~!] 
Explanation of Talbot's Bands. 
But & being the frequency, 
dkV! 
a ae 

epee 
ok hg a 
mae dx Ton ay dX 
hence 
MVE dp 
“Uy ae 
We may put with sufficient accuracy V'=U in this ex- 
pression. To observe Talbot’s bands, the retarding plate 
must be brought in on the side of the thin edge of the prism 
and the best thickness, according to $ 1, is that in which that 
half of the beam which is nearest the thin end of the prism 
is retarded through half the distance RH. The appropriate 
Lew bo 
4 ‘ Ne a= : ; 
thickness is therefore — “P in accordance with the results of 
2 dh 
the previous paragraph. 
5. The previous investigation gives the retardation which 
the plate should produce if the best effect is to be observed. 
If we wish to determine in an actual case the best thickness 
of plate, we must remember that as we have been dealing 
with impulses the group velocity comes into play. Hence 
the usual expression (“—Lje for the retardation, the thickness 
being e, 1s not quite accurate. 
If U be the group velocity, and V’ the velocity of light zn 
. . . . 1 at . 
vacuo, the retardation in time is € la ee a ;_ this corresponds 
to a distance in air of 
(y-1): 
or if V be the velocity in the substance of the plate, the 
retardation is 
Vy 
Lior Ul 
uw’ being the refractive index of the material of the retarding 
plate. 
We obtain the right result by adding to (u—1l)e the 
distance through which the group has fallen behind the wave ; 
this corresponds to the quantity RH calculated as above, if 
for the thickness of the prism we substitute ¢ and write p’ 
