## Refractive Index

### Introduction

For a vacuum, the refractive index is 1.000.  This means that light travels through a vacuum at the speed c.  When light goes through a medium such as glass, the time needed to travel a given distance increases.   The conventional way of looking at this is to say that light is slowed down as it passes through the glass.  An alternative, and equivalent, explanation would be to say that the apparent distance the light has to travel has increased.  The extra distance can be expressed as a ratio, thus a refractive index of 1.4 would mean that the light was slowed by a factor of 1.4 or that the distance was increased by the same factor.  In three dimensions, the refractive index represents the extra volume that appears to exist when light goes through a medium. Thus if a glass had a refractive index of 1.4, it would mean that a 10cc block of it would appear to have a volume of 14 cc, if the volume was determined using light.

Refractive index is related to polarizability, in that it represents the extra volume that appears to exist when light goes through a medium.

The refractive index of a solid cannot be calculated directly.  Nor can the polarizability of a solid be calculated, if translation vectors are used.

### How to Calculate Refractive Index

The polarizability at various energies (wavelengths) can be calculated for the cluster, using POLAR, if translation vectors are removed and the "dangling bonds" are satisfied.  The best atom for this is the capped bond (Cb).  Obviously, the calculated polarizability includes the contributions from the surface, so the surface effects must be removed.  This is easily done by doing calculations on different clusters.  Consider a cluster of size 10x10x10Å.  If this was increased to 15x15x15, the surface area (surface effect) would increase from 6x10x10 to 6x15x15 square Ångstroms, while the volume (what we want) would increase from 10x10x10 to 15x15x15 cubic Ångstroms.

Given the polarizability, a, and the volume, V,  of the cluster, the average refractive index, n,  is readily given by n = (1+a/v).  If LET is used, the system will not be re-oriented, and the individual polarizabilities (in x, y, and z) can be calculated. From these, the refractive indices in different directions can be calculated.