106 Mr Pocklington, Interference bands produced by a thin wedge. 
confused or be invisible when received on a screen at Q or when 
examined by a lens which is focussed on Q. The bands will in 
short appear out of focus. In order that they may be in focus, it 
is necessary that 8 shall not change when the position of P is 
slightly changed, i.e. that 
d8/dp = 0 and d8/d(j) = 0. 
The first of these gives 
r — p cos (0 + (j>) = 0 (2), 
and the second gives 
(r cos 0 + cj) — p) (r — p cos 6 + <£) = 0, 
so that the condition that the bands are in focus reduces to (2), and 
the bands lie on a surface, the principal section of which is a semi- 
circle described on OP " as diameter. 
If the incident light is a parallel beam, P is at infinity, 
p = oo , 
and the phenomena are given by 
8 = 2 ar sin (0 + </>) ; 
equation of principal section of surface on which the bands lie is 
6 + <fc = 7 t /2. 
Hence the bands lie in a plane passing through the edge of the 
wedge and lying perpendicular to the reflected beam. The bright 
band of order n is given by 8 =n\, and hence by r = n\/2a. The 
bands are equidistant, and their distance apart is independent of 
the angle of incidence of the light from the source. 
The only wedge that is practically available is the air wedge 
produced e.g. by two pieces of plane glass which make contact along 
a line and are kept apart at their further ends by a piece of paper. 
The refraction through the glass can cause a displacement of the 
bands and of the plane in which they lie, but leaves the distance 
apart of the bands unaltered if the incident light is parallel. 
With a view to testing the accuracy of the formulae, I have 
determined the wave-length of sodium light by means of these 
bands. The angle of the wedge was determined by causing the 
reflections of two slits to coincide, the distance between the bands 
(which was about ’01 cm.) was determined by direct comparison 
with a rule graduated in millimetres placed in the plane of the 
bands, a hand-lens being used to see the coincidences with. The 
result was correct to about 1 per cent. Greater accuracy could 
of course be obtained by using a vernier microscope, but in this 
case it seems to be as easy to illuminate by vertical light, when 
the bands will lie in the plane of the air film. 
