DOUBLE REFRACTION. 



may be determined at all angles of inci- 

 dence in this plane, in the same manner 

 as if it were acted upon with an ordi- 

 nary force whose index of refraction is 

 1*6543. 



All these observations are equally 

 applicable to all the other crystals with 

 one negative axis. 



The following are the number of prin- 

 cipal sections, or planes of refraction, 

 passing through the axis in the different 

 primitive forms shown mfigs. 3 to 7. 



Rhomb 6 



Hexagonal prism .... Infinite. 

 Octohedron, with a square 



base 4 



Right prism, with a square 



base Infinite. 



The secondary forms of these crystals 

 have, of course, a different number of 

 such planes, some more and some less. 



3. On the Law of Double Refraction in 

 Crystals with one positive axis. 



The mineral called quartz, or rock 

 crystal, crystallizes most commonly in 

 six-sided prisms, terminated with six- 

 sided pyramids, as shown \\\fig. 10. If 

 we grind down and polish 

 the summits A and B, we 

 shall find that there is no se- 

 paration of the images, or no 

 double refraction when the 

 refracted ray passes along 

 the axis AB. Hence AB is 

 the axis of double refrac- 

 tion. 



If in this case we mea- 

 sure the index of refraction, 

 we shall find 



Index of refrac- f 1-5484 ordinary, 

 tion at any axis (_ 1*5484 extraordinary. 



If we measure next the indices of re- 

 fraction in a direction perpendicular to 

 any of the faces E of the pyramid (which 

 are all inclined 3 8 20' to the axis), so that 

 the plane of incidence passes through 

 AB, we shall find them as follows : 



Index of refrac tion I 



perpendicular to 1 1*5484 ordinary ray. 

 the faces of the|P5544extraord. ray. 

 pyramid . . .J 



In like manner, we shall find that the 

 indices of refraction through CD, fig. 1 1, 

 and in a plane perpendicular to the axis 

 A B, are 

 Indices of refraction^ , , rARA Mf r. nQ 



perpendiculartothel f Ord f inar y,'. 



faces of the prism J 1 ' 5582 extraordm, 



From these results it appears that the 

 index of extraordinary refraction of 

 quartz increases from the axis to the equa- 

 tor, whereas in Iceland spar it diminishes. 

 In place, therefore, of being regulated 

 by an ellipse whose lesser axis coincides 

 with the axis of dou- 

 ble refraction, AB, 

 fig. 8, it is regulated 

 by an ellipse whose 

 greater axis AB co- 

 incides with the axis 

 of double refrac- 

 tion, as shown in 



In this case O A will be to O c as 



If we, therefore, call m' the index of ex- 

 traordinary refraction (or the velocity of 

 the extraordinary ray,) and <p the incli- 

 nation of that ray to the axis, it may be 

 shown that 



??i' 2 = 1-5484* + -030261 sin. 2 <p ; 

 that is, the square of the index of the 

 extraordinary ray m' at any inclina- 

 tion <p is equal to the square of the index 

 of ordinary refraction increased by a 

 quantity varying with the inclination to 

 the axis. 



Hence, we see the propriety of calling 

 such crystals positive, because the term 

 which expresses the influence of the 

 doubly retracting force is always posi- 

 tive. The above expression becomes 



m' = A/2'3975 + -030261 sin. 2 <p. 



The existence of a positive axis of dou- 

 ble refraction in quartz was discovered 

 by M. Biot. 



4. On Crystals with two Axes of Dou- 

 ble Refraction. 



The great body of crystals, whether 

 they are mineral or chemical substances, 

 have two axes of double refraction. 

 This discovery was made by Dr. Brews- 

 ter, who traced the double image through 

 the crystals, and found the double re- 

 fraction to diminish as the ray ap- 

 proached two lines or axes, and at last 

 to disappear wholly when the ray passed 

 along either of these two axes. He 

 found also that these lines were not co- 

 incident with any prominent lines in the 

 crystalline form, and that they formed 

 various angles with each other from the 

 smallest angle in glauberite up to 90 in 

 sulphate of iron. 



After examining more than one hun- 

 dred of these crystals, Dr, Brewster also 



