Refraction:

The bending of light when it passes from a rarer medium (Air) into a denser medium (Gemstone).

Single Refraction (Isotropic):

Light passing through a substance is bent from its original path but emerges as a single ray. Only occurs in gem minerals belonging to the cubic crystal system or amorphous materials.

Double Refraction (Anisotropic or Birefringence):

Light passing through a substance is split into two rays, which travel at different velocities causing differing amounts of refraction. Occurs in gem minerals belonging to all other crystal systems.

Example: Doubling of the back facets as seen in either Zircon or Peridot. 

Refractive Index:

Formula:

R.I. =

Velocity of light in air Velocity of light in a gemstone

Example: Diamond

R.I. =

186,000 miles per second 77,000 miles per second

= 2.42

In 1621, W Snell, a professor at Leyden University, discovered the

"Law of Refraction" which states:

1. When a ray of light passes from one medium into another, there exists a definite ratio between the sines of the angle of incidence (NOI) and the angle of refraction (NOR), which is dependent only on the two media and the wavelength of light.
2. The incident ray, the normal (at the point of incidence) and the refracted ray are all in the same plane (a perfectly level surface).

Methods Used to Determine Refractive Index

Approximation of R.I. by Immersion

When a specimen is immersed in a liquid having a similar R.I, the relief is low (i.e the edges tend to disappear). To approximate the R.I. of an unknown specimen, immerse the stone in one liquid after another until one is found in which it most completely disappears.

Liquids used:

Water	1.33
Bromoform	1.59
Alcohol	1.36
Iodobenzene	1.62
Petrol	1.45
Monobromonaphthalene	1.66
Benzine	1.50
Methylene Iodide	1.74
Clove Oil	1.54

Caution: Avoid using porous stones in the above liquids (ie Opal, Turquoise, Chalcedony, Lapis Lazuli)

Critical Angle Refractometer

The refractometer is based on the principle of "Total Internal Reflection" which occurs as incident light rays strike at angles greater than the critical angle (when travelling from a denser medium into a rarer medium) and are reflected back into the denser medium.

It is an optical instrument arranged to show the critical angle of total internal reflection as a shadow edge, on a scale calibrated in refractive indices.

Total Internal Reflection

The name applies to the phenomenon which occurs when a ray of light travelling through a denser medium to a rarer medium at an angle greater than the critical angle suffers complete reflection back through a denser medium.

Critical Angle of Total Reflection

That angle where a ray of light, travelling from a denser medium to one less dense, is refracted at an angle of 90 degrees to the normal, that is it skims along the surface separating the two media. Any further increases of the light ray angle would cause the refracted ray to turn back into the first medium where it obeys the ordinary "Laws of Reflection".

Disadvantages:

 
1. Cannot measure the R.I. of an unpolished stone or rough.
2. The top end of the refractometer is limited by the R.I. of the refractometer glass prism and the contact liquid.
3. The highest reading is attainable using high lead oxide content glass which is soft and susceptible to scratching.

Procedure:

1. Place a droplet of the contact liquid on the glass prism.
2. Carefully lower the table of the gemstone onto the liquidand gently press down to ensure optical contact.
3. Switch on the light source and look for the shadow edge on the calibrated scale.

 Distant "Vision" for Cabochons

1. Apply the smallest droplet of R.I. liquid onto the glass prism. If the drop is too large, most of it disappears beyond the view of the refractometer.
2. Rest the cabochon upside down on the spot.
3. View 12 to 18 inches away.
4. Locate the spot in the eyepiece.
5. Move your head up and down until half of the spot is dark and half is light.
6. When the spot is all light, the R.I. of the stone is lower.
7. When the spot is all dark, the R.I. of the stone is higher.

Determining Birefringence

There are a number of ways of determining whether a gemstone is doubly refractive.

1. The Refractometer
2. The Polariscope

The Refractometer

Doubly refractive stones will display two shadow edges when viewed through the eyepiece of the refractometer. By turning the stone carefully on the glass prism, maximum and minimum birefringence can be calculated by subtracting the lower shadow edge from the higher one. This can be a valuable piece of information to a gemmologist seeking to identify an unknown gemstone.

Optical Character

Anisotropic gemstones possess either one (uniaxial) or two (biaxial) directions along which light is not doubly refracted. These directions of single refraction are called "Optic axes".

Both amorphous and crystalline substances can be grouped under these three headings:

Isotropic : Cubic or amorphous.

Uniaxial : Tetragonal, hexagonal and trigonal.

Biaxial : Orthorhombic, monoclinic and triclinic.

This provides yet another valuable piece of information to the gemmologist.

Uniaxial: Show a fixed refractive index for the ordinary ray and a varying one for the extraordinary ray.

Biaxial: The R.I. of both rays or shadow edges vary.

Optical Sign

Uniaxial

Positive: The moving shadow edge has a higher R.I. than the stationary edge.

Negative: The moving shadow edge has a lower R.I. than the stationary edge.

Biaxial

Positive: If the higher edge moves more than halfway towards the lowest shadow edge.

Negative: If the lower edge moves more than halfway towards the highest reading.

Polariscope

It is sometimes sufficient simply to know whether a gem stone is singly or doubly refractive. For this uncomplicated test, the polariscope comes into its own.

Consists of:

1. Built-in light source.
2. A protected polarising filter over the light source which acts as a platform for the gemstone.
3. A second polarising filter through which the stone is viewed.

 Procedure:

1. Place the stone to be tested on the lower platform.
2. Switch on the light source.
3. Rotate the top filter until it is in a "Crossed" position and does not allow light passing through the lower filter to pass through the upper filter.
4. Rotate the stone 360 degrees.

Reaction:

1. If the stone is singly refractive it will remain dark as it is turned 360 degrees.
2. If the stone is doubly refractive it will transmit light in four distinct positions (at 90 degree intervals)
3. If a crypto-crystalline material is viewed through the filters, it will appear uniformly bright in all positions. This is due to the random orientation of the many minute crystals of which the gemstone is composed.

Caution:

If the stone is viewed along an "Optic" axis (a direction of single refraction) it will appear dark as it is turned.Some stones show "Anomalous Birefringence" caused by internal strain within the stone.

Examples: Spinel, Glass, Diamond.

The Critical Angle

The sine of the critical angle can be calculated using the following formula:

Formula:

Sine of critical angle =

R.I. of the surrounding medium R.I. of gemstone

To determine the critical angle of a gem mineral in air:

Formula:

Sine of critical angle =

1 R.I. of gemstone

Example:

Diamond Sine of critical angle =

1 2.42

= .413

The angle itself can be derived from a set of trigonometric tables

Critical angle = Arc sine 0.413 = 24.26 degrees

Example:

Quartz Sine of critical angle =

1 .649

= 1.54

Critical angle = Arc sine 0.649 = 40.30 degrees

This means:

That if a ray of light travelling through a diamond strikes the pavilion facets at an angle greater than 24.26 degrees, it will be reflected back within the stone (Total internal reflection).

If is strikes the pavilion facets at an angle less than 24.26 degrees, it will not be reflected back into the stone.

To achieve "Total Internal Reflection", the lapidary must adjust the angles of the crown and pavilion facets so that the majority of the rays meet the interior faces of the pavilion facets at angles, to the normal, which are greater than the critical angle.

If the angles are wrong, the rays will pass out through the pavilion facets and the stone will appear dark.

It is also important that the rays reflected back from the pavilion facets meet the crown facets at angles less than the critical angle. If they fail to do this, they will undergo "Total Internal Reflection" again instead of being returned to the eye.

Information rpovided by: http://www.geogem.com