86 INTERFERENCE OF LIGHT. 



being constant for the successive points of the same band, it 

 follows that these points must form an hyperbola, whose foci 

 coincide with the two apertures. It will be easily seen that 

 the curvature of these hyperbolic lines is very small, except 

 close to their vertices ; and that we may, without sensible 

 error, consider them as coincident with their asymptots. 



As the distance of the fringe varies with the length of 

 the wave, it follows that when white light is employed, the 

 fringes will be coloured bands, which, after a few successions, 

 are effaced by the overlapping of the fringes of different 

 orders. "When the light, although coloured, is not perfectly 

 homogeneous, the same effect of the obliteration of the fringes 

 is produced after a greater succession. It has been found 

 possible to purify solar light so far, that 8000 fringes have 

 been counted. 



(105) It is easy to determine the positions of the bands, as 

 dependent on the interval of the apertures, and on the dis- 

 tance of the screen. 



The place of any bright or 

 dark band, m, is determined 

 by the condition that the dif- 

 ference of its distances from 

 the two apertures, m(5' - mO, 

 is an integer multiple of the length of half a wave. Now, 

 drawing the lines On, V, parallel to PA, and denoting the 

 distance AP by , the interval of the apertures 00' by c, and 

 the distance Am by #, the right-angled triangles Qmn, Q'mri, 

 give 



Om = 



Q'm = 



the distance b being very great in comparison with x and c. 



