THE AID OF THE ACHROMATIC FRINGES. 17 



inclination of fringes was usually opposite on the two sides. In spite of differ- 

 ences in size the successive repetitions of fringes were nearly equidistant. Thus 

 four at a distance of Ae = 0.07 5 cm. were seen. At another part of the double 

 half -silver, Ae = 0.085 cm. was measured. Putting a steel clip on the plates 

 to force them more closely together, A? was reduced to 0.040 cm. Taking 

 the clip off increased Ac. No ghosts occurred with a single half -silver plate 

 (no air film). Again, the distance Ae- varied with the angle of incidence of 

 the plate pair with the collimated beam of light. Thus, in case of three vivid 

 interference grids (two repetitions), if i is the angle of incidence, the meas- 

 urements gave, when the plate was placed at different angles i (estimated) 

 t = o ; = 30-40 * = 5o-6o * = 7o-So 



= 0.15,0. 48, 0.87 0.22,0.48,0.79 0.30,0.49,0.70 0.29,0.39,0.49,0.65,0.80 

 In the last case the number of ghosts increased, but they also grew more 

 irregular and confused. 



Hence the cause of this originally puzzling phenomenon must be some 

 reflection on the two sides of an air film, or a glass film. If x is the normal 

 thickness of the film, and i the angle of incidence, the direct rays and those 

 twice reflected interfere with a path-difference of ix cos i. To restore the 

 fringes to the center the main micrometer would have to move over AAT or 

 annul a path-difference of 



AN 



2 A cos ^ 

 Ae 



so that 



x cos i = (AN/Ae)Ae cos * = o.oo33Xo.7Ae = o.oo23Ae 



Thus in the above data the reproductions would be at 



60 = 0.36 0.28 0.20 0.80 



io 5 x= 83 83 82 82 cm. 



*- o 36 54 77 



provided the angles were such as here given, which was sufficiently near the 

 case. 



It is nevertheless difficult to surmise what reflections can occur in the 

 earlier work and in the absence of a specially half -silvered biplate; for the 

 effect of an air film between clear glass plates is only visible with difficulty. 



A similar problem is the measurement of the index of refraction, ju, of a 

 normal film of glass in terms of 8e. The relation is here 



(0* 1)4-2 #/X 2 ) d = 2 (AN/Ae) &e cos 4 = 0.0047 Ae 



A film of mica d 0.0050 cm. thick was inserted between the mirrors of the 

 interferometer and the displacement A0 = 0.65 cm. read off. Hence, if 

 2#/X 2 = 0.026 roughly, 



n= 1+0.0047X0.65/0.0050 0.026 = 1.58 



This is slightly low, for the thickness d and the dispersion constant B are 

 not adequately guaranteed; but the result is interesting, as it may be 

 obtained instantly, either in terms of Ae or AN. 

 2 



