Polarized Light Microscopy and Birefringence

Polarized light microscopy turns many colorless, transparent materials into brilliantly colored images. Recrystallized vitamin C, a starch grain or a thin slice of rock that looks dull in ordinary light can light up in bands of blue, magenta and gold between crossed polarizers. The property behind this is birefringence. This article explains what it is, how a polarizing microscope uses it, and how you can try it with very simple equipment.

The principle of polarization

Ordinary light vibrates in all directions at right angles to its direction of travel. A polarizer passes only light vibrating in one direction (one plane) and blocks the rest. The result is plane-polarized light.

If you put a second polarizer in the beam and rotate it 90° to the first, it blocks the light that the first one passed. The two are now “crossed,” and the field goes dark. In a microscope, the first polarizer sits below the specimen and is simply called the polarizer. The second sits above the objective and is called the analyzer.

With crossed polarizers and nothing on the stage, the field is black. Ordinary glass, water and most noncrystalline materials stay black too. Only materials that change the light’s polarization let any light through to the analyzer.

What birefringence means

Many materials are optically isotropic: light travels through them at the same speed whatever its vibration direction. Glass, water and table salt (a cubic crystal) are examples.

Other materials are anisotropic. Their refractive index depends on the direction in which the light vibrates. When plane-polarized light enters one of them, it splits into two rays vibrating at right angles to each other. Because each ray meets a different refractive index, one travels slower than the other. This splitting is called double refraction, and the material is said to be birefringent.

• Birefringence is the difference between the two refractive indices, often written Δn. Quartz is weakly birefringent, at about 0.009. Calcite is strongly birefringent, at about 0.17, and a clear calcite crystal on printed text shows a visible double image.
• Retardation is how far one ray falls behind the other on leaving the material. It equals the thickness multiplied by the birefringence. Thicker or more strongly birefringent specimens give more retardation.

When the two rays recombine at the analyzer, they interfere. Depending on the retardation, some wavelengths are passed and others canceled. That’s where the colors come from.

So, in answer to a common question: the “birefringence” of a material under polarized light is its ability to split light into two rays traveling at different speeds. Between crossed polarizers, that shows up as brightness and color against a dark background.

How a polarizing microscope works

Polarizer and analyzer

The basic setup is a polarizer below the condenser and an analyzer between the objective and the eyepiece, set at 90° to each other. Many student microscopes can be converted with a simple polarizing filter in the filter holder and a second one placed above the objective, for example in a slot or on top of the eyepiece’s field lens.

Rotating stage and extinction

A true polarizing microscope has a circular rotating stage. As you turn a birefringent crystal, it goes dark four times in each full rotation. Those dark positions, called extinction positions, occur when the crystal’s vibration directions line up with the polarizer and analyzer. Halfway between them, the crystal is at its brightest. The angle of extinction relative to a crystal’s edges helps mineralogists identify it.

Compensators and the first-order red plate

A compensator is a plate of birefringent material of known retardation, inserted into the light path. The most common is the first-order red plate, also called a full-wave or lambda plate. It turns the dark background a magenta color. Birefringent features then shift toward blue or yellow depending on their orientation, which tells you which of their directions is “fast” and which is “slow.” This is the basis for describing a material as having positive or negative birefringence (more precisely, positive or negative elongation for long crystals and fibers).

Research and petrographic polarizing microscopes also use strain-free objectives, because ordinary lens glass under stress can be slightly birefringent itself, and a Bertrand lens for viewing interference figures. You don’t need these to start.

Interference colors and the Michel-Lévy chart

Interference colors follow a predictable sequence as retardation increases. Grays and whites come first, then yellow, orange and red, then repeating “orders” of blue, green, yellow and red that grow paler. The Michel-Lévy chart maps these colors against retardation, thickness and birefringence. Geologists use it with rock thin sections of a standard thickness (traditionally about 30 µm) to estimate the birefringence of the minerals they’re looking at.

