(4),

the first of which embodies Arago’s law of the equality of reflections, as well as the famous “loss of half an undulation.” Using these we find for the reflected vibration,

e(1 − ε−iκδ)
1 − e2 ε−iκδ

(5),

and for the transmitted vibration

1 − e2
1 − e2 ε−iκδ

(6).

The intensities of the reflected and transmitted lights are the squares of the moduli of these expressions. Thus

Intensity of reflected light = e2 (1 − cos κδ)2 + sin2 κδ
(1 − e2 cos κδ)2 + e4 sin2 κδ
= 4e2 sin2 (½κδ)
1 − 2e2 cos κδ + e4