Optical Density and Refraction

name         Violet
status       student
grade        6-8
location     NY

Question -   What is the difference between optical density 
and refraction? I understand that optical density is related to 
the refractive index of a substance, but are they actually the 
same thing, or is there a difference?
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Dear Violet,

I have taught university level courses on optics on numerous 
occasions and have never (as far as I remember) used the term 
"optical density".  I believe it is sometimes used to refer to the 
ability of a given substance to absorb light.  Materials with large 
optical densities absorb light going through that material in a 
shorter distance than materials with smaller optical densities.

I believe the term is also sometimes used to describe the refractive 
index, but I think is a bad thing to do as it can easily lead to 
confusion. Refractive index is well-defined and says everything 
necessary about the refraction of light.

Best, Dick Plano, Professor of Physics emeritus, Rutgers University
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Violet, they are not the same thing.
Very different, from an initial-perception point of view.
Optical index is how slow light goes through the medium (and hence 
how bent a ray will
be);
Optical density is how darkening the medium is to light passing through.

I often wish I could use the phrase "optical density" meaning "index of
refraction".
It seems a logical construction of English scientific language,
   and it fits in some sentences a little better.
But I guess it is taken.

When you see "optical density", think:
   How dense is the "dark smoke" in that smoky quartz?

Optical density number-scale takes a little getting used-to.
It is typically numbered as a power of 10 of the light extinction ratio.
So a pair of medium-dark sunglasses
that pass 10% of the light thru  their lenses
would have an optical density of 1, and probably an index of 1.5 to 1.6.
If you wore an identical second pair over the first,
you would be using an optical density of 2,
(but the index of the glass would still be 1.5).
And only 1% of the light would pass through.
1% is 1/100, and 100 is 10^(2), so the optical density number is 2.
And this number refers to the degree of light extinction
   due to passing through the whole object
of whatever shape it is, regardless of its thickness in inches.

The index number-scale is much different and perhaps more obvious.
If light travels half as fast as in air or vacuum, the index is 2.
The index usually applies to the material an object is made of,
not to the object as a whole.
Pretty different than the optical density number.

When extinction is taken to be proportional to the distance it has traveled
through the dark glass or whatever,
it is called Extinction Rate or absorption rate.
Then it is a characteristic of the material the object is made of.
Units might be OD/cm.
"Nepers/cm" is another unit, using base "e" instead of base "10" :
(Ln(in/out))/cm.

Luckily for physicists, the mathematicians have invented one function
that does both index and optical density.
It is the exponential function, using complex numbers.
In complex numbers each number has two parts a and b,
so the number is "a+(i x b)", where i is the square-root of -1.
Of course there is no real number which can be the square-root of negative
one,
but we pretend there is, consider it a constant, name it "i",
and continue our usual algebra.  Interesting useful effects follow.

When you describe an optical index with a complex number,
the real part (a) expresses the index you are familiar with,
and the imaginary part (b) expresses the extinction rate per wave-radian of
travel.
(A wave-radian is wavelength/(2*pi).)

Having this one function neatly express both the slowing and absorbing
effects
that a substance can have on light
sometimes provokes people into saying they are the "same thing".
Personally, I would not put it that way.
But they are rather related, at the basic-physics level.

Jim Swenson
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