What is Diamond?

Diamond, the world’s hardest naturally occurring material and mineral known, is a solid form of the element carbon. The atoms are arranged in a crystal structure called diamond cubic. They exist in a huge variety of colours. Also, they are one of the best conductors of heat and have a very high melting point.

What is Index of Refraction?

In the simplest terms, index of refraction, also termed as refractive index, is a quantifying comparison between the speeds of light as the light ray travels through one medium into another. When light enters a medium other than vacuum and air, the material’s atoms continuously absorb the light particles and re-emit those particles, slowing them down. This is the reason for change, which is magnitude reduction, in the speed of light.

So, index of refraction, which is a dimensionless quantity, is a number that tells us how much slower does a light wave travel through a specific medium that it would in a vacuum.

Higher the index of refraction, the higher is the density and slower will be the velocity of light in that particular medium.

Vacuum has an index of refraction of one.

These equations are applicable when light is travelling from a rarer medium to a denser medium. The calculation done will give us the refractive index for the denser medium amongst the two.

Definition 1: It is defined as the ratio of the speed of light in vacuum to the speed of light in a specific medium.  The equation is as follows:

n = c ÷ v

where, n is equal to the index of refraction

c is equal to the speed of light in a vacuum which is 3.0 x 10⁸ meters per second

v is equal to the speed of light in a specific medium

When a light ray travels from one medium to another and the angle of incidence is less than the critical angle, the light ray undergoes a process of bending according to Snell’s Law which is known as refraction.

Critical angle (θ_c ) is the angle of incidence (θ_i ) for which the angle of refraction (θ_r) is exactly equal to ninety degrees. Beyond this value the light ray undergoes total internal reflection.

Index of refraction can also be defined and calculated in terms of the angle of incidence and angle of refraction rather than the speed of light in the respective medium.

Definition 2: Index of refraction is the ratio of the sine of the angle of incidence to the sine of the angle of refraction.

n = sin (i) ÷ sin (r)

Index of Refraction of Diamond

In the case of the index of refraction of diamond, the light ray travels from vacuum or air and enters the diamond. So, the denser medium here is diamond and the rarer medium is vacuum.

To calculate the value of the index of refraction using definition 1 we need to know the speed of light in diamond which is 1.24 x 10⁸ meters per second.

If we substitute the values in the equation as follows, we get

3.0 x 10⁸ ÷ 1.24 x 10⁸ = 2.42   near to three significant figures

To put in into words, the speed of light in diamond is 1 by 2.42 times the speed of light in vacuum.

The value is dimensionless because the numerator and denominator have the same physical dimensions. So, they cancel off each other leaving only magnitude and no unit.

Diamond has a high index of refraction. It also has high dispersion when the ray is visible light but almost no dispersion when the rays are infrared waves.

Index of Refraction with Respect to other Material

Earlier we always considered the light ray to be entering the material from vacuum. So, the rarer medium was always vacuum. But this is not always the case; the light ray can be travelling from any other medium. Because of which we will alter the equation a little bit to be written as follows

Index of refraction of denser medium = speed of light in rarer medium ÷ speed of light in denser medium

The equation can be written in terms of the individual index of refraction od the materials with respect to vacuum. Which is as follows

Refractive index of denser medium = refractive index of denser medium with respect to vacuum ÷ refractive index of rarer medium with respect to vacuum

Example 1: We need to calculate the refractive index of diamond, which is the denser medium?

In the case where the light ray is travelling through glass and then entering the diamond. This will change the refractive index from what we had calculated earlier as the rarer medium and the speed of light in that medium has changed. So, to calculate this new value we need to know the value of the speed of light in glass which is 2 x 10⁸ meters per second.

If we substitute this value in the equation, we get the value of the index of refraction to be 1.6.

To put in into words, the speed of light in diamond is 1 by 1.66 times the speed of light in glass.  

Example 2: To find the refractive index of diamond with respect to water.

Using the second version of the equation we need to know the individual value which is index of refraction of water is 1.33 and of diamond are 2.42. Now just substitute these in the equation to get the value which is 1.80.

To put in into words, the speed of light in diamond is 1 by 1.80 times the speed of light in water.  

Why do Diamonds Sparkle?

One reason behind the beauty of diamonds is its property of sparkling. And the reason behind the sparkles produced is optical physics.

Diamonds have a combined advantaged of a low critical angle and a large index of refraction. Because of the low critical angle, which is only 24.4 degrees, the light that enters the material has trouble moving back out and therefore undergoes the process of total internal reflection repeatedly. Diamonds that are good -proper placement of facets and are very clear – only allow light to exit the diamond material in certain places. This results in the light rays undergoing multiple internal reflections and getting concentrated at the specific exit points available for the light rays to travel through. This causes it to sparkle. 

Also, the larger the index of refraction the more the light is reflected. So, if a diamond is compared to a piece of glass of the same shape size, the diamond, because of its large index of refraction, will reflect a larger number of light rays compared to the material glass. Hence, it will sparkle more than glass.

Used to Check Purity of the Diamond

The index of refraction can be used to check the purity of the diamond sample. The deviation of the value from the published value is a quick method of comparing samples. This is done by passing light through the sample and calculating its index of refraction. The more the index of refraction of the sample deviates from the published value of the pure sample of that material, the less pure is the sample in hand.

Common Mistakes

• While calculating the refractive index pay attention to the direction of the ray that it is travelling from the rarer medium to the denser medium.
• It will be helpful to remember some common values for the speed of light in particular mediums like glass and air.

Context and Applications

This topic is studied in

• Bachelors in Science (Physics)
• Class 12^th (Science)