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 = and d8/dcf> = 0. 



The first of these gives 



r-pcos(0 + <f)) = O (2), 



and the second gives 



(r cos + <f> — p) (r — p cos +</>) = 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 = 2ar sin (0 + <f>) ; 



equation of principal section of surface on which the bands lie is 



+ <f) = tt/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 rale 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. 



