Rayleigh Refractometer index of refraction

[n0_3sc]

When constructing a Rayleigh Refractometer the formula for the refractive index of a gas at pressure P and temperature T is:

mu(P,T) - 1 = (gamma) P/T
where,
mu(P,T) = refractive index as a function of pressure and temperature
and
gamma = [n(lambda)Ta]/[L(deltaP)]
where,
n = fringe number
lambda = wavelength
Ta = Ambient room Temperature
L = length of tube containing the gas
and
deltaP = change in pressure causing the movement in fringes.

My question is how do you prove gamma? - I cannot find this in any physics/optics book.

Any suggestions on where to start or look will be good.

 

[dimensionless]

What is gamma? The frequency?

If I'm understanding the rest correctly, you have two tubes filled with gasses of different refractive index. One is known and the other is not.

If $$n_1 &=& 1$$ then the number of wavelengths needed to traverse the tube is $$m_1 &=& \frac{L n_1}{\lambda_{vacuum}}$$. Likewise the number of wavelengths need to traverse the second tube is $$m_2 &=& \frac{L n_2}{\lambda_{vacuum}}$$.

 

[n0_3sc]

yeah I already knew those formula's you listed.
Gamma is a proportionality constant. I think the lecturer just manipulated one of the "Jamin Inteferometer" formulas into this form and used gamma to represent part of the over all equation.

 

[dimensionless]

Well it looks like gamma is a function of the T and p and
$$\frac{T}{p} = \frac{V}{moles\cdot R}$$
Since your volume is fixed I imagine that gamma must be a function of number of moles and the Rydberg constant. The Rydberg constant is given by
$$R_\infty = \frac{m_e e^4}{(4 \pi \epsilon_0)^2 \hbar^3 4 \pi c} = 1.0973731568525(73) \cdot 10^7 \,\mathrm{m}^{-1}$$
I'm not sure if the Rydberg constant is fixed or not, although it is referred to as a constant.

I'm not sure how the following relates but the refractive index can also be represented as
$$n=\sqrt{\epsilon_r\mu_r}$$

Do you have a fixed number of moles?

 

[dimensionless]

Wait. I think I made a mistake. R is NOT the Rydberg constant. It is the ideal gas constant.