Curvature Method or Teaching Optics. 48^ 



Oblique Refraction through Thin Lens. — In the case of a 

 thin lens we may consider the centre of the lens as a parallel 

 plate, and the retardation of the centre of the wave-front 

 is therefore as given above. Hence, if we consider two 

 meridians of the lens, the primary or meridional plane 

 containing the axis of the lens and beam, and the secondary 

 or sagittal plane lying in the axis of the beam perpen- 

 dicular to the other plane, — 



We have in the sagittal plane therefore if (f> is the obliquity 



4> 2 



*=F(l + y. 



In the meridional plane the retardation of the centre of the 

 beam is the same, but the effective aperture of the lens is 

 reduced in the ratio of cos $, and the curvature therefore 



increased in the ratio . = l + d> 2 approx. and hence the 

 cos 2 9 r rr 



meridional convergence 



F (^ &)('+♦■} 



The lens therefore acts as a sphero cylinder of spherical 



1 -f — J and cylindrical power Y<f> 2 , or when (f> is 



in degrees c , , . , ^ / . <f> 2 \ 



fepherical power = I ( 1 -f >-ptt- I- 



\ Db'2'2fjbJ 



Cylindrical ,, = - . - . 

 zobl 



The axis of the cylinder is of course in the sagittal plane. 



The wave-front also evidently reaches one edge of the lens 

 before the other, giving rise to asymmetrical refraction or 

 coma, but this will not be further considered here. 



Primary and Secondary Focal Lines. — We have evidently 



Primary convergence — ,y\ — F <j 1 + (2fi + 1) f - \- 

 -Mean „ =A-F'{_l + (^ + l)^} 



jondarv „ = .;.,= Y -{ 1+-. >. 



L 2/x j 



The mean convergence corresponds to the circle of least 

 Phil. Mag. B. 6, Vol. 9. No. 52. April L905. 1 K 



