502
if ?? = tanh £, so that
ON THE REFLECTION OF LIGHT
& = ± 2
[422 ..(65)
Let us suppose that, as for glass and air, /u, = 1-5,17 = £, making & = 0-40546. The following were calculated with the aid of the Smithsonian Tables of Hyperbolic Functions. It appears that under these favourable conditions as regards 8 and 8', the intensity of the reflected light | <£m|a approaches its limit (unity) when m reaches 4 or 5.
TABLE I.
m »»/3i tanh wi|8i |^Hi|2=tanha?H./31
I 0-4055 0-3846 0-1479
2 0-8109 0-6701 0-4490
3 1-2164 0-8386 0-7032
4 1-6218 0-9249 0-8554
5 2-0273 0-9659 0-9330
6 2-4328 0-9847 0-9696
7 2-8382 0-9932 0-9864
10 4-055 0-9994 0-9988
QO oc ! I'OOOO 1-0000
In the case of chlorate of potash crystals with periodic twinning 77 is very small at moderate incidences. As an example of the sort of thing to be expected, we may take & = 0'04, corresponding to 77 = 0'02.
TABLE II.
m » tanh mpi | <pm \ 2
1 0-0400 0-00160
2 0-0798 • 0-00637
4 0-1586 0-02517
8 0-3095 0-09579
16 0-5649 0-3191
32 0-8565 0-7336
64 0-9881 • 0-9763
According to (58), if 8'— 8 = s\, the same value of sinh2 a obtains as in (63), since we are supposing cos %k8 = 0, and the same consequences follow*.
.(66)
Retaining the same values of 8, that is those included under 8 = we will now suppose 8' = s'\ where s' also is an integer. From (55)
(1 _ ~2\2 sinh2 a = ' = sinh2 alt .....................
* But when rj is small, a slight departure from cos^/c5=0 produces very different effects in the two cases. e~ik(&+s"> = 1, so that in the notation of (50), Aa = A/2 = — 1. The introduction of these values into (54) yields