The argon fill gas between the panes of a double-glazed window has bound-electron…

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Wave propagation and light in media · Wave propagation and light in media

Optics and Photonics, Ch Light as an electromagnetic wave in matter

Problem

The argon fill gas between the panes of a double-glazed window has bound-electron number density

\mathcal{N}_0 = 2.4\times10^{25}

^{-3}

(near atmospheric pressure) and an ultraviolet resonance at

\omega_0 = 2.6\times10^{16}

rad s

^{-1}

. It is tested with a red laser pointer of

\lambda = 650

nm. Use the dilute-gas Lorentz formula

n - 1 \approx \dfrac{\mathcal{N}e^2}{2\epsilon_0 m_e}\dfrac{1}{\omega_0^2 - \omega^2}

, with

e = 1.602\times10^{-19}

m_e = 9.11\times10^{-31}

kg,

\epsilon_0 = 8.85\times10^{-12}

F m

^{-1}

. ((a)) Compute

n-1

for the gas as described. ((b)) Recompute

n-1

if the gas is compressed so

\mathcal{N}

doubles,

\omega_0

unchanged. State whether the sign of

dn/d\lambda

changes. ((c)) Instead, recompute

n-1

\omega_0

is halved,

\mathcal{N}

back at its original value. State whether the sign of

dn/d\lambda

changes. ((d)) Which lever, doubling

\mathcal{N}

or halving

\omega_0

, has the larger effect, and why?