Diamond has applications in optics due to its high refractive index. The document considers using the Clausius-Mossotti and electronic polarizability equations to model the refractive index of diamond, accounting for its density of carbon atoms, valence electrons, and dielectric constant. It then asks to calculate the natural frequency and refractive indices at wavelengths of 0.5 and 5 micrometers.

1. Consider applying the simple electronic polarizability and
Clasius-Mossotti equations to diamond.
Neglecting losses,
α
ω ω e
e o
Ze
m
=
−
2
( 2 2 )
and ε
ε ε ω ω
r
r o e o
NZe
m

2. −
+
=
−
1
2 3
2
( 2 2 )
Dispersion in diamond
For diamond we can take Z = 4 (valence electrons only as these
are the most responsive),
N = 1.8 × 1029 atoms m-3, εr(DC) = 5.7. Find ωo and then find
the refractive index at λ = 0.5 μm and
5 μm.