For hobby use, the chart is mostly a way to understand what you’re seeing. A crystal that shows bright, high-order colors is either thick or strongly birefringent, while gray or white means low retardation.

What you can look at

You don’t need rare samples. Good birefringent subjects include:

• Recrystallized chemicals: vitamin C (ascorbic acid), citric acid, Epsom salt, urea and sugar. Dissolve a little in water or alcohol, put a drop on a slide and let it dry, ideally slowly.
• Starch grains: from potato, rice or wheat. Each grain shows a dark “Maltese cross.”
• Fibers: cotton, silk, nylon, polyester and wool. Fiber identification is a classic application.
• Cellophane and clear tape: stretched plastic is birefringent. Layered strips of tape on a slide make colorful abstract images.
• Plant tissue: cell walls, crystals inside cells and some stem sections.
• Animal tissue: muscle fibers and collagen in prepared histology sections.
• Rock and mineral thin sections: the traditional heart of polarized light microscopy.
• Stress in plastics: transparent plastic rulers or molded parts show stress patterns, which is the same principle used in engineering photoelasticity.

What birefringence means in gout

In medicine, polarized light microscopy is a standard laboratory method for examining joint fluid. Gout is associated with monosodium urate crystals. These are typically needle-shaped and strongly negatively birefringent. With a first-order red compensator, they look yellow when aligned parallel to the compensator’s slow axis and blue when perpendicular to it.

A related condition, calcium pyrophosphate deposition (sometimes called pseudogout), is associated with crystals that are typically rhomboid or rod-shaped and weakly positively birefringent, with the opposite color pattern.

This is a diagnostic test performed by trained laboratory staff on fluid taken by a clinician, and the result is interpreted alongside other findings. It isn’t something to attempt at home. If you have joint pain or swelling, see a healthcare professional.

Phase contrast vs polarizing microscope

Both techniques reveal transparent specimens, but they respond to different properties:

Phase contrast works by turning phase shifts in light, caused by small refractive index differences, into brightness differences. A polarizing microscope ignores those differences unless the material is birefringent. The two are complementary. A living cell may look nearly empty between crossed polarizers but full of detail in phase contrast, while a crystal can look flat in phase but vivid in polarized light. For how phase contrast works, see brightfield vs phase contrast microscopy.

Another technique, DIC microscopy, also uses a polarizer and an analyzer, but it adds special prisms to create relief contrast in non-birefringent specimens.

How much does a polarized light microscope cost?

Costs vary over a very wide range:

• DIY: two pieces of polarizing film, or a polarizing filter kit for your microscope, cost very little and are enough to see birefringence in crystals, starch and fibers.
• Student polarizing microscopes: basic microscopes with a rotating polarizer and analyzer cost more than standard student models, and some include a simple rotating stage.
• Petrographic and research polarizing microscopes: instruments with strain-free optics, centering rotating stages, compensator slots and Bertrand lenses cost far more, often many thousands, new.

Used petrographic microscopes from universities and geology labs sometimes come onto the secondhand market and can be good value if the optics are clean and the stage rotates smoothly. Our used microscope checklist covers what to inspect. Prices change often, so compare current listings rather than relying on any single figure.

Tips for good results

• Cross the polarizers carefully. Rotate one filter until the empty field is at its darkest.
• Use low to medium power first. Crystals and fibers often look best at 4x or 10x.
• Rotate the specimen. If you don’t have a rotating stage, turn the slide by hand, or rotate both polarizers together while keeping them crossed.
• Grow crystals slowly. Slow drying gives larger, more colorful crystals. Covering the drop loosely or warming it gently changes the patterns.
• Combine with other techniques. Partly uncrossing the polarizers, or adding a colored filter or a piece of tape as a homemade retarder, changes the colors dramatically.

For a broader look at how polarized light compares with darkfield, phase contrast and fluorescence, see our overview of microscope contrast.