Does Refractive Index of a Gas Change with Pressure?

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SUMMARY

The refractive index of a gas is directly dependent on pressure, expressed by the equation n_r = 1 + K × p, where K is a constant that needs to be determined. The Clausius-Mossotti equation is also relevant, linking the refractive index to the gas's density and polarizability. This relationship is particularly significant when the refractive index is close to 1, which is typical for gases. Understanding this dependency is crucial for applications in optics and atmospheric science.

PREREQUISITES
  • Understanding of the refractive index and its mathematical representation
  • Familiarity with the Clausius-Mossotti equation
  • Basic knowledge of gas laws and pressure effects
  • Concept of polarizability in materials
NEXT STEPS
  • Research the derivation of the Clausius-Mossotti equation
  • Explore the relationship between gas density and refractive index
  • Investigate the impact of temperature on gas refractive index
  • Learn about applications of refractive index in atmospheric optics
USEFUL FOR

Physicists, optical engineers, and students studying gas properties and their effects on light propagation.

Aeon
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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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