TOTAL INTERNAL REFLECTION. 299 



than - : it would result from the law of sines that if the ray could 



n' 



be refracted outwards under these circumstances, it would tra- 

 verse a path such that the sine of the angle of refraction would 



be greater than - x n, that is greater than 1. Since this is simply 



impossible from the definition of a sine (Expt. 333, footnote) it 

 results that the ray cannot pass out of the denser medium. What 

 happens is that it is entirely reflected (in accordance with the law 

 of reflection) from the surface back again into the denser medium ; 

 whence the term total internal reflection, no absorption of light 

 taking place with this kind of reflection which is not the case 

 with an ordinary mirror, as above shown (Expt. 332). 



The angle where - represents the greatest possible value of the 

 n 



sine of the angle of incidence compatible with refraction outwards 

 is termed the critical angle, and has a value of about 42 from 

 glass to air, and 48^ from water to air. When swimming on 

 one's back under water, with the eyes open, certain portions of the 

 bottom of the bath and other submerged objects may be seen 

 apparently suspended in the air, being reflected from the upper 

 surface of the water in contact with the air to the eye of the 

 observer below the surface ; these objects are so situated that the 

 angle between a vertical line (normal to the horizontal surface of 

 the water) and the line drawn from any given submerged object to 

 this normal at the point where it cuts the surface exceeds 48|. 

 light passing along this line cannot be refracted out of the water 

 upwards, and is consequently reflected downwards again, thus 

 meeting the eye under water, and giving the appearance of 

 being derived from an object situated above the surface of the 

 water. 



The greater the value of the refractive index, the smaller is the 

 critical angle ; consequently highly refractive bodies possess to a 

 great extent the power of reflecting light by internal reflection, and 

 thus appearing extremely brilliant. This is especially the case 

 with the diamond, which owes most of its lustre to its high refrac- 

 tive power; by cutting the surface into "facets," or flat planes 

 slightly inclined to one another, the tendency to internal reflection 

 of light from one or other of the facets is considerably increased, 

 with corresponding increase in the brilliancy of an ornament, such 

 as a necklace consisting of a number of stones so cut. 



Fig. 139 represents a simple illustration of total internal reflec- 

 tion from the surface of water. A glass beaker, b (or, better still, 

 a rectangular glass trough), is filled with water and placed on a 



