Wave Front and Wavelet

According to wave theory of light, source of light sends out wave in all direction in the form of disturbance.

Each point on wave front can act like a new source of small spherical wave which are called wavelets.

Types of Wave Front

Depending upon the shape of source of light, wave front is of three types:

1. Spherical Wave Front

2. Cylindrical Wave Front

3. Plane Wave Front

Huygens’ Principle

It states that:

1. Each point on a given wave front acts as a new source of disturbance which propagates in all direction with a velocity equal to velocity of light.
2. The tangential surface touching the secondary wavelets in forward direction at any instant gives a new wave front called secondary wave front.

Construction of Secondary Wave Front

Suppose AB be a section of given wave front called primary wave front at any instant. Let a, b, c and d be points on this wave front. The distance travelled by light in time t is equal to ct.

At each point as a centre, if spheres of radius ct are constructed, the spherical surfaces represent positions of secondary wavelets. The tangential surface touching these spheres in forward direction represents secondary wave front.

Law of Reflection on the Basis of Wave Theory

The laws of reflection are:

To Prove Law of Reflection on the Basis of Wave Theory

Consider a plane wave front AB incident on reflecting surface XY at an angle of incidence ‘i’. Let the incident rays be perpendicular to wave front AB and AN be normal to reflecting surface.

Let in time ‘t’ one point of wave front reach the reflecting surface. At the same time, secondary wavelet from the point already on the reflecting surface spreads out in the form of sphere of radius ct.

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

Further, the incident wave front, reflecting wave front and reflecting surface are perpendicular to the plane of paper. So incident ray, reflected ray and normal lie in the same plane.

Law of Refraction on the Basis of Wave Theory

The refraction laws are:

To Prove Law of Refraction on the Basis of Wave Theory

Consider a plane wave front AB incident on plane surface XY separating two media. The rays perpendicular to wave front AB represent incident rays and AN is normal to surface XY.

Let v and c be the velocity of light in denser and rarer medium respectively. According to Huygens’ theory, every point on AB acts as source of secondary wavelet.

Let ‘t’ be the time taken by light to reach the next point on the boundary in the rarer medium. Then:

which proves first law of refraction.

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