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Name: Violet
Status: student
Age: N/A
Location: NY
Country: US
Date: N/A

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?

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

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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