Optical Density Determination
Name: Theresa A.
Why does light pass through some pure substances, but not
others (eg. diamond vs graphite ... both are Carbon)?
On a molecular level, what exactly determines optical density (it is not
the same as mass density)?
Why does light slow down in optically dense media?
There are at least two kinds of "optical density", maybe more like three:
1) absorbance (it is clear, but it is to some degree dark, like smoky glass.
Light is diminishing as it travels through.)
2) refractive index (it is clear, but light goes slower through
it. So it changes direction at surfaces.
for large index, some of the light bounces off each
surface. Metallic reflection is an extreme case of this.)
3) scattering density ( it is clear but messy with refractive index
surfaces, so it becomes cluttered or frosty or milky or white)
Any given substance has some amount of each of these three "densities".
Only refractive index has any connection with mass density.
That being: heavy substances are made of high-atomic-number elements,
which have many electrons, which cause higher refractive index.
High concentrations of bound electrons (bound in one place, but
elastically movable by a short distance) are the "water" that slows down
the flight of light.
Viscously-movable electrons absorb light (1) at all wavelengths. This is
graphite black, and it enforces the opacity of metals.
You can see through metals if they are less than 0.1 micrometer
thick. One-way mirrors are this.
But if thicker, the part of light which is not reflected at the front
surface will be completely absorbed. Metallic opacity.
Light is also absorbed by bound electrons using the energy to climb out of
their trapped state, or at least climb to a higher trapped state.
But it has to be the right amount of energy, so it is a more
color-selective absorption. It creates most of the non-neutral colors of
Chemical purity helps a clear substance be clearer, but it cannot help an
inherently absorbing substance like graphite become clear.
Perfect single crystals of graphite are a lighter silvery color than
typical poly-crystalline graphite.
Certain impurities in graphite actually donate more mobile electrons,
which sometimes make it lighter still.
Chemically pure glass is silicon dioxide. Light can go for tens to
thousands of meters in this, depending on color, if it is pure.
Give it unnecessary surfaces by grinding it up, and you have sand: more
white than clear.
Chemically pure aluminum oxide can be white if it is many small
crystallites, or clear if it is one large crystal (colorless sapphire).
Pure water is not a crystal, it is random inside, but it can be clear in a
uniform mass, or milky if dispersed as fog.
Ice can be either clear or cloudy or fractured with flaws.
Diamond vs Graphite:
The carbon atom can make 4 chemical bonds (shared-electron-links) to
In diamond, each atom links to 4 different neighbors, and every electron
is bound (confined) within its own link.
So there are no mobile electrons, and diamond is a dielectric not a
conductor, and it is clear, not absorbing.
In graphite, each atom links to only 3 neighbors, making a flat sheet, and
each has one link left over.
All these leftover links are shared in common by the whole sheet.
The electrons of this pool of links are mobile, so graphite conducts
electricity and absorbs light.
There are not many elements which have a choice of whether or not to be
Those are the classical optical properties.
Iridescence and dichroism are a different story.
If a substance has an unoccupied electronic state whose energy
difference from initial state is the same as the energy of the incident
radiation (light), and given certain other restriction, then the substance
will absorb the incident radiation. The electronic structure of the
substance determines whether or not such unoccupied but accessible
electronic states exist; however, the details of determining such states
is rather involved. The bonding in diamond and graphite is a good example.
Both are carbon, but in diamond the carbon atoms are bonded to one another
by single bonds and these electrons do not respond to visible light. The
electronic structure of graphite on the other hand is stacks of sheets of
carbon in which the electrons are highly delocalized in such a way that
essentially all visible light is absorbed. As a result graphite is black.
The measure of the ratio of the transmitted power, Ptrans. (energy /
sec) to the incident power, Pincid.: Ptrans. / Pincid. = Tr is called the
transmittance (or in the older literature the transmission). This ratio has
a range: 0 < Tr < 1 but it can vary over a wide range of values, for
example: Tr = 10^-1 or
Tr = 10^-5 even though it is a number between 0 and 1. The optical density:
O.D. is defined as:
O.D. = log10( 1/ Tr) = - log10(Tr). The reason for using this "log10" scale
is to make the numbers positive and to make their range smaller since the
O.D. in the power of 10 in the exponent. Despite the use of the same term
"density" O.D. has nothing directly to do with the mass density.
Your second question, Why light slows down in a medium is more subtle
and involved. It is equivalent to the question of why transparent substances
have an index of refraction. The index of refraction, 'n' is:
n = 1 + (electronic term) where the (electronic term) involves a ratio that
involves the charge density of the medium in the numerator and the electron
mass and the frequency of light in the denominator. What is going on is that
the incident light "tries to cause" the electrons in the medium to vibrate
at the same frequency as the incident light, but when the electron moves its
neighboring electrons sense this induced change in the first electron and
respond to try to "pull the electron back into its equilibrium position".
This "pulling back" causes the oscillation of the initial electron to "slow
down". Which, in effect means the speed of the oscillation is retarded --
that is the speed of propagation of light is slowed. This is a very
approximate description of what is happening.
For more details you can refer
to Richard Feynman's
"Lectures on Physics" Vol. 1, Chapter 31, "The Origin of the Refractive
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Update: June 2012