Curvature Method of Teaching Optics. 481 



or the convergence in the plane through the nodal point of 

 emergence is the equivalent convergence ; or the distance 

 between the nodal and focal points is the equivalent focal 

 length. This latter might of course have been directly 

 obtained by taking the back focal leno-th and distance of 

 nodal point. 



Thick Lenses and Refracting Si/stems. 



Refraction at Single Surface. — Up to the present we have 

 not needed to consider refraction at a single curved surface, 

 but it is necessary to do so before studying thick lenses and 

 lens systems. If light passes through a surface (fig. 7) 



Refraction at a Single Spherical Surface. 

 separating two media of refractive indices /jl. 



and 



/*!, we 



have always as our fundamental equation /^_ 1 5_ 1 = yu- 1 5 1 , where 

 5_i and s 1 are the departures or sags of corresponding parts of 

 the incident and refracted wave-fronts from the surface. 

 In the case of a normal homocentric pencil of convergence 



U and a spherical surface of curvature R this 

 immediately 



^_ 1 (R v -U_,)=a*i(Ro-V 1 ) 



or 



Mi^i — m-iU_i = (pi—fM-i jR = F . 

 In the interspace between two surfaces we have 



l _ l-Vii,' 



US 



u,= 



