58 THE MOLECULAR ARCHITECTURE OF PLANT CELL WALLS 



any direction OX are given by the major axis OA and the minor axis 

 OB of the eUiptical section of the ellipsoid made by a plane nonnal to 

 the direction of propagation and passing through O. It is obviously 

 merely a matter of geometry to calculate, from known values of n 



(«) 



(6) 



(«) 



Fig. 27 



Diagrammatic representation of a piece of wall cut with sides parallel to the 

 chain direction and the index ellipsoid drawn in. The ray of light OX\% supposed 

 to be propagated from below upwards towards the front. The ellipse ABC is the 

 section of the ellipsoid made by a plane normal to OX. The corresponding 

 refractive indices are OA and OB. Note that OB is always equal to «a. 

 If a section such as LM (Fig. 27(a)) is cut and examined by light propagated 

 in the direction OX, i.e. normal to the cut surface, then the refractive mdices 

 can be calculated as illustrated here. ARS is the section of the ellipsoid contain- 

 ing the direction of propagation OX and the major axis of the ellipsoid. OA is 

 at right angles to OX and therefore represents the refractive index required. 

 From the equation of the ellipse, if A is the point (x, y) 



I.e. 



{riy'Y sin" e (iiy'Y cos^ d 



ny' 

 iny'r = 



+ 



Hy^na^ 



1, 



ny^ -{ny^-n J) sin^d 



and «„, what the refractive indices will be for light passing in any direc- 

 tion. The ellipsoid is known as the index ellipsoid. In any section of 

 wall material, therefore, say the section LM, Fig. 27(a), light passing 

 through the section at right angles to its surface will be split up into 



