In 1678, Dutch physicist, Christiaan Huygens had proposed the wave theory of light. This later became the cornerstone of wave optics and was used to derive laws of reflection and refraction. 

According to this principle, every single point in a wave front can potentially produce secondary waves, and if you draw a tangent to all these spheres, it will give you the new position of the wave front at a later time.

If the shape of the waterfront at t=0, the Huygens Wave Theory will allow you to determine the shape of the waterfront at a later time τ.

Using an equation set, Maxwell had described the laws of electricity and magnetism and arrived at the famous wave equation. The latter was used to predict the existence of electromagnetic waves.

The wave equation gives the speed of electromagnetic waves in free space, that puts the theoretical value of the speed of light almost close to its measured value. 

His theory posited that light is an electromagnetic wave, that changes with varying electric and magnetic fields. The latter leads to the emergence of electromagnetic waves, even in a vacuum.

A wavefront is defined as a surface of constant phase. A wavefront’s speed is measured by the speed at which it moves outward from the source. The wave energy travels in a perpendicular direction to the wavefront. Wave normal simply denotes a perpendicular drawn to the surface of waves.

In wave optics, there are two types of light sources:

1. Coherent sources emit light waves of the same wavelength and frequency. They have the same phase or a constant phase difference. To produce coherent waves, you can choose either of these two methods:

Division of Wavefront: The process of dividing the wavefront into two or more parts by using mirrors, lenses, or prisms.

Division of Amplitude: In this method, you can divide the amplitude of an incoming beam with the help of partial reflection or refraction.

2.  Incoherent sources emit light waves that are characterized by frequent and random phase differences between photons. A popular example is the typical fluorescent tubes that you come across.

Wherever you witness two or more sources of light illuminating the same point, it means the principle of superposition is at play. This happens because there are interference terms, in addition to the sum of the individual intensities when you consider the intensity of light at the given point. Note that this occurrence is only true when the sources have the same frequency and stable phase difference, or a non-zero average.

In plane polarized light, the component electric field oscillates just like in ordinary light. The only and most significant difference, however, is that here the oscillation takes place in one single plane. The component magnetic field also oscillates within a single plane, and perpendicular to the electric field. In contrast, non-polarized light oscillates in multiple directions.

If you consider the vibration of a string in an x-z plane, generating a z-polarized wave, its displacement is given by,

z (x,t) = α sin (kx – ωt)