Class 12 Physics Wave Optics Huygens Principle

Huygens Principle

• Huygens principle states that each point of a wavefront is the source of secondary wavelets (small waves) which spread in all directions with the speed of the wave.
• The new wavefront is formed by drawing a line tangent to all the wavelets.

For example:-

• If a stone is thrown in the river,waves will be formed surrounding that point.
• These waves look like concentric circles and they are known aswavefronts.
• When the locus of all the waves is joined which are in the same phase, it will be the same as a sphere, and are known as Primary wavefront.
• Secondary wavefront are formed fromeach point on the Primary wavefront.
• The common tangential line that envelopes these secondary wavefronts will further give rise to other secondarywavefronts.
• Conclusion: - According to Huygens principle, every point on a wavefront give rise to secondary wavelets which spread out in all the directions with the speed of a wave.

• Using Huygens principle we can determine the new position of the wavefront after time t.
• Mathematically: To calculate the new position of the wavefront after time t.
• Let the initial time ti =0.
• Each wave will travel =vt1where v=speed of the wave.
• Distance travelled by each wave is equal to the radius of the sphere.
• Therefore radius of sphere = v t1.
• Common tangent joining all the spheres will give the position of the new wavefront at time t=t1.
• There are 2 possibilities: - outer tangent and inner tangent.
• The amplitude of the back wave is 0. Therefore the back wave is neglected and the forward wave was considered.
• New wave front will arise from each point on the outer wavefront.
• Therefore the distance covered by these wavefronts = vt2.
• And again spheres will be obtained and by drawing common tangent will tell the position of all the new wavefront after time t2.
• Again back wave is neglected and forward wavefront is considered.
• This shows the wavefront keep on spreading with time.

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