1913]
FINE SLITS IN THIN OPAQUE SCREENS
177
(luminous) waves transmitted by a similar slit in a thin perfectly opaque screen, provided that the electric vector is perpendicular to the length of the slit.
In curve A, fig. 1, the value of the modulus from the third column of Table IV is plotted against Icb.
0-5
1-0 1-5.
Fig. 1.
2-0
2-5
When Jcb is large, the limiting form of (67) may be deduced from a formula, analogous to (12), connecting NP1 and d<f>/dii. As in. (11),
dx J dx > in which, when x is very small, we may take D = log r. Thus
or
Now, when Jcb is large, d^r/dn tends, except close to the edges, to assume
the value ik, and ultimately
r+b o .'M,
(67)= ¥dy = £**£, ........................ (69)
-b
of which the modulus is 1kb ITT simply, i.e. 0*637 kb.
We now pass on to consider case (ii), where the boundary condition to be satisfied over the wall is 0 = 0. Separating from <£ the solution (%) which would obtain were the wall unperforated, we have
Xm = e-ikx-eikx, ^=0, ..................... (70)
giving over the whole plane (x = 0),
R. vi.
12alues of fa The first three have been calculated from the simple formula, see (20).