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Dr. S. P. Thompson on 



It is required to find the combination consisting of one thin 

 cylindrical lens and one spherical lens which will be the optical 

 equivalent of the system ; or, the sphero-cylindrical lens that 

 is also equivalent. The problem is completely solved when we 

 shall have ascertained the two components, cylindrical and 

 spherical, of the equivalent lens and the angular position of 

 the cylindrical component. 



In any lens having at one surface a radius of curvature r, 

 the curvature which that surface will impress upon a plane 

 wave is (/n — l)/r; where fi is the refractive index of the 

 material. If the lens is cylindrical, having a curvature in 

 one meridian only, the impressed curvature will also be 

 cylindrical; if it be spherical, the impressed curvature of the 

 wave-front will be correspondingly spherical. First approxi- 

 mations only are here considered. 



Let (fig. 2) A A ; be the axis of a cylindrical lens, and 



Fig, 2. 

 Q A 



Vf- 



N'- 



p'-~ 



--^0 



P 



A' Q' 



NFa line normal to that axis. A plane normal to the axis 

 intersecting the lens in NF will have as its trace through 

 the curved surface of the lens a line of the same curvature 



as the lens, viz. — . Let now an oblique intersecting plane 



be drawn through the optic axis of the system (i. e. the line 

 through normal to the plane of the diagram) ; its intersection 

 P P making an angle NOPb</. with the fine N W. The 



