A certain substance has a molecular polarizability 
and a molecular concentration of 
.
[a] Show that this is an optically dense material.
[b] Calculate its refractive index.
SOLUTION:
A substance is said to be optically dense if there is sufficient interaction between the
molecular electric dipoles to cause the local electric field experienced by a molecular dipole
to be enhanced by the polarizing fields of the other dipoles.
[a]In lectures we formulated an expression for the refractive index n of an optically dense material of the form:
where 
is the polarizability and N the molecular concentration.
The magnitude of the self-polarization is indicated by the magnitude of 
compared to unity. To be optically dilute (the opposite of dense) we must have:
In this example we have:
Clearly this is an optically dense material.
The refractive index is thus:
