Introduction

Light is vital for everything ranging from day-to-day activities to even agricultural purposes. Light is essential for sight; conversely, light is the reason animals see. Without light, there is no difference between a blind man and a man with functional eyes.
The physics and chemistry behind production of light; how light is emitted has been explained explicitly in my previous publish Optics #1. It is imperative you take a good read before proceeding further.

Centuries ago, an English Physicist demonstrated that light is a particle; around that same time another scientists demonstrated equally that light is a wave. So the contention between two schools of thought began_is light a wave or particle? Both the school of thought that proposed light as a wave and the school that proposed light as particle did what they could to convince people of their respective theory of light.

Light As A Wave

What is wave? this question might not be easy as it appears if one tries to give a concise answer.

_{Image Credits:CC by SA 3.0|| Source: Wikimedia}

Wave is a disturbance which transfers energy from one point to another but does not transfer mass. Wave can be mechanical or electromagnetic.
Mechanical wave requires a physical medium to transfer energy from one point to another while electromagnetic wave transfers energy through space.

Scientists like Francesco Maria Grimaldi, Christian Huygens, James Clerk Maxwell and some others discovered that light exhibit some of the boundary properties/characteristics of wave and came up with their various ideas of light with respect to light as a wave. Some characters sound waves and radio waves exhibit is also exhibited by light. This was what led these great scientist to conclude that light is a wave. The wave characteristics of light includes reflection, refraction, diffraction, interference and some others as below:

Reflection

Reflection is the a change in direction of a wave-front when it encounters an obstacle while travelling from a medium. So two media must be present for reflection to occur; the medium in which the wave travels and a medium which would serve as an obstacle.
Have you ever shouted in a solitary place? You would hear an echo. This happens because the soundwave hits an obstacle(maybe a wall) and bounced back(reflection); echo is a reflection of sound wave. Similarly, when you incident a torchlight at an angle on a smooth surface, you would see a beam of the torchlight appear as if it is slightly coming towards you or a bounce back of the torchlight depending on the angle of incidence. All these happens due to reflection
From these point, I would be using the terminologies in optics The law of reflection states that the incident wave's angle and the reflected wave's angle are equal. In our sound wave analogy, we can assume the angle of the incident wave is the angel at which your shout hits an obstacle(maybe wall) and the reflected wave angle is the angle at which the echo followed while bouncing off the wall. However, this two angels are equal.

_{Image Credits: CC by SA 3.0|| Source:Wikimedia|| Author: Epzcaw}

Where
θ₁= angle of incidence = angle of reflection
θ₂= angel of refraction
Credits to French physicist Augustin-Jean Fresnel, who in 1815, discovered that light exhibits reflection, proposed that light has extremely short wavelength and mathematically proved the interference of light_ref

Refraction

Refraction is another boundary characteristic of waves which light exhibit. Refraction is a change in direction of a wave-front as it propagates from one media to another. This causes a change in the speed and wavelength of the involved wave.
The speed at which a wave travels, depend on the properties like density and elasticity of the medium which it travels through and the properties of different medium are different.

In my childhood days, I would bring two empty containers(tins) of tomato, join the two tins with a rope. Then I would give my friend one tin to use as a microphone and hold the other one close to my ear; I discovered that each time my friend talked to through that tin, I heard what he said in a shorter time compared to when he talked without it. This means, the speed of sound in that rope is faster than the speed of sound in air.

Similarly, the speed of light in free space differs from the speed of light in other medium. The speed of light in free space is 3 * 10⁸m/s while in water, it is 2.25 *10⁸m/s. Therefore, when light travels from air to another medium of different properties, it would change slightly its direction of propagation, this leads to a bend

_{Image Credits: Creative commons|| Source:texample}
This is in correspondence to Snell's law of refraction:

For a pair of media, the ratio of the sines of angel of incidence θ₁ and angel of refraction θ₂, is equal to the ratio of phase velocities in the pair f media. _ref.
Mathematically, this can be represented as below:
Sinθ₁/ Sinθ₂ = V₁/V₂

This is the reason why when you incident a torchlight in a container filled with water, you would notice a slight bent in the direction of the torchlight rays inside the water

Diffraction

Diffraction is the third boundary property of wave which is exhibited by light. Diffraction is the bending of waves around obstacles as it propagates; diffraction is the reason waves can travel through an aperture or opening of an obstacle
Amount of diffraction is dependent on wavelength and the size of the aperture or opening in the obstacle. If the opening is larger than the wavelength of the wave, then the diffraction would not be obvious; if the opening is approximate, less or equal to the wavelength in size, the diffraction would be noticeable.

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_{Image credits:CCSA 4.0|| Source: Wikimedia|| Author: Diwaker}
If torchlight is pointed toward a wall with very wide opening, the diffraction would be unnoticed; but if there is a considerably small opening in the wall, the rays of the torchlight would be seen in the other side of the wall in a diverging manner. This solidly convinced scientists to consider light as a wave.

Another feature of light that made James Maxwell propose that light is an electromagnetic wave is that light can travel through vacuum. Maxwell predicted the existence of electromagnetic wave, a special wave that requires no medium for propagation. Prior to the time he predicted this, the magnetic field of magnets, electric current and the electric field produced by two plates in a charged capacitor, were considered not to be related to each other. However, Maxwell change this thinking when he presented his equations(Maxwell equations) which linked the magnetic field of a magnet, electric charges and the electric field produced by a plate in a charged capacitors together. _ref

Conclusion

Light exhibits the boundary properties of wave, this is the reason wave theory of light was scientifically and mathematically proved. However, some properties of light such as Compton-effect and photo-electricity could not be explained by the wave theory; hence another entirely different theory of light which would be discussed on my next publish

Thanks for your time, I remain your brethren @ikchris

References

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Optics #2_ The Dual Nature Of Light; The Wave Theory