cf
----------------------------------- (3).
1 - e^2[epsilon]^(-i[kappa][delta])
The quantities b, c, e, f are not independent. The simplest way to
find the relations between them is to trace the consequences of
supposing [delta] = 0 in (2) and (3). This may be regarded as a
development from Young's point of view. A plate of vanishing thickness
is ultimately no obstacle at all. In the nature of things a _surface_
cannot reflect. Hence with a plate of vanishing thickness there must
be a vanishing reflection and a total transmission, and accordingly
b + e = 0, cf = l - e^2 (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 - [epsilon]^(-i[kappa][delta])}
----------------------------------- (5),
1 - e^2[epsilon]^(-i[kappa][delta])
and for the transmitted vibration
1 - e^2
----------------------------------- (6).
1 - e^2[epsilon]^(-i[kappa][delta])
The intensities of the reflected and transmitted lights are the
squares of the moduli of these expressions. Thus