Huygen's principle states that every point on a wavefront can be considered a source of waves.
Making each point on a wavefront a source of secondary waves and applying the principle of superposition gives a new wavefront which is again a plane wave.
The laws of refraction and reflection can both be derived using Huygen's Principle.
In the time it takes for the incident ray to go from B to B' the reflected ray at A goes from A to A'. The speed is constant so BB'=AA'. AB' is common to triangles ABB' and AA'B' so∡BAB' equals ∡A'B'A, but ∡BAB' + i = A'B'A +r so i=r.
In the timethat the incident wavefront travels from B to C the refracted wavefront travels from A to E.
Hence(1) and(2) since ∡ACB = ∡AEB = 90 degrees.
Dividing (1) by (2) gives