Can you deduce Snell's law from Huygen's Principle without knowing in which medium the velocity is going to less? Of all the derivations I have seen of Snell's law using Huygen's Principle (light going from rarer to denser medium with $v1$ and $v2$ velocities respectively), they assume $v2 < v1$ and hence a smaller circle is drawn in denser medium and Snell's law follow immediately. I get that. What I want to know is what if you didn’t know that velocity is less in denser medium can you still derive Snell's law from Huygen's principle? I remember reading somewhere that Huygen's proved that velocity is less in denser medium. I was wondering if someone could show me how.
What I want to know is what if you didn’t know that velocity is less in denser medium can you still derive Snell's law from Huygens principle?
No. It is impossible to predict the behavior of the wave front crossing the boundary between two media and, therefore, the angle of refraction, essential to Snell's law, by just applying Huygens principle: you need to know the ratio of velocities or some other additional information describing the two media.
I remember reading somewhere that Huygens proved that velocity is less in denser medium.
He must have relied on some additional information - not just Huygens principle.
For instance, if he observed refraction and applied Huygens principle, he could conclude that the velocity in the two media was different.