Answer:
  Soap containing a whitening reagent such as titanium oxide is both coloured and opaque. The transparency of soap without additives depends on the crystal condition (crystal size) of the soap. The optical index of a substance is no longer homogeneous when crystal and amorphousness are mixed. In this case, the incident light is scattered in the substance, and as a result it is apparently opaque. Therefore, the key point in making transparent soap is the prevention of the growth of soap crystals.
  
  In the manufacture of transparent soap (see photo at left), a whitening reagent such as a mixture of glycerin and sugar is added, then it is dried slowly, evaporating the flammable solvent mixture of water and ethanol. It is thought that the whitening reagent is interposed between the molecules of soap, preventing the growth of soap crystals. Another method, if the composition (saponification number) of the soap is the same, is to age the soap under cool conditions also preventing crystal growth.
 
  However, I cannot be specific about the details of this cool condition because it depends on the composition of the soap.
 
 
Acknowledgement
  We would like to thank Kao Corporation, Chemical Business Division for their careful teaching and kind support for this answer.
 
 
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