38 THE MOLECULAR ARCHITECTURE OF PLANT CELL WALLS 



angle with the line of points. If, however, the line of points is now re- 

 garded as the intersection with the paper of a plane of points lying at 

 right angles to the page surface, then it can be shown quite simply (see 

 e.g. 13) that a beam of X-radiation falling on the sheet, as represented in 

 Fig. 14, will have reflected beams as shown. Ignoring higher orders (with 

 path differences greater than zero), then any parallel beam of radiation 

 will produce a reflected beam whose angle of reflection is equal to the 

 angle of incidence. 

 Turning now, therefore, to the three-dimensional lattice, the same 



Fig. 15. AB, CD, etc., represent loci, in the plane of the paper, of molecular planes 

 spaced d A. apart and standing normal to the plane of the page. The construction 

 shows that the ray reflected by the plane CD has a path difference greater than that 

 reflected by AB by an amount 



XM+MY==2ds[nd. 

 Hence reflection from successive planes will fortify each other if 



2i/sin d = nK, 

 n being an integer. 



conditions must apply; except that now account has to be taken of the 

 interference between "reflections" from neighbouring planes. Clearly, 

 there will always be a finite path diff"erence between the reflections from 

 one plane and the next; if this difference is a whole number of wave- 

 lengths then reflections from the planes wiU fortify each other and 

 reflection will occur. Again, the strongest reflection will be the first 

 order, when the diff'erence is one wavelength, and under these circum- 

 stances it will be clear from Fig. 15 that the wavelength A, the reflection 

 angle 6 and the interplanar spacing d are related in the form 



?.=2dsmd, ..(1) 



first derived by the Braggs and known as the Bragg Law. If, therefore, 

 A is known and 6 can be measured, then the value of Jean be calculated. 



