Curvature and Refractive Index. 33 



great. Either of these systems will give accurate results ; I 

 prefer the first, as tiring the eye less and being, especially with 

 small lenses, the more accurate. 



A convenient support for the lens is made by boring a hole, 

 with a less diameter than the lens, in a piece of thin parallel- 

 sided wood. The lens may be slipped under two clips, so as 

 to rest against the edge of the hole on one side of the wood* 

 On the other side a piece of plate glass, blacked at the back, 

 is cemented or held in a similar way by clips. If this piece 

 of wood is fixed vertically on a horizontal slide, it may be 

 moved away from the prism-plate, and the distances/' and F 

 determined in a few minutes. Fig. 2 is a horizontal section 

 of the arrangement when the principal focus F is being deter- 

 mined. The dotted line shows the position for/. 



If instead of a lens a single surface only is to be measured, 

 there is of course no difficulty in the case of a concave sur- 

 face ; but a convex surface may have its curvature determined 

 in the following way: — Arrange the prism-plate and flame as 

 before. At a distance in front of the prism-plate more than 

 its focal length fix a converging lens, preferably achromatic. 

 Observe the position of the aerial image on the other side of the 

 lens, and make it coincident with the edge of a plate of metal, m. 

 The positions must be so adjusted that the distance of m from 

 the lens is greater than the radius of curvature of the given 

 surface. Now place this surface between the metal plate and 

 the lens, and move it till an image is formed accurately by 

 the side of the prism. Then the light impinging on the convex 

 surface has been reflected back along the path whence it came, 

 and has therefore struck that surface normally; therefore the 

 place m, where those rays would have met had they not been 

 intercepted, is the centre of curvature of the convex surface. 

 Its radius of curvature can therefore be measured by suitably- 

 formed callipers. Fig. 3 is a horizontal section of the 

 arrangement. 



I have stated above that R — xv^ m tne case of a tnm ec l u i- 



convex lens. This must now be proved, and the more general 

 case of any kind of lens treated next. First, consider that 

 the lens is so thin that any normal to either surface cuts each 

 at points appreciably equally distant from the axis. Since the 

 image which is produced is partly formed of rays which are near 

 the axis, these rays meet the axis at angles so small that the 

 tangent, the sine, and the arc are convertible terms. If the lens 

 is large and not of very long focus, this will not be true of rays 

 from near the edge of the lens ; but as these rays are not 

 necessary for the image, the central ones alone may be 

 Phil. Mag. S. 5. Vol. 14. No. 85. July 1882. D 



