Question

Define the following and use the terms to explain the sparkle or brilliance of a diamond.

*Refractive index
*Critical angle
*Total Internal reflection

Answer 1

Refractive index is defined as

The ratio of speed of light in vacuum to its speed in a specific medium.

The speed of light in a medium depends on the properties of the medium. In electromagnetic waves, the speed is dependent on the optical density of the medium. Optical density is the tendency of the atoms in a material to restore the absorbed electromagnetic energy. The more optically dense material is, the slower the speed of light. One such indicator of the optical density of a medium is the refractive index.

Refractive Index Formula

Refractive index is dimensionless. It is a number that indicates the number of times slower than a light wave would be in the material than it is in a vacuum. Refractive index, represented by symbol n, is the velocity of light in vacuum divided by the velocity of light in a medium. The formula of the refractive index is as follows:

n=c/v

Critical angle

If the light rays are travelling from a denser to a rarer medium, there might be an incident angle when the refracted angle becomes 90 , this incident angle is known as the critical angle for that pair of mediums.

The critical angle for a pair of mediums can be found out by using Snell’s law by putting refracted angle as 90 in the equation:

Here incident angle is critical angle for the two mediums.

Total internal reflection is defined as:

The phenomenon which occurs when the light rays travel from a more optically denser medium to a less optically denser medium.

Consider the following situation. A ray of light passes from a medium of water to that of air. Obviously, the light ray will be refracted at the junction separating the two media. Since it passes from a medium of a higher refractive index to that having a lower refractive index, the refracted light ray bends away from the normal. At a specific angle of incidence, the incident ray of light is refracted in such a way that it passes along the surface of the water.

This particular angle of incidence is called the critical angle. Here the angle of refraction is 90 degrees.

Total Internal Reflection

What is the Formula of Total Internal Reflection?

Total internal reflection	n1/n2=sinr/sini
Critical angle, Ө	sinΘ=n2/n1

Notations Used In The Total Internal Reflection Formula And Critical Angle

• r is the angle of refraction
• i is the angle of incidence
• n1 is the refractive index in medium 1
• n2 is the refractive index in medium 2
• Ө is the critical angle

Diamond:

When the incident ray falls on every face of the diamond such that the angle formed the ray is greater than the critical angle. The critical value of the diamond is 23°. This condition is responsible for the total internal reflection in diamond which makes it shine.

Diamond sparkle because of total internal reflection.

Along with total internal reflection, following are the three other factors that determine the sparkling of the diamond:

• Reflection
• Refraction
• Dispersion

Reflection takes place when the light ray hits the diamond and bounces back giving away an instantaneous shine. Refraction and dispersion are the reasons why the light ray travels through the diamond. Diamond acts like a tiny complicated prism through which the light ray travels at different angles.

Diamonds have a very high refractive index (about 2.42 compared to about 1.5 for glass). The secret that diamonds hold regarding their brightness and diamond sparkle is inside a diamond and is a mix of light refraction, total internal reflection & dispersion

The refractive index of diamond is 2.42. This means that the speed of light in diamond will reduce by a factor of 2.42 as compared to its speed in air.
In other words, the speed of light in diamond is 1/2.42 times the speed of light in vacuum