Snell's law of refraction using Huygen's Principle:Consider a plane wavefront \\\\(AB\\\\) incident on a surface \\\\(PQ\\\\) separating two media 1 and 2.The medium 1 is a rarer medium of refractive index \\\\(n_1\\\\) in which light travels with a velocity \\\\(C_1\\\\). The medium 2 is denser medium of refractive index \\\\(n_2\\\\) in which light travels with a velocity \\\\(C_2\\\\).The angle between the incident ray \\\\(FA\\\\) and the normal \\\\(NA\\\\) at the point of incidence \\\\(A\\\\) is equal to \\\\(i\\\\).The angle is also equal to the angle between the incident plane wavefront \\\\(BA\\\\) and the surface of separation \\\\(PQ\\\\).So \\\\(\\angle BAD\\\\) is the angle of incidence of the incident plane wavefront \\\\(AB\\\\).Similarly, the angle between the refracted wavefront and the surface of separation \\\\(PQ\\\\) is equal to the angle of refraction \\\\(r\\\\).i.e. \\\\(\\angle ADC = r\\\\).Consider the triangles \\\\(BAD\\\\) \\\\(ACD\\\\) figure above.\\\\(\\sin i = \\sin \\angle BAD = \\dfrac{BD}{AD} = \\dfrac{C_1r}{AD}\\\\)\\\\(\\sin r = \\sin \\angle ADC = \\dfrac{AC}{AD}= \\dfrac{C_2r}{AD}\\\\)\\\\(\\dfrac{\\sin i}{\\sin r} = \\dfrac{C_1t}{C_2t} = \\dfrac{C_1}{C_2}=\\\\) constantThis constant is called the refractive index of the second medium (2) with respect to the first medium (1).\\\\(\\dfrac{C_1}{C_2} = \\dfrac{n_2}{n_1} = 1n_2\\\\)This equation proves the Snell's law.