Why Do Diamonds Shine? Ft. Snell's Law

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Why Do Diamonds Shine? Ft. Snell's Law

Why Do Diamonds Shine? Ft. Snell's Law

Let's start off by labelling parts of an ideal diamond!

LET'S BACKTRACK...Diamonds are one of the hardest materials. They are three dimensional stones of carbon atoms held together by a strong colvalent bond; they are and isotope carbon. Diamonds are also one of the easiest mediums for light to travel through due to their transparency, which enhances the amount of light that travels through it. The reason diamonds "shine" and are seen to be "lit up" by the human eye is due to Total Internal Reflection (TIR) as well as a process called dispersion. You'll find that the terms brilliance, fire and scintillatio are also commonly used to desribe the light emitted from a diamond. Likewise, the angle of light, where is enters the diamond and the shape of the diamond changes the way the ray of light travels which will be described further on. Another factor that changes the way a diamond plays with rays of light rather than any other media is due to its refractive index. A diamond has a very high index of refraction of around 2.42. It is also dispersive- it's dispersive value being 0.044, as well as the critical angle of a diamond is actually considered very small, it is around 24.5 degrees, Due to these three aspects, the percentage of incident rays which go through total internal reflection before leaving the diamond is actually siginificantly larger than any other media. Various straight cuts and polishes of a diamond also ensure maximum internal reflection inside the diamond after the light ray refracts if it is done precisely. (See below image)WARNING: DO NOT WORRY IF YOU DO NOT FULLY UNDERSTAND THESE CONCEPTS! FURTHER EXPLANATION IS AHEAD!

Typically in an ideal diamond, light rays travel through the crown facets and go through 'TIR' twice at the pavilion facets before exiting out the table of the diamond. (You can see this through the red ray present in the image to the left). We can see how these light rays must be perfecty straight for this process to happen, which is why diamonds are polished- it ensures the "shine".

The blue ray of light on the other hand is going through a process known as dispersion (A.K.A "fire"). Fire is only apparent in diamonds and raindrops. As a recap, the dispersive value of a diamond is very high. Basically what dispersion is, is the ability of a stone (in this case) to split a white light ray into its other colour forums. Fire is known as a type of refraction. Fire is apparent all throughout a diamond however, not all of it is visible. The only dispersion visible is when a light ray refracts out of the diamond through the crown facets. This is what our eyes see as a optical indifference otherwise known as the rainbows throughout the diamond. When the light ray hits the air-diamond line the light hits at such an angle that the line divides into different wavelengthes which all protrude in different colours. This is due to the different refraction that occurs within each colour and due to the ideal diamond's cut, brilliance and dispersion are able to happen because they will never pass the critical angle in an ideal diamond. An ideal diamond is precisely cut to prefrom these functions to optimize maximum possible "shine" (otherwise known as reflection), however a diamond that is "too deep" will only reflect the light ray once and emit out and a diamond that is "too shallow" will just refract the light ray. These properties of a diamond also all ensure that light will never pass directly through it- due to refraction and reflection laws that occur at different angles of a diamond. (See below)

You need to know...Scintillatio is white light that is reflected from the stone, it is how the human eye sees the physical property of luster as well as the stones surface. Without scintillatio the surface of the diamond would not have "shine". Brilliance can be decribed as scintillatio. It is the ratio of light going out to the light going in. Visible scintillatio of the light that goes out of the diamond. However scintillatio that travels into the diamond help us see the shine as if all scintillatio was visible we would not be able to see the diamond itself due to the extreme amount of reflection. When the light ray travels into the stone, light bends towards the normal, as it hits the pavillion at an angle greater than critical, it will either exit through the table as white light is the initial incident ray entered through the crown facet or, the light will be dispersed is the initial incident ray came in through the table.

I am Willebrord Snellius! I am a Dutch atsronomer amd mathematician from 1591-1626. I formulated Snell's Law in 1621.

Let's Review Snell's Law...By using Snell's Law we can calculate three things:1. Index of Refraction2. Angle of incidence3. Angle of refraction_________________The formula:n1sinθ1= n2sinθ2_______________________What they mean:n1 and n2= the two incidences of refraction of the two mediaθ1 and θ2= The angle of incidence and the angle of refraction________________Application!Now let's try and find the angle of refraction for a diamond with an angle of incidence being 20 ° (from air to the diamond...)

Step #1: Rearrange the Equation*Isolate sinθ2*_____________sinθ2=n1sinθ1/n2_____________***If you do not know how to isolate the variable click here!***

Step #2: Substitute Values__________________Index of refraction in air (n1)- 1.00Index of refraction in diamond(n2)- 2.42Angle of incidence (θ1)-20°____________sinθ2= 1.00sin(20°)/2.42

Step #3: Eliminate "sin"__________________sinθ2= 1.00sin(20°)/2.42________________On calculator:Press 'sin' button, then press '2' then '0' and lastly press the equals sign. This should give you a very long decimal number. In this case rounding to the fourth decimal point of acceptable._________________sinθ2= 1.00(0.3420)/2.4_________________Now it is basic bedmas...You should end up with:sinθ2≈0.1413______________Now we need to isolate just 'θ2'This is reversing 'sin'.This is shown as 'sin-1'_______________Press 'shift' on calculator and then press 'sin'. This will give you sin-1(.Now press in your decimal number (0.1413).______________The end result is....θ2≈8.12 _____________The angle of refraction in this case is around 8.12 degrees.

Conclusion:Due to the fact that the processes that constantly reoccur in diamond-air media are mainly due the occurance of refraction, by knowing Snell's Law it can help us find the angles which exceed, nearly exceed or do not exceed the crtitical angle which will inform us if dispersion, brilliance or refraction is taking place and at what angles they are taking place at.

Citationshttp://www.gemology.ru/3dbook/eng/crypted/1_03.htmhttp://physics.stackexchange.com/questions/43361/why-do-diamonds-shinehttp://www.classicgems.net/Dispersion.htm http://www.jewelry-secrets.com/Diamonds/Diamond-Fire-Dispersion/What-Is-Diamond-Fire-Dispersion.html


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