Curvature Method of Teaching Optics. 4 71 



thicknesses ; large letters for the corresponding curvatures, 

 and Greek letters for the angles*. The conjugate distances 

 and focal lengths being denoted by u, i\ and/ respectively : 

 we have U. V, and F as the corresponding curvatures or 

 convergences. If the distances w, r, &c. are expressed in 



metres, we have U= -, V= - 3 &o., the curvatures in dioptres, 



while it' u and u are in mm. U and V are in kilodioptres. 



In like manner, if we denote the radii of the surfaces of a 

 lens by i^ and r 2 , we should have R, and E 2 as the curvatures 

 of the surfaces, and = 1^ — R 2 the total curvature in the 

 case of a thin lens. Curvatures of wave-fronts may be 

 reckoned positive when they are convergent, and surfaces 

 are said to have positive curvature when they are curved in 

 the same direction as convergent emergent light. This 

 harmonizes the formula? for reflexion and refraction at curved 

 surfaces. 



Part I. — Elementary Optics. 



In dealing with this subject it was the writer's first intention 

 to give a fairly complete exposition of the methods he has 

 adopted, but a subsequent perusal of Dr. Thompson's article 

 in the Phil. Mag. has shown him that the procedure he has 

 followed is so closely identical with that advocated by Dr. 

 Thompson as to render this unnecessary. For the sake of 

 completeness, however, the various steps in the development 

 of an elementary optical course may be briefly given here. 



Nature and mode of Propagation of Light. — The first im- 

 portant step is to familiarize the student with the notion of 

 waves and their propagation. A beginner is easily convinced 

 by a few simple illustrations that light must be either pro- 

 pagated by projectiles or undulations. The ripple tank can 

 then be used to demonstrate the propagation of waves, and 

 the effects of reflexion, &c. shown simultaneouslv by optical 

 projection, and in the tank. The justification for the undu- 

 latory theory can be well shown by interference, ripples being- 

 excited from two simultaneouslv vibrating points, and the 

 results compared with interference from a bi-prism. Even 

 elementary students can quite appreciate that the wave theory 

 i- the only one which can satisfactorily account for the dark 

 interference-bands. The finite rate of propagation of waves 

 i- then pointed out with references to determinations of the 

 speed of light, and it is al>o shown that ripples of different 

 frequencies can be excited and that the wave-lengths differ. 



* This appears to be almost identical with the notation employed by 

 Ilerschel and by Dr. Thompson. 



