Question

The optical density is the property of a medium that provides a relative measure
of the speed at which light travels in that medium. Does the speed of propagation
of light increase or decrease with an increase in the optical density of the medium?

Answer 1

Optical density is the measure of the ability of the medium to allow the light to pass through. This can be synonymously used as refractive index of the medium. It is important to note that the refractive index of the material is not dependent of density (physical) of the medium.
By definition of the absolute refractive index of the medium, it is the ratio between the speeds of light in vacuum and the medium, if the optical density increases, the speed of light in the medium decreases.