Huygen was the first scientist who proposed the idea of wave theory of light. He said that the light propagates in form of wavefronts. `A` wavefront is an imaginary surface at every point of which waves are in the same phase. For example the wavefronts for a point source of light is collectionof concentric spheres which have centre at the origin. `w_(1)` is a wavefront. `w_(2)` is another wavefront.

The redius of the wavefront at time `'t'` is `'ct'` in this case where `'c'` is the speed of light. The direction of propagation of light is perpendicular to the surface of the wavefront. The wavefronts are plane wavefronts in case of a parallel beam of light.

Huygen also said that every point of the wavefront acts as the source of secondary wavelets. The tangent drawn to all secondary wavelets at a time is the new wavefront at that time. The wavelets are to be consid-ered only in the forward direction (`i.e.` the direction of propagation of light) and not in the reverse direction. If a wavefront `w_(1)` at time `t` is given, then to draw the wavefront at time `t+Deltat0` take some points on the wavefront `w_(1)` and draw spheres of radius `'cDeltat'.` They are called secondary wavelets

Draw a surface `w_(2)` which is tangential to all these secondary wavelets. `w_(2)` is the wavefront at time `'t+Deltat'.` Huygen proved the laws of reflection and laws of refraction using concept of wavefronts.
A point source of light is placed at origin, in air. The equation of wave front of the wave at time `t,` emitted by source at `t=0,` is (take refractive index of air as `1`)

Options

A. `x + y + z = ct`
B. `x^(2) + y^(2) + z^(2) = t^(2)`
C. `xy + yz + zx = c^(2) t^(2)`
D. `x^(2) + y^(2) +z^(2) = c^(2) t^(2)`

Answer

D

Explanation

Wave fronts are spherical in shape of radius ct. Hence `(D)`.