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.
- The wavefronts gradually spread in all the directions.
- 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.
- All wavefronts will gradually fade after some time.

**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 t
_{i}=0. - Each wave will travel =vt
_{1}where v=speed of the wave. - Distance travelled by each wave is equal to the radius of the sphere.
- Therefore radius of sphere = v t
_{1}. - Common tangent joining all the spheres will give the position of the new wavefront at time t=t
_{1}. - 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 = vt
_{2}. - And again spheres will be obtained and by drawing common tangent will tell the position of all the new wavefront after time t
_{2}. - Again back wave is neglected and forward wavefront is considered.
- This shows the wavefront keep on spreading with time.

- Let the initial time t

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