Chapter-10|Wave Optics|NCERT 12th Physics:
Proof For Law of Refraction at a Plane Surface(By Huygens’ Wave Theory):
Let after t time a ray comes from B to D and cover a distance V₁t. Now we will form a wavelet at point D. Now, after t time a wave comes from A to C with speed V₂ and cover a distance V₂t, reached at point C. Here we will form another wavelet. The common tangent of point C and D form refracted wavefront.
The incident wave front AB, surface AD and refracted wavefront CD are perpendicular to the plane of paper.
Since, Incident ray is perpendicular to AB, normal is perpendicular to AD and refracted ray is perpendicular to CD.
Therefore, the incident ray normal and refracted ray lies in the same plane of the paper.
This is called second law of refraction.