4 ELEMENTARY PRINCIPLES OF MICROSCOPICAL OPTICS 



-p) rp "C 1 T r 



Now, as sine I C N = -^ and sine R C N' = ^, then, by 

 PC r C 



FT 



Snell's law, - -= fj.. 



FIT 



As any points may be taken in I C and R C if the points had been 

 more judiciously selected, we might have greatly simplified the above 

 expression. Thus, if we take two other points, K and E, such that 

 K C = E C, and draw the perpendiculars as before, we shall have 



K^S 



sine I C N = ?-? and sine R C N' = ? ^, and therefore JL = . 

 Iv C Ju C 



But as K C = E C by construction, we can write K C for E C 

 KS 



jr & 



thus : = fj.. K C is cancelled, which leaves = 

 ED ED 



As p can be experimentally determined for any two particular 

 media, it follows that if one of the other terms is known, then the 

 remaining term can be found. Thus, if /i and the angle of incidence 

 are known, the angle of refraction can be found ; and if /n and the 

 angle of refraction are known, the angle of incidence can be found. 

 The unknown quantity can be found either geometrically or by cal- 

 culation when the other two terms are given. 



It will, of course, be understood that, for the same medium in 

 every case, a red ray would be bent or refracted less than a violet 

 ray. The value therefore of p. for a red ray will be less than that of 

 // for a violet ray. As a practical illustration : The refractive in- 

 dex for a red ray in crown glass is 1'5124 = ^u, and for a violet rav 

 is 1-5288 = /, the difference being / /u = '0164. 



The refractive index for a red ray in dense flint glass is 1-7030 

 = /u, and for a violet ray is 1-7501 = //, the difference being n' fj. 

 = 0471. 



Consequently there will be a greater difference between the bend- 

 ing of the refracted red and violet rays in the case of dense flint than 

 in the case of crown glass, the angle of the incident ray with the 

 normal being the same in either case. 



Where air (more correctly a vacuum) is not one of the media, 

 then the refractive index is called the relative refractive index. 



The normal to a plane surface is always the perpendicular to it ; 

 the normal to a spherical surface is the radius of curvature. The 

 angle of the incident ray and the angle of the refracted ray are 

 always measured with the normal, and not with the surface. 



Fig. 2 a, bj shows the normals A, B to both a plane and a 

 spherical surface, C D. 



In the case of the spherical surface, B is the centre of curvature, E F 



