State Huygens' principle and hence explain the construction of spherical and plane wavefront.
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Huygens' postulated that light is a wave, which travels through a hypothetical medium called ether. This hypothetical medium has the strange property of occupying all space, including vacuum. The vibrations from the source of light propagate in the form of waves and the energy carried by them is distributed equally in all directions. The concept of wavefront is central Huygens Principle. The Huygens Principle states that
(a) Each point on a wavefront becomes a source of secondary disturbance which spreads out in the medium.
(b) The position of wavelength at any later instant may be obtained by drawing a forward common envelop to all these secondary wavelets at that instant.
(c) In an isotropic medium, the energy carried by waves is transmitted equally in all directions.
(d) If the initial shape, position, the direction of motion and the speed of the wavefront is known, its position at a later instant can be ascertained by geometrical construction. Note that the wavefront does not travel in the backward direction.
PROPAGATION OF WAVES :
Now let us use Huygens' principle to describe the propagation of light waves in the form of propagation of wavefronts. The figure shows the shape and location of a plane wavefront ABAB at the time t=0t=0 You should note that the line ABAB lies in a plane perpendicular to the plane of the paper. Dots represented by a,b,ca,b,con the wavefront ABAB are the sources of secondary wavelets.
All these sources emit secondary wavelets at the same time and they all travel with the same speed along the direction of motion of the wavefront ABAB. In the figure the circular arcs represent the wavelets emitted from a,b,c,...a,b,c,...taking each point as center. These wavelets have been obtained by drawing arcs of radius, r=vtr=vt, where vv is the velocity of the wavefront and tt is the time at which we wish to obtain the wavefront. The tangent, CDCD, to all these wavelets represents the new wavefront at time t=Tt=T. Let us take another example of Huygens' construction for an expanding circular wavefront . Refer to fig., which indicates a circular wavefront, centred at OO, at the time t=0t=0. Position A,B,C,...A,B,C,... represent point sources on this wavefront. Now to draw the wavefront at a later time t=Tt=T, what would you do? You should draw arcs from the points A,B,C,...A,B,C,... of radius equal to the speed of the expanding wavefront multiplies by TT.
These arcs will represent secondary wavelets. The tangents drawn to these arcs will determine the shape and location of the expanding circular wavefront at time TT. We hope you have now understood the technique of Huygens' construction. Now, you may like to know the physical significance of Huygens' construction. By determining the shape and location of a wavefront at a subsequent instant of time with the help of this shape and location at an earlier instant, we are essentially describing the propagation of the wavefront. Therefore, Huygens' construction enables us to describes wave motion.
I HOPE THIS WILL HELP YOU
Huygens' postulated that light is a wave, which travels through a hypothetical medium called ether. This hypothetical medium has the strange property of occupying all space, including vacuum. The vibrations from the source of light propagate in the form of waves and the energy carried by them is distributed equally in all directions. The concept of wavefront is central Huygens Principle. The Huygens Principle states that
(a) Each point on a wavefront becomes a source of secondary disturbance which spreads out in the medium.
(b) The position of wavelength at any later instant may be obtained by drawing a forward common envelop to all these secondary wavelets at that instant.
(c) In an isotropic medium, the energy carried by waves is transmitted equally in all directions.
(d) If the initial shape, position, the direction of motion and the speed of the wavefront is known, its position at a later instant can be ascertained by geometrical construction. Note that the wavefront does not travel in the backward direction.
PROPAGATION OF WAVES :
Now let us use Huygens' principle to describe the propagation of light waves in the form of propagation of wavefronts. The figure shows the shape and location of a plane wavefront ABAB at the time t=0t=0 You should note that the line ABAB lies in a plane perpendicular to the plane of the paper. Dots represented by a,b,ca,b,con the wavefront ABAB are the sources of secondary wavelets.
All these sources emit secondary wavelets at the same time and they all travel with the same speed along the direction of motion of the wavefront ABAB. In the figure the circular arcs represent the wavelets emitted from a,b,c,...a,b,c,...taking each point as center. These wavelets have been obtained by drawing arcs of radius, r=vtr=vt, where vv is the velocity of the wavefront and tt is the time at which we wish to obtain the wavefront. The tangent, CDCD, to all these wavelets represents the new wavefront at time t=Tt=T. Let us take another example of Huygens' construction for an expanding circular wavefront . Refer to fig., which indicates a circular wavefront, centred at OO, at the time t=0t=0. Position A,B,C,...A,B,C,... represent point sources on this wavefront. Now to draw the wavefront at a later time t=Tt=T, what would you do? You should draw arcs from the points A,B,C,...A,B,C,... of radius equal to the speed of the expanding wavefront multiplies by TT.
These arcs will represent secondary wavelets. The tangents drawn to these arcs will determine the shape and location of the expanding circular wavefront at time TT. We hope you have now understood the technique of Huygens' construction. Now, you may like to know the physical significance of Huygens' construction. By determining the shape and location of a wavefront at a subsequent instant of time with the help of this shape and location at an earlier instant, we are essentially describing the propagation of the wavefront. Therefore, Huygens' construction enables us to describes wave motion.
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