Q.1047: When paper soaked in oil/fat, why does it become translucent?
Ans. When light falls upon paper, a part of it is transmitted, a part is scattered, a part is absorbed, and a part is reflected. The degree of transparency and/or opaqueness of a medium will depends on the ratio of light transmitted versus light reflected or scattered. Higher the light transmitted and lesser is reflected or scattered, more will be the transparency.
The amount of scattering depends on many things, such as the size of the fibers/ filler, and the difference in the index of refraction between the particles and the surrounding medium. Normally when we look at paper the surrounding medium is air, with an index of refraction only slightly greater than 1.0. The paper fibers have a much higher index of refraction -- probably much greater than 1.5.
The fat also has a high index of refraction so that it nearly matches the index of refraction of the paper fibers and it reduces the scattering significantly. The fat adhering to the cellulose fibers lowers the index of refraction of the cellulose and also fills in air voids, so that visible light passes through the bag with significantly less scattering. Now we only see the light that is reflected from the paper and much of the light that was formerly scattered back to our eyes is now transmitted through the paper.
The fat connects the fibers in the paper with a liquid which can transmit by refraction (rather than scatter) light that falls upon it. As a result, the paper (if thin enough) seems almost transparent.