Huygen was the figure scientist who proposed the idea of wave theory of light he said that the light propagates in form of wavelengths. A wavefront is a imaginary surface of every point of which waves are in the same. phase.
For example the wavefront for a point source of light is collection of concentric spheres which have centre at the origin `w_(1)` is a wavefront `w_(2)` is another wavefront.
The radius of the wavefront at time 't' is 'ct' in thic case where 'c' is the speed of light the direction of propagation of light is perpendicular to the surface of the wavelength. 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 considered only in the forward direction (i.e., the direction of propagation of light) and not in the reverse direction if a 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 wavefront.
Q. A point source of light is placed at origin, in air. the equation of wavefront 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 front of point source is sprical. The point source is at origin and distance travellled by wave in 't' time with a speed of light 'c' is 'ct'. Hence radius of wave front is'ct'
`therefore` equation of sphere `x^(2)+y^(2)+z^(2)=(ct)^(2)`