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Derivation of Snell’s law

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 normal.

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

**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 normal.

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 / sin rso we get v1 / v2 = n2 / n1 = sin i / sin r