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</4(2x),
2x being the diameter of the disk. If 2r = 1000 cm., 2x = 1 cm.,
[lambda] = 6 X 10^-5 cm., then dx = .0015 cm. Hence, in order that
this zone may be perfectly formed, there should be no error in the
circumference of the order of .001 cm. (It is easy to see that the
radius of the bright spot is of the same order of magnitude.) The
experiment succeeds in a dark room of the length above mentioned, with
a threepenny bit (supported by three threads) as obstacle, the origin
of light being a small needle hole in a plate of tin, through which
the sun's rays shine horizontally after reflection from an external
mirror. In the absence of a heliostat it is more convenient to obtain
a point of light with the aid of a lens of short focus.
The amplitude of the light at any point in the axis, when plane waves
are incident perpendicularly upon an annular aperture, is, as above,
cos k(at - r1) - cos k(at - r2) = 2 sin kat sin k(r1 - r2),
r2, r1 being the distances of the outer and inner boundaries from the
point in question. It is scarcely necessary to remark that in all such
cases the calculation applies in the first instance to homogeneous
light, and that, in accordance with Fourier's theorem, each
homogeneous component of a mixture may be treated separately. When the
original light is white, the presence of some components and the
absence of others will usually give rise to coloured effects, variable
with the precise circumstances of the case.
[Illustration: FIG. 2.]
Although the matter can be fully treated only upon the basis of a
dynamical theory, it is proper to point out at once that there is an
element of assumption in the application of Huygens's principle to the
calculation of the effects produced by opaque screens of limited
extent. Properly applied, the principle could not fail; but, as may
readily be proved in the case of sonorous waves, it is not in
strictness sufficient to assume the expression for a secondary wave
suitable when the primary wave is undisturbed, with mere limitation of
the integration to the transparent parts of the screen. But, except
perhaps in the case of very fine gratings, it is probable that the
error thus caused is insignificant; for the incorrect estimat]]>
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