1. Snells law
2. Refraction of a plane wave. (To prove Snell’s law):
AB is the incident wavefront and c_{1} is the velocity of the wavefront in the first medium. CD is the refracted wavefront and c_{2} is the velocity of the wavefront in the second medium. AC is a plane separating the two media.
The time taken for the ray to travel from P to R is
O is an arbitrary point. Hence AO is a variable. But the time to travel a wavefront from AB to CD is constant. In order to satisfy this condition, the term containing AO in eq. (2) should be zero.
∴ \(AO\Big(\frac{sin\,i}{C_1}-\frac{sin\,r}{C_2}\Big)\) = 0
\(\frac{sin\,i}{C_1}=\frac{sin\,r}{C_2}\)
\(\frac{sin\,i}{sin\,r}=\frac{C_1}{C_2}\) = ^{1}n_{2}(constant)
where ^{1}n_{2} is the refractive index of the second medium w.r.t. the first. This is the law of refraction.