
Explanation of Talbot’s Bands, 3 
A, pass through F later than those coming from Ag, A,41, Kc., 
and hence there cannot be any interference. 
If at a certain point of the spectrum corresponding to a 
wave-length > there is a maximum of light, the relative 
retardation of the two interfering impulses must be equal to 
mA, m being an integer; the next adjoining band towards the 
violet will appear at a wave-length ’ such that 
mrX=(m+1)r. 
Hence for the distance between the bands 

=v) _ 1 
iy > Seas 
with the best thickness of interposed plate, m=4N, and hence 
ee 
ee in De 
where 2’ in the denominator may with sufficient accuracy 
be replaced by A. If A” be that wave-length nearest to » 
at which there is a minimum of light, it follows that 
A ae a i 
r N 
If a linear homogeneous source of light of wave-length » 
be examined by means of a grating, the central image extends 
to a wave-length A, such that 
<iopbtiales Ge 
r 
where N, as before, is the total number of lines on the grating. 
Hence the following proposition :—If, in observing Talbot’s 
bands, that thickness of retarding-plate be chosen which 
reduces the minimum illumination of the dark spaces to zero, 
the distance between each maximum and the nearest minimum 
is equal to the distance between the central maximum and | 
the first minimum of the diffractive image of homogeneous 
light, observed in the same region of the spectrum with the 
same optical arrangement. This proposition holds for all 
orders of spectra; but the appropriate thickness of the 
retarding plate increases in the same proportion as the order. 
Lord Rayleigh’s remark * that “the thickness of the plate 
must not exceed a certain limit, however pure the spectrum 
may be,” requires the qualification that for infinite purity the 
limiting thickness also becomes infinite. 
To examine the casein which the thickness of the retarding 

y) 
Al ee 

* ‘Encyclopedia Britannica’ and ‘ Collected Works,’ vol. iii. p. 133. 
B2 
