more complex theory. It was Fresnel who first discovered the 

 real cause of diffraction. In order to obtain satisfactory- 

 solutions, Fresnel had to make somewhat arbitrary assumptions 

 on the nature of the secondary waves. Most of the difficulties 

 of Fresnel 's theory were overcome by Kirchhoff, who used Helmholtz's 

 formulation of Huygens ' principle for monochromatic phenomena. 

 13. Diffraction of light by a black half -plane 



The first type of diffraction problem to be considered is one 

 in which plane monochromatic light is incident on a black screen 

 of infinite extent and bounded by a straight edge (figure l8). 



For the portion of the y-axis covered by the screen (S), a 

 physical optics solution has been obtained in the form 



00 



tt/dn _ 1 C ^iKp coshT^-iKct sincp ■,7-' n :j T> 



U^P^ - ' -^ J ^ coshr'+ coscp ^^ ^^3.1) 



U = wave profile 



K = constant 



p = distance from the edge of the screen 

 T^ = variable of integration 



c = velocity of light 



t = time. 

 This expression holds only v;hen P, the point of observation, is 

 in the geometrical shadow. If it isn't, the additional term 

 £U(P), which is the wave function according to geometrical optics, 

 must be added to (I3.I), where 6 = or 1 depending on whether 

 P is or is not in the geometrical shadow. If we write the expression 



6. Baker, B. B. and E.T. Copson, 1950; Math ematical Theory of 

 Huygens' Principle , Oxford at the Clarendon Press, pp. 

 ■54^92. 



42 



