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#### Wavefront and wavelet

According to the wave theory of light; source light is sent out waves in all directions in the form of disturbance. Wavefront is defined as the locus of all points equidistant from the source of light which are vibrating in the same phase.

Each point on the wavefront can act as a new source of the small spherical wave which is wavelets.

#### Types of wavefront

Depending upon the shape of sources of the light wavefront is of three types

#### 1. Spherical wavefront

The wavefront produced by the point of source of light is called a spherical wavefront.

fig: Spherical wavefront

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#### 2. Cylindrical wavefront

The wavefront produced by the linear source of light is called a cylindrical wavefront.

**Fig: Cylindrical wavefront**

#### 3. Plane wavefront

A small part of a spherical or cylindrical or distance source forms a wavefront in the form or plane is called a plane wavefront.

### Huygen’s Principle

It states that

1. Each point on a given wave front acts as a new source of disturbance that propagates in all directions with a velocity equal to the velocity of light.

2. The tangential touching the secondary surface in forwarding direction at any instant gives ‘μ’ wavefront called secondary wavefront.

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**Fig : Huygens principle**

Suppose AB is a section of a given wavefront called primary wave front at any instant. Let a, b, c, and d point on this wavefront. The distance traveled by light in each second is equal to ct. At each point as a center and constant a sphere of radius ct. The spherical surface touching this sphere in a forwarding direction respected the secondary wavefront.

#### Law of reflection on the basis of the wave theory

The law of reflection is

1) The angle of reflection ‘r’ is equal to the angle of incident ‘I’ for all wavelengths and for any pair of mediums.

i.e < i = < r

The incident ray, the reflectent ray, and the normal to the reflecting surface, all lie on the same plane.

To prove the law of reflection on the basis of wave theory, consider a plane web front AB incident on refracting surface XY at an angle of the incident i. Also, let QPR are perpendicular to wavefront AB represent incident ray and AN normal to the reflected surface. Also let, by the time ‘t’ point of wavefront reach at point ‘A’. As the same time secondary wave plates from A speed out in the form of a sphere of radius AB.

So, AB’ = BA’ = Ct [Where c= velocity of light]

Similarly the light from C’ reaches B at the same time the light from D reaches C’.

°If we draw a tangent to the surface of a sphere, the tangent A’B’ represents the reflecting wavefront, and P’, Q’, and R’ represent reflected rays all shown in the figure above.

Now from △ABA’ and △ AB’A’

(i) AB’ = BA’ ( Distance travel by light is same time)

(ii) ∡ABA’ = ∡AB’A’ = 90° (Given)

(iii) AA’ = AA’ (common side)

It shows that two tringle are congrunt

∡BAA’ = ∡ B’A’A

i.e ∡i = ∡r

Therefore the angle of incident is equal to the angle of reflection which is the first law of reflection of light.

Further, the incident wavefront AB, reflecting wavefront A’B’, and reflecting surface are perpendicular to the plane of the paper. So incident ray, reflecting ray, and normal lie in the same plane.

### Law of refraction on the basis of the wave theory

The reflection laws are

1. The ratio of the sine of the angle of the incident to the sine of angular reflection is constant for any two given mediums.

i.e μ = sini / sinr

where, μ = refractive index of medium

2. The incident ray, the refracted ray, and the normal point of incidence lie on the same plane.

**Fig: Refraction at a plane surface**

To prove the law of refraction on the basis of wave theory consider a plane wavefront AB incident on plane surface XY separating two media. The rays P, Q, and R are perpendicular to the wavefront AB represents incident rays and AN is normal surface XY.

Also, let V and C be the velocity of light in denser and rare mediums respectively. According to Huygens’s theory, every point on AB is a source of Secondary wavelet. Also, let ‘l’ be the time taken by light to reach A from B.

i.e. BA’=ct

But the secondary wave originating A to B traveled or Distance in the time ‘t’ is

AB’ = Vt

If we draw a tangent to the sphere of the secondary wavelet, a secondary wave

Front A’B’ is formed in the denser medium.

Now from ∆ABA’

And from ∆AB’A’

which proves 1st law.

Further the incident wave front AB refracting wave front A’, B’ and refracting surface are perpendicular to the plane of the paper. The incident ray, refracted ray and normal lie on same plane.

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