# Finding refractive index by interpolation

The problem is described here:
http://phstudy.technion.ac.il/~wn117066/Problems2.pdf [Broken]

In question 1 I need to find the refractive indices for both polarizations at 760nm. I'm not quite sure how to go about this - which model of dispersion best fits Calomel?

(I'm done with the exercise itself, now I just need to plug in the refractive indices values to get a numerical result...)

Thanks,
Chen

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OlderDan
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Interpolation is the process of estimating a value from a discrete set of ordered pairs of data. You could use a linear interpolation, or since you have three rather widely spaced points you could use a second degree polynomial (parabola) to fit the data and extract the interpolated data point. Most graphing calculators have a built in fitting program for this, probably called a quadratic regression. Or you could derive the equation from the three data points you are given and use it to find the additional popint you need.

http://en.wikipedia.org/wiki/Interpolation

I'm well familiar with the definition of interpolation, thank you.

Or you could fit the data to find the sellmeier coefficients:

http://en.wikipedia.org/wiki/Sellmeier_equation
I considered that route, but having only 3 data points available makes it a bit hard to find those coefficients...

You could also use other models with fewer coefficients -- since yeah, you only have three points and probably don't want to trucate the Sellmeier series approach by too much (sorry I didn't notice that :uhh:):

http://www.optics.arizona.edu/Palmer/cgi-bin/index/dispeqns.pdf [Broken]

The Cauchy model is common.

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Thanks, that seems sensible. I'll report back if anything goes awry...