Ordinary density is not the key. Light is an electromagnetic wave, also it is quantized into photons that have particle properties. Anyway the speed depends on the electromagnetic properties of the material. The Maxwell Equations show that the electric force and the magnetic force are two sides of the same mathematical coin. Empty space-time has two fundamental properties. First, "permitivity" is the natural electrical capacitance, that is, the ratio that relates electric flux to electric field. Also "permeability" is the natural electrical inductance, the ratio of magnetic flux to magnetic field. I like to think of the permitivity and permeability as how elasitc or chewey space-time is to the fundamental forces. Permitivity and permeability are the most fundamental properties of the universe, and are expressed in 4 units of measure: meters, seconds, amps and volts. Two space-time units and two electrical units. We can combine these two numbers to cancel the space-time units we are left with electrical impadance of 120 * pi ohms. This is the natural electrical impedance of space-time. If we arrange the two numbers to cancel the electrical units, we are left with almost 300,000,000 meters per second, or the speed of light. These are done as in Fig 2. The index of refraction is the square root of permittivity times permeability.
When we introduce matter into space-time the properties of the atoms and molecules multiply the magnetic permeability and electrical permitivity by some factor. By using the new permeabiltiy and permitivity we obtain exactly the speed of light in the material, as well as the electrical impedance of a photon in the material. The index of refraction is still the square root of permittivity times permeability. So the Maxwell equations always gives us the right answer for the index, speed of light and impedance. Now high values of permittivity and permeability usually go with high mechanical density, but not always. We often seek special materials that have extreme values of one of the electomagnetic properties, but the mechanical properties may not have such an extreme value. As you can see, the Maxwell equations have a special magic, Maxwell shows how electricity, magnetism and light are all really the same thing.