Question

How can determine that this is rare medium & this is denser?

Answer 1

you need another medium to compare with it, it cannot be told wether a medium is rarer or denser unless u have another medium to compare .
hope it helps!

Answer 2

The speeds in the two different mediums, or the refractive indices, or the amplitude of the two different light waves that pass through it. for all of these cases, the one having a larger value is denser.

or

If no values have been given and you had to do it simply by observation, simply the one that feels more substantial would be denser. the scientific justification for this is that the one that is heavier (given they both have same volumes) is denser.

or

If you know the materials you can determine its density by having a look at this chart, detailing densities of various common and uncommon substances.

or

you can look at the direction of the bent light. if the angle it makes with the normal drawn to its surface in medium 1, is greater than the angle made by it with the normal in the medium 2 then medium 1 is denser. vice versa.

hope that helped :)