Wavefront: Wavefront at any instant is defined as the locus of the particles of the medium vibrating in the same phase. Every point on the wavefront acts as a source of a new disturbance; these disturbances from the points are called wavelets. Each point on a wave surface can act as a new source of smaller spherical waves which are called wavelets. The wavelets may originate from the primary as well as a secondary source of light. Wavefronts are the envelope of these wavelets.

Refraction on the basis of the wave theory:

Let XY be a plane surface separating air from a denser medium 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 the surface at A, then ∠LAN = i is the angle of incidence as shown in the figure. Again the wavefront arrives at point A first of all and will arrive at points B, C,...later in time but in this order. Therefore, different points on the surface XY will become a source of secondary wavelets at different instants of time. When the disturbance from point P on the incident wavefront has reached point P' on the surface, the secondary wavelets from point A on the surface will have acquired a radius, say equal to AA' and those from points B, C, ... respectively. The refracted wavefront will be the tangent plane A'P' touching all the secondary spherical wavelets. The lines A'L' and P'M' perpendicular to the refracted wavefront A'P' are refracted rays. If P'N' is normal to the surface of separation at point P', then ∠N'P'M' = r is the angle of refraction.

Let c be the velocity of light in the air and v, the velocity in the denser medium. As the distance PP' in the air and the distance AA' in the denser medium are covered by the light at the same time, therefore.

\(\frac{PP'}{AA'}=\frac{c\times t}{v\times t}=\frac cv\) ------ (i)

As the angle between two lines is the same as the angle between their perpendiculars, therefore,

∠PAP' = i and ∠AP'A' = r

From triangle APP', we get

\(\sin\left(i\right)=\frac{PP'}{AP'}\)

And from the right angled triangle AA'P', we get,

\(\sin\left(r\right)=\frac{AA'}{AP'}\)

∴ \(\mu=\frac{\sin\left(i\right)}{\sin\left(r\right)}=\frac{PP'}{AP'}=\frac{AP'}{AA'}\Rightarrow\frac{\sin\left(i\right)}{\sin\left(r\right)}=\frac{PP'}{AA'}\)  ------ (ii)

From equation (i) and (ii), we have

\(\frac{\sin\left(i\right)}{\sin\left(r\right)}=\frac cv=\mu\) , which is the Snell's law.

Here, \(\frac cv=\mu\), is a constant and is called the refractive index of denser medium with respect to the rarer medium.

∴ Thus, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant for the given pair of media. Furthe, it can be proved that the incident ray (LA), the normal (AN) and the refracted ray (AA'L) all lie in the same plane. This proves another law of refraction.

Hence, the laws of refraction are proved on the basis of wave theory.