Huygen's principle is a geometrical construction of a wavefront which is used to determine the position of a wavefront at a later time from its position at any instant. The principle is based on the following assumptions.
- Each point on the primary (given) wavefront acts as a source of secondary wavelets, the light waves sending out from secondary sources travel in all directions with the speed of light.
- The new position of the wavefront at any instant is given by the forward envelope of the secondary wavelets at that instant.
Reflection on basis of the wave theory
Let XY be a reflecting surface and AP be a plane wavefront just incident on it. The lines LA and MP which are perpendicular to the incident wavefront AP, represent incident rays. If AN is normal to reflecting surface at A, then ∠LAN = i is the angle of incidence as shown in the figure.
The wavefront arrives at point A first of all and will arrive at points B, C, ... later in time, but in this order. Thus, different points on the reflecting surface will become the source of secondary wavelets at different instants of time. When the disturbance from point P on incident wavefront has reached point P' on the surface the secondary wavelets from A, on the surface will have acquired radius, say equal to AA' and those from points B, C,.. equal to BB', CC',... respectively. The reflected wavefront will be the tangent plane A'P' touching all the secondary wavelets. The lines A'L' and P'M' perpendicular to the reflected wavefront A'P' are reflected rays. If P'N' is normal to reflecting surface at P', then ∠N'P'M' = r is the angle of reflection.
Now, in the right-angled triangles APP' and AA'P',
∠APP' = ∠AA'P' (both are right angles),
AA' = PP' (distance travelled by the light in the same time),
AP' = AP' ( common side )
Therefore, two triangles are congruent and hence
∠PAP' = ∠A'P'A ---------- (i)
As the angle between two lines is the same as the angle between their perpendiculars, therefore,
∠PAP' = i and ∠A'P'A = r
Hence from equation (i) we can conclude that,
i = r
i.e., the angle of incidence is equal to the angle of reflection. Further, as the incident wavefront (AP), the reflecting surface (XY) and the reflected wavefront (A'P') are all perpendicular to the plane of the paper, therefore the incident ray (LA), normal (AN) and reflected ray (AA'L'), which are respectively perpendicular to AP, Xy and A'P' all lie in the same plane. This proves the second law of reflection. Hence, the laws of reflection are proved on the basis of wave theory.