|
Crown Glass |
1.52 |
|
|
Light Flint Glass |
1.58 |
|
|
Dense Flint Glass |
1.66 |
|
|
Zircon |
1.923 |
|
|
Diamond |
2.417 |
|
|
Rutile |
2.907 |
|
|
Gallium phosphide |
3.50 |
<--highest optical density |