Curvature and Refractive Index. 39 



found that 



e2 - r (f^7 +2/ ) = ^-' 2 ' • • ' ' (7) 



from which B. may be found if H?,f, and t are given. If t is 

 made equal to 0, equation (7) gives 



R==SL, or -/. 



The first result is the same as that already found for a thin 

 lens ; while the value — / seems to have no physical meaning. 

 If the thick lens is not equiconvex, there are five observa- 

 tions possible — the distances of the two apparent centres from 

 the surfaces, the distances of the two principle foci from the 

 surfaces, and the thickness ; but there are only three things 

 to be determined — the two real radii and the refractive index: 

 therefore the equations for R 1; Eg, and /a must be capable of 

 solution. The following are the expressions which may be 

 found by a similar treatment of fig. 5 to that already employed 

 in the case of the equiconvex lens, if it be remembered that 



all the angles made by surface 1 are ^ times those made by 



surface 2 at the same distance from the axis. They are 



— — jEl— t __-. It2~* 



>(R 1 + R 2 -0+*' V(R 1 + B 2 -0 + ^ 



T> f "R / 



/l = E V(R x + R 2 -0-(Ri-0 J •^ =E V(E 1 + B a -0-(B.-0' 



The first two of these equations give 



F 2 p-B^-1)' 



and the second two give 



_ Rg+Z^Rx— t , _ Ri + f\ R 2 — t 



""TiCRZ+Rs-O and ^-/ 2 (R 1 + R 2 -0' 

 By these yu, may be eliminated. The solution for R x and R, 

 I have not obtained ; but I do not think there is any difficulty. 

 The following application to the case of liquids of the prin- 

 ciple of making the rays return along the path whence they 

 came, forms a neat though impracticable method of deter- 

 mining their refractive index when greater than V2 : — Re- 

 place the cross-wires of a telescope by a prism-plate, as already 

 described, but in which the slit is longer and adjustable. Fix 

 opposite the object-glass a piece of parallel-sided plate-glass, 

 with its plane at right angles to the optical axis. The cor- 



