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Specific Rotation

The angle (in degrees) through which the plane of the polarized light is rotated on passing through the solution of an optically active substance depends upon the following factors:
(i)    Nature of the optically active substance.
(ii)    Concentration of the solution (in g/ml).
(iii)    Length of the solution i.e. the length of the tube through which the light passes (in decimeters).
(iv)    Wavelength of the light used.
(v)    Temperature of the solution.

Thus if m grams of the substance are dissolved in ml of the solution. (So that the concentration of the solution is m/ g per ml), is the length of the tube (in decimeters) and α is the angle of rotation (in degrees), then it is found that
                                       (Concentration in g/ml) x (length of the tube in dm)
Whereis a constant  characteristic of the nature of the substance and depends upon the wavelength of light used  and the temperature of the solution . It D line of the sodium light is used and the temperature of the solution is 250 C, then it written , as . This constant is called ‘specific rotation’ of the substance. Thus form the above equation
Hence specific rotational a substance may be defended as the angle of rotation produced when one gram of the substance is dissolved in one ml of the solution through which light passes is 1 dm.

In all reported values , the concentration of the solutions taken in grams/100 ml of the solution. Thus if c grams are dissolved in 100 ml of the solution, then we may put m=c and . This gives [form equation (6.2.2]
Further, if instead of solution, substance taken is pure liquid or a solid, then is replaced by density d of the pure substance. This gives [form equation (6.2.2.)]
In case of pure solid, is taken as the thickness of the solid in dm. specific rotation with the molecular weight (M) of the substance and dividing the result by 100 (to reduce the magnitude of the number). It is usually represented as   Thus

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