A rethink of light dispersion through a prism:

Jzz

May 10, 2021
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I don’t know if this contribution is worth a Nobel prize or not, Ha, Ha, but it is still pretty important! Returning now to the subject at hand.

Light is composed of several different wave-lengths and frequencies that are superimposed on each other to give white light. Under certain conditions white light can be split into its constituent colours giving the colours of the spectrum: Violet, indigo, blue, green, yellow, orange, red. These colours are superimposed on each other to give white light. The dispersion and recombination of white light was first demonstrated by Sir Isaac Newton by sending a beam of light first through a single right angled prism to disperse light into its constituent colours and later the spectrum of colours was sent through another right angled prism set parallel to the first prism to recombine into white light. According to the widely accepted theory, dispersion occurs because violet light travels slower through glass than red light, BUT is this conclusion wrong?

The result of numerous experiments with the dispersion of light seems to demonstrate that different colours of light travel at different speeds through a prism. The explanation is that light of higher frequency experiences a higher refractive index than red light which would have a lower refractive index while travelling through the same medium. For instance violet light is thought to experience a refractive index of 1.65 in glass while red light experiences a refractive index of 1.61 in the same glass. Surely, this is an absolute contortion of the facts and has no basis at all in reality? The reality is that light travels at the same speed through any given medium, this property is not restricted to the propagation of light in air or a vacuum. ALL the encyclopaedias and ALL of the text books seem to deny this fact, they state that the speed of light through any medium other than air which has a refractive index of 1, varies with the frequency of light.

There is no doubt that refraction exists, there is no doubt that light experiences dispersion when travelling through a right angled prism. The doubt arises over the reason that dispersion takes place. One of the established facts is that dispersion occurs when light travels through a dispersive medium. For instance the speed of Ocean waves vary with the depth, waves of different wave-lengths travel at different speeds.

It was a Dutch mathematician by the name of Willebrord Snell (1591–1626), who formulated the laws of refraction in 1621. He found that n1 sin θ1 = n2 sin θ2 where n1 is the refractive index of air and n2 is the refractive index of the second medium, sin θ1 is the angle of incidence and sin θ2 is the angle of refraction. This means that the angle of refraction can be calculated by multiplying the reciprocal of the ratio of the refractive index of air to the refractive index of the new medium by the angle of incidence sin θ1. The same formula can be used to calculate the speed of light through the new medium.

Having set out the basic scenario behind the phenomenon of refraction and dispersion, it is time to examine it in a little more detail. Light is made up of the superposition of several colours each having a different frequency, wave-length and energy. The manner in which the different frequencies and wavelengths combine to give white light is called Superposition. When two electromagnetic waves travel together they always interfere with each other giving rise to a new wave form, but they don't destroy any information in the process. This is the superposition principle in classical electrodynamics. The fact the electromagnetic waves can travel undisturbed from one another arises from the fact that photons - as opposed to electrons - carry no charge, so they do not interact with one another. So in summary, there is interference, and the electromagnetic waves lie on top of one another just like waves in a pool. These waves can regain their individual identity at any time. This is how the dispersion and recombination of light takes place. When looking at superposition it is possible to see that the frequencies (beats) of the different colours of light combine to give a new colour, white. The highest frequency in this case violet light has the most beats and therefore interacts strongly with all of the other colours (frequencies, wave-lengths) red with the lowest frequency has the least interaction. Therefore, these colours are stacked on each other in order of their interaction with red on top and violet below. When white light meets with a dispersive medium such as a prism, (the slope of the prism makes it dispersive) the dispersion of light takes place. How does this happen. Here it is necessary to note that for dispersion to take place light has to enter the prism at an angle if light enters the prism at 90 degrees to the normal, no dispersion takes place.

When angle of incidence is 90 degree then angle of reflection (no refraction takes place) will also be 90 degree, which means that the light ray will get reflected along the same path but it means that the incident ray and reflected ray will join to form a straight line. Look at the image below:


Remember that when white light enters a prism it consists of different frequencies and wave-lengths stacked one on another. Therefore when light enters the sloped prism surface it is the lowest layer of light (violet) possessing the highest frequency that interacts with the prism first. The violet light looks around for its companion colours and seeing none of them enters the prism alone and gets deviated (refracted) according to Snell’s law. A miniscule instant later the ‘indigo’ colour enters the prism, looks around sees no other colours and is refracted. The same sequence continues through all the colours until finally red enters the prism and is refracted. In each case the angle of incidence is different and therefore the angle of refraction of each colour is also different.

The point to note here is that the dispersion of colours by a prism does not take place because light of different frequency travels at different speeds through the prism, dispersion takes place because the angle of incidence of each of the colours is different. Therefore, the statement that light of different frequencies travels at different speeds through a prism is one of the biggest canards of present days physics.

If for instance the angle of incidence is 30 degrees and the glass has a refractive index of 1.5 then according to snells law :

Solving Snell’s Law for sin θ2 yields

sin θ 2 = n1/n2 sin θ 1

Entering known values,

sin θ2 = 1/1.5 sin θ 1 = (0.666) (0.5) = 0.333

The angle is thus


θ2 = sin-1(0.333) = 19.5 degrees

Similarly: if the next angle of incidence is 35 degrees then:

sin θ2 = 1/1.5 sin θ 1 = (0.666) (0.7536) = 0.382

The angle is thus


θ2 = sin-1(0.382) = 22.45 degrees

and so on.

Therefore the angle of incidence has an appreciable effect on the angle of refraction, perhaps this is the explanation as to why there is such a great difference between the angle of refraction for violet and the angle of refraction for red when light is dispersed through a prism. It is certainly not due to the fact that light of different frequencies travels through the prism at different speeds!
 
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