R E F 



Case 4. 



2. To find the direction of a ray after refraction through a lens. 



The method here is to consider a ray refracted at the first surface, as 

 incident on the second, and there again refracted. 



Let A" be the distance of the focus after the second refraction, r' the 

 radius of the second surface, t the thickness of the lens, the other sym- 

 bols as above ; then 



To find the principal focal distance F, put A infinite in the above ex- 

 pression, i.e. suppose the rays parallel, and we have 



a,nd then = ^- + ~. 



Ill -*- 



If we put for ~ in the above equation, 



Hence arise different values of rr according" as is positive or 

 negative. 



In the concavo-convex lens, either r is less than f and F positive j or 

 when the lens is turned the contrary way and r greater than r> they are 

 both negative, we have then 



In the moniecut, either r ia greater than f, both beicg positive, and. 

 then 



or : 4 if leso than r' and both are negative, 8<Vthat 

 235 O 



