What is a wavefront? What is the geometrical shape of a wavefront of light emerging out of a convex lens, when a point source is placed at its focus? Using Huygens' principle show that, for a parallel beam incident on a reflecting surface, the angle of reflection is equal to the angle of incidence.
Solution
Wavefront: the locus of all points of a medium oscillating in the same phase. Shape from convex lens: a point source at the focus of a convex lens produces a parallel emergent beam, so the emergent wavefront is plane. Law of reflection (Huygens): let a plane wavefront AC strike a reflecting surface XY, with A reaching the surface first. While the secondary wavelet from A travels a distance AD in the medium, the disturbance at C travels CE=AD to the surface. Draw the reflected wavefront DE (tangent to the wavelet of radius AD centred at A).
In △ACDand△AED:AD=CE,∠ACD=∠AED=90∘,ADcommon
Hence the triangles are congruent, giving ∠CAD=∠EDA, i.e.
i=r
so the angle of incidence equals the angle of reflection.