CATALOGUE OB' GEMS. 



483 



Fig. 1. 



DIAGRAM TO ILLUSTRATE REFRACTION. 



ever great or sniall the !ino-l(> of incidence may ])e, there i.s alway.s a 

 constant relation between it and the angle of refraction for two given 

 substances. This constant relation is the ratio between the sines of 

 the incident and refracted angle, and is called the index of refractiooi. 

 When a ray of light passes from one medium into another which is 

 less refracting, as from water into air, the angle of incidence is less 

 than the angle of refraction. Hence 

 when light is propagated in a mass of 

 water there is always a value of the angle 

 of incidence such that the angle of refrac- 

 tion is a right angle, in which case the 

 refracted vax emerges parallel to the sur- 

 face of the water. This angle is called 

 the critical angle, since for any greater 

 angle the incident ray can not emerge, 

 but undergoes an internal reflection, 

 which is called total reflection because 

 the incident light is entirely reflected. 

 From water to air the critical angle is 

 48° 3.5'. In th(^ example given, air and water, r = 48° 35'. Now, sup- 

 posing the light to go from 1> to r>, the line oc will coincide with the 

 line of (the critical angle). If the value of /• is increased, the ra}^ 

 will no longer pass from water into air, 1)ut undergoes total reflection 

 at the surface o. 



In total reflection there is no loss of light from absorption or trans- 

 mission, and accordingly it produces the 

 greatest brilliancy. The luster of trans- 

 parent bodies bounded b}^ plane surfaces, 

 'i such as the luster of gems, arises mainly 

 from total reflection. This luster is the 

 more frequent and the more brilliant the 

 smaller the limiting angle. The diamond, 

 having the smallest value for its limiting 

 angle, is the most brilliant of all gems. 



There are certain transparent substances 

 which possess the power of splitting the 

 refracted I'ay into two. The most famil- 

 iar example of this is furnished l)y the 

 minei-al calcit«\ If ef</h (flg. 2) be a cleavage piece of calcite and a 

 ray of light meets it at o, it will in passing through be divided into 

 two rays, ot\ od, one of which follows the ordinary law of refraction, 

 the other a more complicated law. Similarly, a line seen through a 

 piece of calcite ordinarily appears double. This phenomenon is called 

 double refraction. The diamond, garnet, and all other minei-als belon- 

 ging to the isometric system are singly refracting. The ruby, topaz, 



Fig. 2. 



DIAGRAM TO ILLUSTRATE DOUBLE 

 REFRACTION. 



