Question

Optical density of a medium depends on:
(A) Density of the medium
(B) Thickness of the medium
(C) Velocity of light in that medium
(D) None of these

Answer 1

Hint The more optically dense, a material is, the later a light ray striking its first surface will be ejected from the other end. They also affect the value of the index of refraction of a material.

Complete step by step answer
Optical density and density (mass density) are two entirely different quantities. While mass density is the measure of how heavy a unit volume of substance is, the optical density measures the degree of absorption of a material, after incident light rays fall on it. It can also be defined as a measure of the degree of transmittance through a medium. By this definition, it can be given by
$\Rightarrow D = {\log _{10}}\left( {\dfrac{1}{\tau }} \right) = {\log _{10}}{\tau ^{ - 1}}$
$\Rightarrow D = - {\log _{10}}\tau $
Where $D$ is the optical density, and $\tau $ is the transmittance.
This implies that the higher the transmittance, the lower the optical density, and the lower the transmittance, the higher the optical density.
Microscopically, when light or other EM waves strike a material, the atoms absorb the ray and re-emit it. Some are emitted away from the medium (reflection), while some are re-emitted into the medium (transmission). The optical density can be related to how quickly the atoms re-emitted the wave. When the re-emission time is slow, the material is said to be optically dense.
This re-emission time is what determines the velocity of a light in a medium, hence determines the refractive index. Hence, we can say the optical density is determined by the velocity of light in the medium.
Hence, the correct option is C.

Note
Although, with the velocity known, we can infer the optical density and thus the relationship. In actuality, however, the optical density is the more fundamental property of the material which determines the velocity. Hence, it is much more appropriate to say that the velocity of light in the medium is dependent on the optical property.