Birefringence, as the prefix 'bi' implies, is 'two' refringences. Refringence loosely means refractive power. Polarizing microscopy makes use of the phenomenon of the birefringence of light passing through substance.

Refraction is a very common property of matter. We have all seen how objects in a pool of water appear to be located somewhat larger than they should be, or somewhat away from their actual position in the water. Another common example of refraction is in a prism, where light is refracted or 'bent' as it passes through the prism, to emerge as a spectrum of color on the opposite side.

[[image:prism width="359" height="271"]]

Anisotropy simply means directionally specific, as opposed to isotropy which means that something is the same in all directions.

The refractive index is simply the degree to which the path of light travel is bent. A higher refractive index means that the direction is changed more than for lower indices.

Refringence, also commonly means refractive power. However, use of the word birefringence carries with it the additional connotation that not just any light, but //polarized// light is being refracted, or that unpolarized light is being polarized into two planes.

there is one more basic concept to introduce here, that of polarization, before moving on. Light, (photons,) are said to cause electromagnetic waves to 'ripple' out at right angles to the direction of their travel. A good analogy for this effect is to consider dropping a pebble into a pool calm water. The pebble drops straight down to the bottom of the pool, and ripples of water spread out in every direction along the surface of the water, //at right angles// to the the direction of the pebble in other words. Light waves are regarded as operating according to this scheme as well, however when we speak of polarizing light, we mean that the 'ripples' only occur in one plane rather than in a circle. To put this to our pebble analogy, it would be like if you dropped the pebble, and a ripple spread out only in a single straight line to the east and west, rather than in every direction of the compass!
[[image:ripple.jpeg]]

When we speak about polarization, we mean that the entering light is 'rippling' in 360 degrees, but that the exiting light is sending out ripples in only one east-west, or north-south direction.

When we speak of refraction, we mean that light enters a substance at an angle, and is bent in a new direction while passing through the substance.

When we speak of birefringence in the context of polarizing microscopy, we mean that incoming polarized light is simultaneously refracted into two directions while passing through the substance. Some prisms, as the one shown above, do not split light according to polarity, but some prisms, such as the Nicol's prism shown below, split light according to its polarity, whether or not it is isotropic or anisotropic.



[[image:360px-Nicol-prism.png width="368" height="253"]][[image:birefringence.jpg width="248" height="253"]]
This picture is of a Nicol's prism, which illustrates the idea that the degree to which light is bent can be dependant upon the plane it is rippling in as it encounters the prism. East-west light, (the o-ray) is more strongly refracted than the north-south, (//e//-ray,) Birefringence microscopy is very similar to this. You need only imagine that if all of the incoming light were east-west, that the light would still be split into two paths; east-west and north-south. (shown below)

[[image:polarizedheader.jpg]]
Looking carefully at the red and blue sections of light, we see that the incoming plane-polarized red light is split into two planes; one red and one blue. The microscope is capable of visualizing the difference of polarities of the light to the observer, and so objects normally transparent to the naked eye can be seen as a result of the difference between the two rays of light emerging from the sample.

So, we can see that anisotropic substances, (@ 90% of known substances,) act as prisms of a sort, and which can be visualized according to the differences between the entering and exiting light.

There is a third related effect which substances can have upon light: //optical rotation.// Optical rotation can be most easily defined as a plane, (or all planes,) of light being rotated clock-wise or counter-clockwise while passing through a substance. This effect is distinct from birefringence. Although from the above picture of the microscope the 'red' light seems to have been rotated 90 degrees upon passing through the substance, what has actually occurred is somewhat more complicated. The incoming, or 'incident' light is composed of photons of two opposite 'spins.' The birefringent substance separates the photons of the two spin types into opposite planes of polarization.

So, we see that light can be split out by the common prism by refracting different wavelengths of light more strongly than others.. The prism shows us that the longer wavelengths, (red,) are refracted less than the shorter wavelengths, (violet.) (refraction)

Or it can be split out according to the plane of rotation of light, refracting some planes more strongly than others, depending upon the orientation of the substance through which it passes. (refringence)

Or it can be split out according to the spin of the photons. (birefringence)

Or it can be rotated. (optical rotation)

Polarizing light microscopy used to detect birefringence is involved with light which is changed according to the way a single plane of light is refracted into two planes of light.


[[image:nonrefring.jpg width="445" height="274"]][[image:refringe.jpg]]


The picture on the left is of filamentous sulfur bacteria taken without the polarizing microscope. The picture on the right is taken with a polarizing microscope. Notice all of the bright specks in the picture on the right. These specks are accumulated elemental sulfur.

Elemental sulfur has a rather high index of birefringence, meaning the difference between the angle at which the two emerging rays of light strike the recombiner of the microscope. Not only is the incident light split according to spin, but also each type of ray is refracted at a different angle as it passes through the substance under observation.

[[image:birefringencefigure4.jpg]]

Crystal have the most obvious properties of birefringence, due to the regular nature of the alignment of their atoms into a lattice structure. Light can be either aligned with the crystal, or unaligned, and the degree of birefringence will change depending upon alignment. The polarizer and analyzer of the polarizing microscope can be rotated in order to orient the light towards, or away from alignment with the crystal or other substance under observation.
In the case of elemental sulfur, each molecule is an 8-atom crystal of sulfur at least, and further crystallization can result in crystals visible to the naked eye.

[[image:sulfur1.jpg]][[image:s8.gif width="225" height="225"]][[image:sulfurs8a-fig1-alpha.jpg width="166" height="224"]][[image:sulfurs8a-fig1-gamma.jpg width="215" height="226"]][[image:sulfurs8a-fig1-beta.jpg width="200" height="229"]]

While the large crystal may be visible to the naked eye, the sulfur crystals in the bacteria of the above picture are still too small for observation. However, because there are so many of these microcrystals in the bacteria, we are assured that there will always be plenty in every orientation,so that some degree of birefringence is observable through the microscope without having to adjust the polarizer or the analyser filters, (see above picture of microscope.)

However, as may be the case with geological samples or metals, where the entire substance is in a 'fixed' position, visualization can be obtained by rotting the polarizer dial until the incident light is aligned with the lattice of the substance.