Study of Huy gens' s Secondary Waves, 213 



of the reflecting sheet, including the aperture in it, this 

 difference is zero. It follows therefore that the disturbance 

 passing through the aperture is given by the integral (d) 

 taken over the area of the aperture alone, with its sign 

 reversed. It follows therefore, that considerations such as 

 those that apply to the case of reflexion at oblique incidences 

 apply to this also. 



Light incident on a perfectly reflecting screen, the waves 

 being polarized in a plane at right angles to the plane of 

 incidence. 



The magnetic vector f in the incident waves is parallel to 

 the axis of z and to the reflecting screen. Since £ satisfies 

 the general differential equation and also, at the screen, the 



7 y 



condition -=- = 0, the expression for fin the secondary waves 



is exactly the same as that for cf> in the preceding paragraphs. 

 As for the other components of the magnetic vector in the 

 secondary waves, they are zero at all points in the plane of 

 incidence and we need not at present trouble about them. 



Light incident on a perfectly reflecting screen, the waves 

 being polarized in the plane of incidence. 



The electric vector £ in the incident waves is parallel 

 to the axis of z and to the reflecting screen. The expression 

 for the vector f in the secondary waves can still be 

 deduced from the integral (d), if the sign of this is changed 

 and the operand d/dx is replaced by d/dn, where dn is an 

 element of the normal to the reflecting surface, both directions 

 of this being regarded as positive. On the side of the screen 

 on which the waves are incident and at points close to it, 



Y a z>i^(V£-j- a? cos i — y sin i) * p ik(Vt—x cosi—y sin i) 



which is zero if x = 0. 



On the other side, at points close to the reflecting sheet 



c. _ a ik(Jt+x cos i—y sin i) » ik(Vt-\-x cos i—y sin i) 



= 0. 



The other components of the electric vector in the secondary 

 waves need not be considered here. 



Apertures in Perfectly-Reflecting Plates, 



The results for these cases can be deduced from the ex- 

 pressions for reflexion, in exactly the same way as was done 

 for aerial waves. On the side on which the waves are incident, 



