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Full text of "Scientific Papers - Vi"

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1917]   REFLECTION OF LIGHT FROM A REGULARLY STRATIFIED MEDIUM       493                                         {#$
where ^ is the refractive index, T the thickness, and a! the angle of refraction                                 |Mi
within the plate.   Also k = 27T/X, X being the wave-length,    Adding together                                 l||
the various reflections and summing the infinite geometric series, we find
In like manner for the wave transmitted through the plate we get
the incident and transmitted waves being reckoned as at A,
The quantities &', c', e', f are not independent. The simplest way to find the relations between them is to trace the consequences of supposing 8 = 0 in (2) and (3). For it is evident a priori that, with a plate of vanishing thickness, there must be a vanishing reflection and an undisturbed total transmission*. Accordingly,
b' + e'-Q,   c'f = l~e/2   ........................(4)
1                      '            /                                  3                                                                         \    J
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, and substituting ^ for e, we find for the reflected vibration,
_^il^!)j .................................(5)
and for the transmitted vibration
In dealing with a single plate, we are usually concerned only with intensities, represented by the squares of the moduli of these expressions. Thus,
T                f    n       i i- i         o Intensity of reflected light = tf .- J                                (1
Intensity of transmitted light = jir^
the sum of the two expressions being unity, as was to be expected.
According to (7), not only does the reflected light vanish completely when 8-0, but also whenever ^kS^srr, s being an integer;  that is, whenever
Returning to (5) and (6), we may remark that, in supposing k real, we are postulating a transparent plate. The effect of absorption might be included by allowing k to be complex.
*  " Wave Theory of Light," Ency. Brit. Vol. xxiv. 1888; Scientific Papers, Vol. in. p. 64.n the understanding that the ratio of the right-hand side of (12) to that of (11) is zero when n = 0, which is not the case when a absolutely = 0. W. F. S.]