(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 |