Define the term wavefront. Using Huygens' wave theory, verify the law of reflection.
Answer: A wavefront is the locus of points vibrating in the same phase; Huygens' construction gives ∠i=∠r.
Solution
Wavefront: the surface (locus) joining all points of a medium that are vibrating in the same phase at a given instant. Law of reflection: let a plane wavefront ABC be incident at angle i on a reflecting surface AD, the wave speed being v. In time Δt the disturbance from C reaches D (CD=vΔt), while the secondary wavelet from A spreads a radius vΔt; the common tangent DEF from D is the reflected wavefront.
In △ACDand△DFA:AD=AD,CD=AF=vΔt,∠ACD=∠DFA=90∘
By the RHS rule the triangles are congruent, so ∠CAD=∠FDA, i.e.
∠i=∠r
Hence the angle of incidence equals the angle of reflection, and the incident ray, reflected ray and normal are coplanar.