A polarizing microscope is a tool that uses the specialized properties of plane polarized light. Although I have not used a polarized microscope, I have done photostress analysis of mechanical components and used polarizing filters in photography. This is a fairly complex principle that is not easy to describe without figures. A Nikon website has some information on this instrument: http://www.microscopyu.com/articles/polarized/polarizedintro.html There are two types of polarizing filters: plane and circular. Polarized light measurement tools use a linear polarizing filter to create plane polarized light from normal light. Light is composed of waves oscillating in all directions, with no coherent alignment. A polarizing filter passes only those light waves that are aligned with the direction of the polarizing element. Light waves that pass through a plane polarizer all have the same direction of 'vibration'. Any lights waves that are not aligned with the orientation of the polarizing filter are blocked. Circular polarizers are similar in concept, except that the light passed through the filter is aligned with a rotating vector (a somewhat more difficult picture to visualize). Light can become plane polarized by reflecting off of a surface, such as a mirror or water. When this plane polarized light is passed through a linear polarizing filter, differing amounts of light will be passed depending on the orientation of the filter. If the polarizing filter is placed in line with the axis of vibration, all of the light will pass through the filter. As the filter is rotated, less light will pass through the filter until, when the filter is oriented 90 degrees from the axis of vibration, all light is blocked. A polarizing filter can be used in photography to block reflected light from the surface of water or glare off of a window, for example. This approach can be used to examine the structure of a material or the amount of structural stress in an object. In stress analysis, light is first plane polarized and then passed through a transparent plastic material that has a plane structure or reflected off the surface of a an object that has been coated with such a material. Changes in the structure bend the axis of vibration of the polarized light. The light is then passed through a second plane polarizing filter. The materials used to coat objects or to build structures from are designed to bend the light in a predictable way. The amount the polarized light has 'bent' passing through the material or reflecting off the material on which it is coated can be measured using an instrument that shows interference fringes. The number and location of the fringes is directly proportional to the amount of stress in the material. The fringes are counted to obtain numerical stress values and concentrations of fringes show where stress risers exist in the structure. In minerology, thin slices of material are cut and polarized light passed through them. This can reveal the nature of the underlying structure. You should be able to find information on "polarizing microscopes" using a search engine. There is a lot of material available on "photoelastic stress analysis", which uses the same principles. Hope this has helped, even without any pictures available.

Red John's answer is a very good one; However, as he has admitted that he has not used a polarizing microscope to do geology, I thought that I would fill in these details. First of all, in a petrographic microscope (the type of polarizing microscope used in geology), we only use plane polarizing filters. (At least I had never heard of the circular ones until I read John's answer.) When examining a rock sample, we will usually use both plane-polarized light and cross-polarized light. For plane-polarized light, the light passes through a plane polarizing filter before it reaches the sample. For crossed-polarized light, another plane polarizing filter is added to the optical path between the sample and the observer's eye. This second filter is oriented with its lines at right angles to those of the first polarizer. lokki6, in his description of pleochroism pretty well describes what we see when looking at a sample in plane-poloarized light. However, the real fun is in cross-polarized light. many minerals will change the orientation of the light as interacts with the mineral. When viewed with cross-polars, these minerals can produce spectacular colors in a phenomenon known as birefringence. By examining these colors, we can tell something about the internal structure of the mineral. Most of the time when examining rock samples with a petrographic microscope, we do use things called thin sections. For these, we will mount a thin sample of the rock on a glass slide and then grind the rock sample down until it becomes transparent. An economic geologist will often not bother with this. He will be more likely to use think section because the minerals in which he will be interested are opaque even in thin section. So, this brings us to another characteristic of petrographic microscopes. They usually have two light sources, one in the base for examining a thin section in transmitted light (that is light that passes through the sample) and one higher up for examining the sample in reflected light. Both light will be plane polarized so that the sample can be viewed in both plane- and cross-polarized light using either source. If you want to know more about this and to see some examples, you might want to check out PetroGlyph (http://www.geology.byu.edu/Petroglyph/default.htm). It is a computer simulation of a petrographic microscope that I helped to create while I was working on my Master's Degree. You can find there some actual photographs and a demo of the program (I don't know how well the demo will work on a modern computer though. I know that it won't work in Mac OS X, but I am not sure about post 98 versions of Windows.)

HOW DO MICROSCOPES WORK AND HOW IT CHANGES LIGHT