Derivation of Snell’s law
n2 / n1 = v1 / v2 or,
n2 sin r
= n1 sin i
is to be done using Huygens wavefronts..
Let us take two points (secondary wavefronts) on the same wavefront AC in medium
1. We can treat a large spherical wavefront to be approximately planar in
a small region. The wavefront travels v1 * t distance in t seconds
in medium 1. We take a wavefront perpendicular to the light ray.
Thus the wavefront plane is inclined at angle i to the surface of
separation, same angle of incidence i between the light ray and the
After the refraction in to the second medium, the secondary wavefront that
enters the secondary medium travels v2 * t and it makes an angle r, with the
surface of separation. r is also the angle of refraction of light ray
with normal to the surface. So after time t, the wave front is at position FB. Energy at Point A moves to point F. and that at C reaches B.
Thus (v1 t / sin i ) = v2 t / sin r = AB
=> v1 / v2 = sin i / sin r
refractive index is defined as the ratio of speeds of light in vacuum and medium.
v1 = c / n1 and
n2 = c/ v2
so we get v1 / v2 = n2 / n1 = sin i /