When light falls on a paper it gets transmitted,absorbed and reflected and scattered.
The amount of scattering depends on many things, such as the size of the fibers, and the difference in the index of refraction between the particles and the surrounding medium.
Butter has higher index of index of refraction.The paper fibres have a refraction of about 1.5--- so both indexes match and thus reducing the scattering of light making it translucent. So when butter is applied on paper, it becomes translucent.
-regards ( queries will be entertained )
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