Wavefront : A wavefront is a locus of all particles of medium vibrating in the same phase.
Huygen’s Principle : There are some phenomena like interference, diffraction and polarisation which could not be explained by Newton’s corpuscular theory. They were explained by wave theory first proposed by Huygen.
The assumptions of Huygen’s theory are : (i) A source sends waves in all possible directions. The locus of particles of a medium vibrating in the same phase is called a wavefront. For a point source, the wavefront is spherical; while for a line source the wavefront is cylindrical. The distant wavefront is plane.
Each point of a wavefront acts as a source of secondary wavelets. The envelope of all wavelets at a given instant gives the position of a new wavefront.
Proof of Snell’s law of Refraction using Huygen’s wave theory : When a wave starting from one homogeneous medium enters the another homogeneous medium, it is deviated from its path. This phenomenon is called refraction. In transversing from first medium to another medium, the frequency of wave remains unchanged but its speed and the wavelength both are changed. Let XY be a surface separating the two media ‘1’ and ‘2’. Let v1 and v2 be the speeds of waves in these media.
Suppose a plane wavefront AB in first medium is incident obliquely on the boundary surface XY and its end A touches the surface at A at time t = 0 while the other end B reaches the surface at point B¢ after time-interval t. Clearly BB' =v1t. As the wavefront AB advances, it strikes the points between A and B' of boundary surface. According to Huygen’s principle, secondary spherical wavelets originate from these points, which travel with speed v1 in the first medium and speed v2 in the second medium.
First of all secondary wavelet starts from A, which traverses a distance AA' (=v2t) in second medium in time t. In the same time-interval t, the point of wavefront traverses a distance BB' (=v1t) in first medium and reaches B', from, where the secondary wavelet now starts. Clearly BB' =v1t and AA' =v2t.
Assuming A as centre, we draw a spherical arc of radius AA'(=v2t) and draw tangent B' A' on this arc from B'. As the incident wavefront AB advances, the secondary wavelets start from points between A and B', one after the other and will touch A' B' simultaneously. According to Huygen’s principle A' B' is the new position of wavefront AB in the second medium. Hence A' B' will be the refracted wavefront.
First law : As AB, A' B' and surface XY are in the plane of paper, therefore the perpendicular drawn on them will be in the same plane. As the lines drawn normal to wavefront denote the rays, therefore we may say that the incident ray, refracted ray and the normal at the point of incidence all lie in the same plane. This is the first law of refraction.
Second law: Let the incident wavefront AB and refracted wavefront A' B' make angles i and r respectively with refracting surface XY.
As the rays are always normal to the wavefront, therefore the incident and refracted rays make angles i and r with the normal drawn on the surface XY i.e. i and r are the angle of incidence and angle of refraction respectively. According to equation (3):
The ratio of sine of angle of incidence and the sine of angle of refraction is a constant and is equal to the ratio of velocities of waves in the two media. This is the second law of refraction, and is called the Snell’s law.
When a light wave travels from rarer to denser medium, the speed decreases. It does not imply reduction its energy. This is because energy of wave depends on its frequency and not on its speed.
