What is meant by "Index" and Coefficient (B)?

[treddie]

Maybe this will help some people who are confused by the term "refractive index". I finally had to get it all straightened out in my own head, and I think this explains it. I hope so anyway!

In reading the Octane manual it appears that Octane models diffraction based on Cauchy's two-term method:
n(λ) = A + B/λ2,

where (n) is the refractive index, (λ) is the wavelength, and the coefficients (A) and (B) are specific for different types of transparent media as determined from experiment. As examples:

In the graph below, refractive index is plotted against wavelength for a specific type of glass, BK7. It is clear then that refractive index as a single value has no meaning unless it refers to a specific wavelength. But, in looking at the (A) values in the table, these are strikingly similar to refractive indices when published as single values for an entire material, regardless of wavelength. So what is going on here?! In one breath, science tells us refractive index is wavelength dependent, and in the next, it is telling us that refractive index is a single value for a given material, INDEPENDENT of wavelength!

If we take the table's (A) value for Borosilicate glass (BK7), and use that as the BASE VALUE for refractive index in the BK7 graph below, then, it appears that TRUE refractive index is a known base value "index" PLUS some other term that is dependent on wavelength. Indeed, the Cauchy equation is a sum of a constant coeffecient (A) plus a second term that is dependent on wavelength. Therefore, the indicated red line shows the correct position for this lower "index" value. This line, then, is the asymptotic lower boundary for the blue curve as wavelength approaches infinity.

This can only mean that the term, "refractive index" is confusingly used in two different contexts...A classic case of science not being very scientific In the ACCURATE usage of the term, it means a changing value based on wavelength. In the other case it means the fixed, lower asymptotic limit of the blue, logarithmic curve as wavelength approaches infinity. In other words, the blue curve gets closer and closer to the red line, but can never reach it. It would take a wavelength of infinity for the blue curve to touch and become tangent to the red line.

So, Octane apparently uses the less stringent use of the term, "Index" when it would be more accurate to use the term, "Coefficient (A), without ambiguity. But Octane's usage would seem legitimate since (A) really does represent an index, or reference value from which all others are based. However, in the case of optics, the term can too easily be mistaken for refractive index as a wavelength dependent value.

In the graph, a dashed green line is also present. This curve represents the true equation that much more accurately describes the behavior of light in nature, especially outside the visible light range. This equation (Sellmeier's Equation) is however a much more complex equation with four terms, three of which are more complicated than the second term in Cauchy's equation. That represents far more computation time in a very iterative algorithm where optimization is very important. Also, Octane is only concerned with the visible light range. In this range, both the Cauchy and Sellmeier equations agree very closely.

[Daniel]

In simple terms, different wavelengths of light travel at different speeds within a more or less dense medium than the one it's currently travelling in (usually air). Imagine throwing rocks of different size into water. The rocks of lighter mass will stop suddenly and drop sooner where the ones with higher mass. This goes the same for the different wavelengths of light. Longer wavelengths, like red light (the heavy rock) bend less (continue travelling in a straighter line after entering the water, in terms of the rock example) when entering a more dense substance like light, where as shorter wavelengths, like blue light bend more. White light is a combination of all the different wavelengths of visible light (from red to violet), so when white light enters a more dense medium (like a glass prism), each individual wavelength bends at a different angle, "splitting" the white light into the different colours. That's why it comes out like this:

When the angle of incidence from light towards the medium it's entering is too sharp, depending on what medium it is, the light will reflect away from the medium instead of bend into it. This is what the Fresnel effect is. The easiest way to observe this is to look at a pool of water from a distance, and as you approach it you'll see it reflects what is above the surface far less and you'll be able to see into the water more. The Fresnel value doesn't exist in Octane as it does in biased renderers because this value goes hand-in-hand with the refractive index to offer a physically accurate representation of a material (although may be manipulatable with the new falloff feature, I haven't looked into it yet).

Oh, and I forgot to mention; different mediums (like water, glass, diamond, etc.) have different refractive indices. So you can look up a table of refractive indices to get the right value to put into Octane. A more dense medium has a higher refractive index. Air is slightly over 1 (with a vacuum being 1), water is 1.333, glass is 1.5 and diamond is 2.4. Those are generally the ones people like to use.

[treddie]

A good preamble for my post since it puts the refractive index thing in a physical context. Then, hopefully my post will help clarify the confusion between the two different meanings of the words, "refractive index". I still feel that Coefficient (A) should never be referred to as the "index", since it is no longer of a phrase than "Coefficient (B)", and clarifies it is one of the two important values in Cauchy's equation, that together with everything else in the equation gives you the unambiguous refractive index. But scientists have already made it ambiguous, so I guess we're stuck with it. If they MUST have some other descriptive name for it, why not call it the "Base Value", or something?