

OPTICAL I'KOI'KKTIKS or CRYSTALS 



This is the maximum value of r for water and air. and i> termed the 

 critical angle, or the angle of total reflection; for if a ray, as oan, 

 should reach the surface at the point o, in which the angle anoni is 

 greater than 48 36', the critical angle for water and air, there 

 i> no possible value for sin i and no light could pass out of the water 

 into the air. hut all is 

 reflected back along 

 the direction of oa m . 

 Viewed from am un- 

 der suitable condi- 

 tions, there will be a 

 light field outside of 

 the critical angle of 48 

 36' and a dark field in- 

 side of t his angle, as in- 

 dicated by the circle 

 in the figure. The di- 

 viding line between 

 these two fields will 

 measure the critical 

 angle. 



By measuring the critical angle of any substance, its index of 



refraction is easily determined, as n = - - . 



sin (of the critical angle) 



The determination of the index of refraction by the total refrac- 

 tometer is based upon this principle. 



The minimum value of sin i is o 



then n = - becomes zero, 

 sin r 



or there is no refraction, and light passing in the direction of the 

 normal to the surface is not refracted. 



.All isotropic substances have but one index of refraction, for the 

 reason that light is transmitted with the same velocity in all direc- 

 tions ; the wave front is a sphere. In anisotropic substances 

 there are two and even three indices of refraction, and the velocity 

 of light varies with the path followed through the crystal. The 

 wave front is no longer a sphere, as in isotropic substances, but its 

 shape and curvature will depend upon the substance. 



The wave fronts in anisotropic substances are surfaces all of 

 which agree in being symmetrical to three planes of symmetry at 

 right angles, as the axial planes of the orthorhombic system. These 

 three planes intersect each other in three straight lines at right 



