40 



GENERAL CHARACTERS OF PRECIOUS STONES 



Fig. 11. Total reflection. 



the angle of incidence J CZ> becomes greater and greater so the angle of refraction 5C£ 

 also becomes greater and greater. When the angle of incidence reaches a certain value, 

 represented by A^CD, the corresponding angle of refraction B^CE will be a right-angle ; 

 the refracted ray will then emerge from the stone in a direction parallel to the bounding 

 surface MN. 



Obviously at 90° the angle of refi-action has reached its maximum value and no further 



increase is possible. Should the angle of inci- 

 dence now be increased, even by a small amount, 

 it will then be impossible for the ray of light 

 to leave the stone, and it will be refracted no 

 longer, but simply reflected by the bounding 

 surface back into the stone. In Fig. 11, the 

 incident ray Afi is reflected from the surface 

 MN, along the line CB^ inside the stone. 

 This takes place according to the usual laws 

 of reflection, the angle of incidence AfiD 

 being equal to the angle of reflection BfiD. 

 In the same way, every ray incident upon the 

 surface MN at a greater angle than AfiD, 

 will be unable to pass out of the stone, and will be reflected back again by the surface 

 MN ; AJOB^, for example, is the path of such a ray and its reflection. 



When light, travelling in one medium, as, for example, air, strikes the surface of a 

 denser medium, such as a precious stone, a portion of it enters the stone and is refracted as 

 described above, while the remaining portion is reflected from the surface. This takes 

 place invariably, whatever may be the angle at which the incident light strikes the surface of 

 the denser medium. In the reverse case, when light travelling in one medium, for example a 

 precious stone, strikes the surface of a rarer medium, for instance air, the same thing may 

 happen, that is, the light may be partly reflected and partly refracted, but this does not 

 happen invariably as in the former case. 



It was seen from Fig. 11, that when the angle of incidence exceeds a certain fixed value 

 (A^CD) the light is not refracted at all, but is reflected from the bounding surface back 

 into the stone. In all other cases, as has been shown, light incident upon the surface of 

 separation of two media is divided into a refracted portion and a reflected portion. Since 

 in this particular case the light is not so divided, but the whole of it is reflected, this 

 kind of reflection is known as internal total reflection, or, briefly, as total reflection. 



Total reflection takes place at the surface of separation of two media only when the 

 light travelling in the denser medium strikes the surface at an angle exceeding a certain 

 degree of obliquity. Total reflection never takes place when light passes from a rarer to a 

 denser medium. In this case there will always be refraction, for when the incident angle 

 reaches a maximum of 90°, since the refracted ray is bent towards the normal, the angle of 

 refraction will be less than 90°, and the light will pass out of the rarer into the denser 

 medium. It is always possible then for light to pass from air into a precious stone, but it 

 cannot pass out again unless it strikes the surface of the stone at an angle not exceeding a 

 certain degree of obliquity. 



I^he limiting angle A^CD in Fig. 11 is known as the critical angle or the angle of 

 total reflection. Its value depends upon the refractive indices of the two substances at the 

 boundary of which reflection and refraction takes place. The greater the difference in the 

 refractive indices the smaller will be the angle of total reflection, AMD. If the diff'erence 



