ox C'EKTAIX DIFFKACTTOX PHEXÛMEXA. 



317 



Fresnel's Diffraction Phenomena produced by a Slit 

 on a Cylindrical Surface. 



Fiff. 3. 



Let A B he n section of 

 tlie slit, cut by ;i plane passino- 

 throiio'h the sonrce of lig-lit L, 

 and the point D at which the 

 illumination is recpiired. I shall 

 -X suppose that the point D is not 

 YQvy far from tlie line joining- 

 any ])oint on the slit with 

 the source of light. Also, the 

 problem will be still further 



simplified if the plane L A B is made to contain the axis of the 



cylinder. 



For calculating the intensity of the ditfracted Hg-ht, assume tlie 



point wliere L I) meets the cylindric:d surfice as tlie origin of 



coordinates. Let the x axis be parallel to the axis of tlie cylinder, 



and y perpendicular to the plane LAB. 



In this case, 

 where d is very small, 



a = 0, 



Thus 



H = cos LOA = Ö, 



and 



1 nearly 



{}( or- + /j.y 4- i.z)-= 2 Ö x s + :2^ 



neglecting d' u]i wards. 



Recurring to formuhi (II). 



A 11 + A R= Q ÖXZ- {x'Jr ?/)] (^ + ^). 



