of Problems on the Diffraction of Light. 



83 



The amplitude at P at the first maximum will be that due 

 to half the complete wave in addition to that due to the first 

 strip OMj, or *5 + *6'725 = 1*1725. This being the amplitude, 

 the intensity will be 1*3748. Fresnel gives for the intensity 

 of the first maximum 1*3707 ; so that the approximate calcu- 

 lation yields results which for all practical purposes are 

 identical with the true ones. For the subsequent intensities 

 of maxima and minima the agreement is still closer, as will 

 be seen from the following Table : — 





Intensity according 

 to Fresnel. 



Intensity from 

 approximate calculation. 



First Maximum 



1 

 1 

 1 

 1 

 1 

 1 



3707 

 7785 

 1995 

 8433 

 1511 

 8720 

 1262 

 8892 

 1103 

 9007 

 0993 



1-3748 



•7774 

 1-1995 



•8429 

 1-1509 



•8718 

 1-1259 



•8891 

 11107 



•9006 

 1-0994 



•9092 



Second Maximum 



,, Minimum 





Fourth Maximum 



„ Minimum 









■9093 









The irregularity in the differences is partly due to in- 

 accuracy of the last decimal place in the values of ( cos v 2 dv 

 and sin v 2 dv, as given by Fresnel, but it would hardly repay 

 the trouble to recalculate the numbers. 



As regards the position of the maxima, they will according 

 to our calculation occur when PA is equal to 



PO+|x, PO+^\ ; &c; 



o o 



the minima lying at points for which PA is equal to 

 PO+gX, P0+y\, &c. 



It is known that these positions agree very well with those 

 obtained by the rigorous analysis ; thus Verdet gives as a 

 second approximation for the first maximum 



PA = PO+|x-*0046X, 



o 



and first minimum 



PA = PO+^\ + *0016X, 



