What's the relationship between concentration and refraction rate in a solution? I am supposed to determine the concentration of a solution of ethyl alcohol and cyclohexane by measuring its refraction rate. Now I have some standard sample of the solution at concentrations 10%, 20%, ... , 100% and I measured their refraction rates respectively. I'm now supposed to perform a non-linear fit to the data, but which fitting model should I use? Someone had suggested exponential, and the data look like an exponential growth, but is there a theoretical equation for this?
 A: The theoretical equation you are looking for is actually referred to as a model, which you must hypothesise based on sound reason. The exponential model is one that allows for a rate of change proportional to the current value--for experiments such as objects being decelerated by air resistance (air resistance depends on how fast the object is moving), or amount of radiation emitted by a small radioactive source (amount of radiation depends on how much radioactive material remains), etc. To me this doesn't suit the behaviour of light in media, I would hypothesis a power law instead..of which an example is the inverse square law($r^{-2})$ of light intensity at a distance for example, or inverse square root law ($\rho^{-0.5})$ for terminal velocity due to air density. 

I hypothesise that the speed of light decreases as the density of the
  medium increases according to some exponent. Paraphrased, the
  hypothesis suggests a power law relation between solute concentration
  of a liquid medium and its refractive index.

With concentration(x) and refractive index(n), the power model is $n=Ax^B+D$. This opposed to a linear model $n=Ax+B$ (a.k.a y=mx+c), where $A$ $B$ and $D$ are constants. Note that you can swap n with x here, the polarity of B will flip automatically as a result.
The trick is to transform the nonlinear equation by applying $lg$ to both sides of $n=Ax^B+D$:
$\lg (n)=B \lg(x)+ E$, where $E=\lg(A^BD)$, itself a constant since it involves neither $n$ or $C$. 
Clearly plotting $ \lg(n)$ vs $\lg(x)$ produces a straight line with $B$ instantly found by calculating gradient of best fit line, and $E$ also immediately known from the y-intercept of that line. Then it is just a few more steps to obtain A and D.
The exponential form would be $n=n_0 exp(Ax)$, where $n_0$ is the starting refractive index (which increases exponentially with concentration as alternately hypothesized) at zero concentration. To transform this model to linear form, apply natural log to both sides to obtain:
$\lg(n)=Ax + \lg(n_0)$, where $A$ is the gradient and $\lg(n_0)$ is the y-intercept of the graph of $\lg(n)$ vs $x$. Note the difference...
Lastly, both power law and exponential models may seem to be able to fit the data. With few data points this is very possible--and also dangerous (it is tempting to choose exponential model because of ease of manipulation). But the advantage of the power law is that it allows for diminishing growth (exponent <1), whereas exponential model leads to always increasing values for positive arguments. This is another reason in hindsight where I wouldn't use a exponential model, since it predicts boundless growth of refractive index with increasing solute concentration--something which I find will be easily refuted by inspection of your data.
suggestion:

