Does Refractive Index of a Gas Change with Pressure?

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Dependence of refractive index on pressure

Homework Statement

Show that, in a gas (for which the refractive index is close to 1), the refractive index depends on the pressure as $$n_r = 1+ K\times p$$, and find the value of K.

Homework Equations

$$n_r = 1+ K\times p$$
Clausius-Mossotti equation: $$\frac{\epsilon_r - 1}{\epsilon_r + 2} = \frac{\rho N_a \alpha}{3M\epsilon_0}$$
$$\alpha^'\ = \frac{\alpha}{4\pi \epsilon_0}$$
$$n_r = \epsilon_r^{1/2}$$

The Attempt at a Solution

I wish I could do organic chemistry...

 

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