DOUBLE REFRACTION. 



spar is turned in a lathe to an exact 

 sphere ABC T),fig. 8, whose centre is 



Fig. 8. 



O, and whose axis A B corresponds with 

 the axis of the rhomb AB, Jig. 3. 

 Through O draw c O d at right angles 

 to the axis A B, and set off O c, O d, so 

 that O A or O B is to O c or O d as 



1 7*543 isto - oras 



. 6742, and through the points A, B, c, d 

 draw the ellipse A c B c?. Then, if 

 R a b is a ray of light incident on the 

 rhomb at b, at an inclination to A B of 

 ROA or 44 36' 34", the radius Oa 

 of the ellipse will be found either by 

 projection or calculation to be .6361 



or - . Hence, the index of refrac- 



1 D / ^U 



tion for the extraordinary ray formed by 

 R b will be 1.572. 



As the reciprocal of this index in- 

 creases from A to C, it will itself dimi- 

 nish, and consequently, though the suc- 

 cessive increments a b, C c of its reci- 

 procal increase also, the successive de- 

 crements of the index (viz. C c= . 1710 

 and a b= . 0823) will be negative, or to 

 be subtracted from the maximum index 

 1.654. 



If we now call m' the index of extra- 

 ordinary refraction, (or the velocity of 

 the extraordinary ray,) and <p the incli- 

 nation of that ray to the axis, then it 

 may be shown that 



w'* =1.0543* + 0. 5365 10 sin. 2 <p 

 that is, the square of the index of extra- 

 ordinary refraction at any inclination <p 

 is equal to the square of the greatest 

 index of extraordinary refraction (or the 

 index of ordinary refraction) diminished 

 by a quantity varying with the inclina- 

 tion to the axis. 



Hence, we see the propriety of calling 

 such crystals negative, because the term 

 which expresses the influence of the 

 doubly refracting force is always nega- 

 tive. 



The above formula becomes 



m'= V'2. 736693- 0.53610 sin. 2 <p . 



Having thus explained the law which 

 regulates the variation of the variable 

 index of extraordinary refraction, we 

 shall proceed to illustrate some of the 

 other properties of double refraction 

 as they appear in calcareous spar. 



Let A C B T>,J!g. 9, be a section of the 

 rhomb passing through the axis AB (see 

 fig. 3). This and every section passing 



Fig. 9. 



through the axis is called a principal sec- 

 tion of thecrystal. DrawPQ perpendicu- 

 lar to the surface AC at r. A ray, P r, inci- 

 dent perpendicularly at r, will be divided 

 into two rays, the ordinary oner Q, which 



point 



nations to P r, or at equal angfes of in- 

 cidence, but in the plane of the section 

 A C B D, the extraordinary rays of each, 

 viz. rT, rS, will be so refracted that 

 T M = S M, and these refracted rays, as 

 well as the ordinary ones r t, r s, will be 

 all in the same plane. 



The force which produces the extra- 

 ordinary refraction exerts itself as if it 

 emanated or proceeded from the axis 

 A B of the rhomb ; for when the plane 

 of incidence passes through the axis, the 

 extraordinary ray is always in the same 

 plane. But 'if the plane of incidence is 

 inclined at any angle to the axis, the 

 extraordinary ray is pushed out of that 



Elane by the force proceeding, as it were, 

 om the axis ; and hence it is tedious, 

 either by a graphic projection or by cal- 

 culation to determine, in that case, the 

 position of the extraordinary ray. 



When the plane of incidence is per- 

 pendicular to the axis, or is in what 

 may be called the equator of double 

 refraction, where the force is a maxi- 

 mum, the extraordinary ray is always 

 in the plane of incidence, and its position 



