as applied to Micrometric Observations. 



451 



One further point should be noticed : if a be very nearly 

 equal to (3 sin & + a sin 6 the fringes become too broad to be 

 observed, whatever the source may be. 



Fig. 5. 





zy 



T) ' 



/e\ 



r 



/>/N 



sj&' 





^K 



n 



n' 



?' 



To see the physical meaning of this condition, and also of 

 the condition ft cos 0' = a cos 0, we notice that a point source 

 of light P at the centre of one of the slits appears after re- 

 flexion at the two mirrors a, b, to be at/?, where Pp is equal to 

 twice the distance between the mirrors and is perpendicular 

 to their plane (fig. 5). Hence the double reflexion removes the 

 image of the slit a distance 2a cos 6 behind the diaphragm and 

 2a sin 6 closer to the centre. In the same way the image of 

 the other slit is brought 2/3 cos 6' behind the diaphragm and 

 2/3 sin & nearer the centre. 



Our condition {3 cos 6' = a cos 6 therefore means that the 

 images of the two slits must be in the same plane parallel to 

 the plane of the diaphragm itself, and our second condition 

 shows that they must be some distance apart. 



To find the minimum of this distance, remember that the 

 fringes will be invisible if the distance between successive 

 maxima exceeds the vertical dimension of the visible rect- 

 angle : in other words, if 



b\/2{a- (/3 sin 6' + a sin 6)) > b\/k 9 



or distance in question < k, 



which means that the centre of the image of either slit must 



