TOTAL REFLECTION 



41 



Fig. 12. Total reflection 

 in diamond when surrounded 

 by air. 



which are incident at an 



is very small the incident ray will make a large angle with the normal before total reflection 

 takes place. 



In diamond, which has a very high refractive index relative to air, the angle of total 

 reflection is small, namely 24° 24', which is represented by the 

 angle A-fiD in Fig. 12. A ray of light inclined to the normal at 

 an angle slightly less than A^CD will be refracted and pass out 

 into air in the direction CB^ while one inclined at a slightly 

 greater angle will be totally reflected in the stone in the 

 direction CB\. The ray A^C, making a still larger angle with 

 the normal, will be totally reflected along CB^, while the ray 

 Afi will pass out of the stone along CB^, not undergoing total 

 reflection. 



If the optically denser body is, instead of diamond, glass, 

 having, say, a refractive index of 1-538, then the angle of total 

 reflection will no longer be 24° 24' but 40° 30', the body, as 

 before, being surrounded by air. In this case, only those rays 

 angle greater than 40° 30' will be totally reflected. 



Since the angle of total reflection increases when the difference between the refractive 

 indices of the two media decreases, it follows that the angle of total reflection will be greater 

 if the stone is surrounded by water instead of air. The angle of total reflection for a diamond 

 placed in methylene iodide, the refractive index of which is 

 1-75, will be 46° 19', the angle A^CD in Fig. 13. Some of 

 the rays, the obliquity of which causes them to be totally 

 reflected when the diamond is surrounded by air, will be 

 refracted when the surrounding medium is methylene iodide ; 

 thus fewer rays will in this case be totally reflected. The 

 use made of this fact will be mentioned later. 



Total reflection has a considerable influence on the path 

 taken by the rays of light in a transparent cut stone. The ^i«- 13. Total reflection in dia- 

 beauty of transparent cut stones largely depends on the fact lene"iodidr '""°"°'^^'^ bymcthy- 

 that the light which falls on the front of the stone is totally 



reflected from the facets at the back and passes out again from the front to the eye of 

 the observer. If the light were allowed to pass out at the back of the stone, the latter 

 would lose much of its brilliancy ; only when there is total reflection at the back of the 

 stone does it appear, as it were, to be filled with light. The greater the proportion of light 

 thus reflected from the back of a stone, the more brilliant will be its appearance. But to 

 enable us to trace out the exact path of a ray of light in a cut stone, we must first consider 

 some of the phenomena of refraction rather more closely. 



Up to the present we have considered only the behaviour of a ray of light at the 

 boundary of different bodies, namely, in passing from air into a liquid or into a precious 

 stone, and vice versd, in passing from a precious stone into air or liquid. By combining 

 these observations, the complete path of a ray of light passing through a precious stone 

 is easily arrived at. 



In Fig. 14, let MN, PQ, be parallel sides of a transparent body, and let AB be a ray of 

 light from a source, such as a small bright flame, falling obliquely upon MN". On passing 

 into the plate, the ray is bent towards the normal, DE, and takes the path BC. This 

 portion of the ray meets the second surface PQ at C, the angle of incidence, BCD^, being 

 equal to the angle of refraction, since the normals are parallel. On passing out into the 



