Question

How can we find more denser object from a refractive index of some materials?​

Answer 1

Explanation:

It is important to note that the equation you mention gives the index of refraction of one medium with respect to another. If light travels from one medium with refractive index ni and incident angle i, to another medium with refractive index nr and refraction angle r, then the relationship is described by Snell's Law as such:

nisin(i)=nrsin(r)

which can be rewritten like this:

sin(i)sin(r)=nrni

If we say that ni<nr meaning the light propagates from a rarer to a denser medium, then the above equation gives the index of refraction of the denser medium in relation to the index of refraction of the rarer medium.

If instead we wanted to consider the case where light travels from a denser to rarer medium, then the only change would be that now ni>nr in which case the above equation would yield the index of refraction of the rarer medium in relation to the denser medium. Notice that in this second case if we still desire the index of the denser medium with respect to the index of the rarer medium we must rearrange the equation like this:

sin(r)sin(i)=ninr

But this is simply a consequence of which ratio we are looking for. For example, say we consider the propagation of light from air to some unknown denser material. In this case, ni≈1, the index of refraction of air, and nr=nx the index of refraction of the unknown material. We would then say that from the first relationship defined the index of refraction of the unknown material is:

nx=sin(i)sin(r)

If instead we said this light traveled from the denser unknown medium to the air, then ni=nx and nr≈1. In which case we would find the index of the unknown material by using the second relationship:

nx=sin(r)sin(i)