Refraction n 1 = 1 n 2 > 1 11 22 1 2 Radius = vT = (c/n)T 11 22

n 1 sin  1 = n 2 sin  2 Triangle hce sin  1 = 1 /hc Triangle hcg sin  2 = 2 /hc sin  1 /sin  2 = 1 / 2 = (v 1 /f) / (v 2 /f) = v 1 /v 2 = (c/n 1 )/(c/n 2 ) = n 2 /n 1 Snell’s Law

n 1 sin  1 = n 2 sin  2  2 =  /2 ==> sin  c = n 2 /n 1 Water n=1.5 Air n=1.  c = Reflection refraction

11 22 33 44 Halo

n sin  2 =sin  1 n sin  3 =sin  4 Deflection =  1 +   2 +  3 = 60 0 Sun Dogs n=1.33 11 22 33 4

n red < n blue v red =c/n red > v blue =c/n blue prism

The path taken by light in travelling from one point to another is such that the time of travel is a minimum Fermat’s Principle 

Refraction Minimize t with respect to x dt/dx=0 using dL 1 /dx=x/L 1 =sin  1 and dL 2 /dx=(x-d)/L 2 = -sin  2 dt/dx=(n 1 sin  1 - n 2 sin  2 )/c = 0 Time?