# Derivation of Snell's law

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by snellslaw

## Answers

2015-09-20T02:41:44+05:30

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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 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 r

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