A second feature is the increased brilliancy of the light. According to (7) the intensity of the reflected light when at a maximum (sin ½κγ = 1) is 4e2/(1 + e2)2. At perpendicular incidence e is about 1⁄5, and the intensity is somewhat small; but, as cos α′ approaches zero, e approaches unity, and the brilliancy is much increased.
But the peculiarity which most demands attention is the lessened influence of a variation in λ upon the phase-retardation. A diminution of λ of itself increases the retardation of phase, but, since waves of shorter wave-length are more refrangible, this effect may be more or less perfectly compensated by the greater obliquity, and consequent diminution in the value of cos α′. We will investigate the conditions under which the retardation of phase is stationary in spite of a variation of λ.
In order that λ−1 cos α′ may be stationary, we must have
λ sin α′ dα′ + cos α′ dλ = 0,
where (α being constant)
cos α′ dα′ = sin α dμ.
Thus
| cot2 α′ = | λ | dμ | |
| μ | dλ |
(9),
giving α′ when the relation between μ and λ is known.