56 Mr. A. Wbitwell on Refraction 



In concliisionj I should like to call attention to a mis- 

 leading statement made by Prof. S. P. Thompson, in a ])aper 

 on this subject read before this Society on December 8th, 

 1899 *. He says : " In any lens having at one surface a radius 

 of curvature ?•, the curvature which that surface will impress 



upon a plane wave is ; where /x is the refractive index 



of the material. If the lens is cylindrical, having a curva- 

 ture in one meridian only, the impressed curvature will also 

 be cylindrical/^ 



" Let AA' be the axis of a cylindrical lens, and NN' a 

 line normal to that axis. A plane normal to the axis inter- 

 secting the lens in NN' 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 ; its intersection 

 PF making an angle 1^0V = 4> with the line NN'. The 

 curvature at O lof the trace of this plane, where it cuts 



the curved surface along PP^, will be -cos^^.... We may 



further consider the intersection QQ^ of another oblique 

 plane at right-angles to PP^ The curvature at along 



the line QQ' will be — sin^ <^ If light were admitted 



through narrow parallel slits set respectively along PP' and 



QQ', the convergivity of the two beams respectively im- 



cos sm 

 pressed by the lens would be (yu, — 1) — — (^and (//, — !) <^. 



If r is expressed in metres, then these two convergivities will 

 be expressed in dioptrics — '' 



Now if a plane wave lall on a thin piano-cylindrical lens 

 the emergent wave-surface, for small aperture, will be a 



cylinder of radius . Every refracted ray will pass 



through a line or narrow band parallel to the axis of the 

 cylinder and at a distance =- from the lens. If we sup- 

 pose a card with a narrow diagonal slit to be placed in front 

 of the lens it is obvious that a great part of the cylindrical 

 wave-surface will be cut off, but the portion that remains 

 will still be cylindrical, and will have the same radius. The 

 rays that pass through the slit still pass through the line at 



T 



the distance r^ , and the convergivity is the same as before. 



* Phil. Mao-. March 1900. 



