Why does paper become translucent when smeared with oil or fat?

When light is incident upon a medium or surface, three processes occur, viz., (1) transmission, (2) absorption, and (3) reflection.

`Transmission' is the process by which the incident light leaves a medium or surface from a side other than the incident side, usually, the opposite side. `Absorption' is the process by which incident light is converted into another form of energy, usually, heat. `Reflection' is the process where a fraction of the light incident on a medium or surface is returned to the surface which contains the incident light. `Transparency' is that property of a medium or surface by which it transmits light rays.`Translucency' is that property of a medium by which it transmits light rays, so diffused, that objects cannot be seen distinctly. That is to say, it is only partially transparent.

Based on the measurement of angles (`goniometric'), materials can be classified under three heads, viz., (1) exclusively reflecting — Eg., mirror, lacquer and enamel coatings, oil and paint films, (2) weakly transmitting, but strongly, reflecting — e.g. Sun glasses, highly turbid glass, paper, and (3) strongly transmitting but weakly reflecting — e.g. Plastic film, window glass. Now, consider a sheet of (ordinary) paper. It is weakly transmitting and strongly reflecting the incident light. Hence, it is somewhat transparent. Suppose, one side of the sheet is smeared with oil. Thus, we are superimposing an exclusively reflecting material, (Zero transparency) over a weakly transmitting but, strongly reflecting material, paper. This results in the further reduction of the transmission in the paper. The paper, therefore, becomes translucent.

Source : The Hindu