Dr. H. Stanley Allen on Optical Rotation. 427 



Part I. 



Optical Rotation. 



Rotation o£ the plane of polarization of light by a pure 

 liquid or a vapour has presented serious difficulties to the 

 theoretical physicist. Drude and Voigt have shown what 

 type of electromagnetic equations are required to account for 

 the rotation, but " there is no satisfactory representation of 

 the mechanism by means of which an asymmetrical molecular 

 structure turns the plane of polarization " *. In the ordinary 

 theory of dispersion the equation of motion of an electron 

 (mass m, charge e) is of the form 



where f is the .r-component of the displacement from the 

 equilibrium position, X is the .^-component of the exterior 

 electric force, and the last term represents the restoring 

 force called into play by the displacement of the electron. 

 Drude includes also a frictional term which represents a 

 force retarding the vibrations. In an isotropic medium the 

 only possible extension of the equation is by the introduction 



of a term of the form ef'l ^ - — ^— ). By combining the 



equations thus modified with Maxwell's equations for the 

 electromagnetic field, it can be shown that when plane- 

 polarized light falls on the medium, two waves are propa- 

 gated through it with different velocities, the first representing 

 right-handed circular polarization, the second left-handed 

 circular polarization. The superposition of the two waves 

 yields a plane-polarized wave in which the plane of polariza- 

 tion rotates through a definite angle for each unit length of 

 optical path. The terms which have been added to the 

 equations may be taken to represent a torsional electric force. 

 Drude gives a graphical representation by conceiving that 

 because of the molecular structure the paths of the electrons 

 are not short straight lines, But short helices twisted in the 

 same direction, with their axes directed at random in space. 

 ■ ; A rifle bullet lying in its rifle barrel would be displaced in 

 a similar manner along the barrel both by a pulling and 

 twisting force. But if we take the dimensions of a single 

 electron to be very small, we exclude the possibility of a 

 constraint which would enable a couple to cause a motion in 

 one direction. We must in that case draw the conclusion 

 * Schuster, ' The Theory of Optics/ § 162, 1904 edition. 

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