336 A. TA.NAKADATE 



The terms depending upon tlie thickness t ubsohitely vanish, when 

 Î1 = — ri/{ß — 1) and consequently (Za = ^'-i/iß ~ 1)>— «• ß-, when the dis- 

 tances of the object and image from their nearest faces of the lens are 

 proportional to the radii of curvature of those faces. In this case, the 

 pencil of light becomes cylindrical within the substance of the lens; 

 This condition may be experimentally realized by using the ap- 

 proximate values of ß and r as given in (7). There are two cases 

 however in which this correction vanishes without using approximate 

 values: — (1.) A^^hen the lens is plano-convex, and the parallel rays 

 of light pass in at the plane surfice ; (2.) when the lens is double 

 convex with equal curvatures, and the object and image are equally 

 distant from their respective nearest faces of the lens. 



The above method fails with meniscus lenses in the cnse when 

 the " equivalent mirror " becomes convex : but in such instances, 

 the curvature of one face can always be found by direct reflection, and 

 when the lens is reversed the equivalent mirror becomes concave. 

 Thus in general, the curvatures of the faces and index of refraction of 

 the substance of a convex lens can be found by a method which is 

 essentially the same as that f )r finding the focal length of a concave 

 mirror. 



The method was tested experimentally and gave for curvatures 

 and index of refractixm of a particular lens 



ri = 103.8 cm. r, = 105.3 cm. u = 1.515 

 Measured with a spherometer these quantities were found to be 

 ri = 104.5 cm. r.j. = 105.0 cm. ß = 1.514 



A clear aperture of 1 cm. diameter is sufficient for applying the 

 method. 



