4.3 Parallel index of refraction

The parallel index of refraction is defined as

(41)

Here B^j are the contravariant coordinates of B, given by

(42)

where

(43)

such that the contravariant coordinates of B are

(44)

where α is the angle between to such that

(45)

Because is orientated outward we have -π∕2 < α < π∕2. Then (??) yields

(46)

where P = and T = .