Birefringence using a Motic Polarizing Microscope and the Michel-Lévy Chart (Part I)

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Polarizing microscopes like the Motic BA310 Pol can be utilized for both qualitative and quantitative analysis of a wide range of anisotropic substances. In this article, I will describe how to use a polarizing microscope to distinguish between isotropic and anisotropic materials, determine the refractive index, detect Pleochroism and learn how to use a Michel-Lévy chart to estimate Birefringence which can be used as an aid to identify minerals and fibers.

Motic BA310 Pol Labeled

The Motic BA310 Polarizing microscope shown above features a flip-out condenser, rotating stage, center-able objectives, Bertrand lens for viewing interference patterns of crystals (conoscopy), a rotatable analyzer with Vernier scale, and a slot for accepting retardation plates. The condenser and objectives are strain-free.  It includes all the features of a modern analytical polarizing microscope.  A digital camera at the top of the microscope permits photographic documentation and recording HD movies. I recently reviewed the Motic BA310 microscope (R. Berdan, 2021).

Anisotropic substances act as beam splitters dividing incoming polarized light into two orthogonal light rays that travel at different velocities through the crystal and emerge out of phase and undergo interference. If the thickness and refractive indices of the two rays are sufficiently different certain wavelengths undergo destructive interference resulting in interference colors. The colors can be compared to a Michel-Lévy Interference chart so that the birefringence, which represents the two different refractive indices of the substance, can be determined. Birefringence, although not completely unique, can be used to help identify many substances and is a constant.

Michel-Levy Interference Chart with Motic BA310 POL
Michel-Lévy Interference Chart that comes with the Motic BA310 microscope.

The Michel-Lévy Interference color chart comes in many varieties and graphically relates the thickness, retardation (optical path difference), and birefringence (numerical difference between the principle refractive indices) for views of transparent or lightly-colored substances. These characteristics allow unknown materials to be identified.  The Michel-Lévy chart along with a polarizing microscope is used to identify minerals, synthetic textile fibers, chemicals, food processing ingredients, biologicals, abrasives, drugs, catalysts, ores, fertilizers, and combustion products (J.G Delly, 2017, Watanbe et al. 1985).

With polarizing microscope substances that appear bright on a dark background between crossed polarizers are anisotropic, that is they have more than one index of refraction.  Anisotropic substances which are uniaxial possess two principle refractive indices and belong to the tetragonal or hexagonal crystal systems.  Biaxial crystals have three principal refractive indices and belong to the orthorhombic, monoclinic, or triclinic crystal systems.

Birefringence of anisotropic substances can be approximated by comparing interference colors of the specimen to those of the Michel-Lévy color chart, or it can be done precisely using the compensation method described in Part II of this article. Both methods require knowledge of the specimen thickness.

Table of Contents: 

  1. How to determine the Thickness of the Specimen?
  2. How to measure the Refractive Index?
  3. The Becke Line Method to determine Refractive Index
  4. How to determine whether a Mineral is Opaque or Transparent?
  5. How to determine Pleochroism with a Polarizing Microscope?
  6. Minerals that exhibit Pleochroism
  7. Isotropic versus Anisotropic Substances
  8. What is Birefringence?
  9. How to use Michel-Lévy Interference Chart to estimate Birefringence?
  10. How to calculate Birefringence?
  11. Summary

Determining the Thickness of the Specimen

Prepared mineral slides are made 30 microns thick (0.030 mm), whereas cylindrical fibers can be measured using a calibrated eyepiece reticle. Non-cylindrical fibers or thin films can be cut with a razor at 45 degrees and the horizontal projection of the cut measured. Small fragments can be measured by rolling them or pushing the coverslip until the particle rolls over. Rolling the particles is sometimes facilitated by immersing them in a viscous liquid e.g. oil immersion fluid.   

A fourth method to measure thickness involves determining the vertical travel of the microscope stage using the fine focus graduated in 1-2 microns per division depending on the microscope. To do this choose a 40X objective and focus on the top of the specimen, focus in only one direction to the bottom of the specimen sitting on the microscope slide, and note the number of graduations which is the height of the specimen in microns. However, this is not the true thickness. The position of the lower surface is influenced by the refractive index of the mineral and the refractive index of the surrounding medium.  The true thickness D is shown in the formula below:


D = Refractive index (RI) of crystal/Refractive index of air 1.0003 (or substitute RI of the mounting fluid) x focus height

E.g. For Quartz RI = 1.55

D= 1.55/1.0003 x focus height (10 divisions 2 µm/div) = 31 µm


For specimens in the air, the refractive index (RI) can be ignored, however when using glycerol substitute RI=1.47, Canada Balsam RI 1.5, or Immersion oil RI = 1.518. Using Canada Balsam the calculated thickness above would be 20.7 µm (after M.M. Raith et. al. 2011). If the mineral and refractive index isn’t known you can measure or estimate the refractive index using the Becke line method.

Measuring the Refractive Index

Refractive index is the single most important optical characteristic for the identification of non-biological unknown material. Refractive index is a measure of the extent to which light is slowed as it passes through the substance in different directions and is compared to the fixed velocity of light in a vacuum. The more the light is slowed as it passes through a substance the higher the refractive index.


Refractive index (RI) = Velocity of light in a vacuum
                                    Velocity of light in the substance

                                        RI = 3 x 1010 cm/s in a vacuum
                                               2 x 1010 cm/s in glass

                                        RI = 1.5


Elements with a higher refractive index are more effective in slowing down light (Delly 2017). Refractive index can be measured in a variety of ways. One simple method is to view the particles or fibers with a light microscope when the specimens are mounted in solutions of varying refractive index. There are several companies that sell solutions of different refractive index and it is possible to make your own standards One can make different concentrations of sugar solutions or mix clove oil and nitrobenzene and then measure the solutions refractive index with a refractometer. Below are glass chips made by crushing glass coverslips with a mortar and pestle. I embedded the glass in air, water, and immersion oil fluid under a coverslip. When the particles of glass match the refractive index of the surrounding medium it becomes transparent with little to no relief and it indicates the specimen and medium have the same refractive index.

Glass chips Bright Field Microscopy

Above are photomicrographs of glass chips from a crushed coverglass viewed by bright field microscopy at 100X in different refractive index medium  A) medium was air RI = 1.0003,  coverglass chip has good contrast and relief B) coverglass in water RI = 1.3 coverglass, the chip still exhibits a strong relief  C) Coverglass chip in immersion fluid  RI = 1. 5810, the glass chip becomes transparent with little relief indicating it has the same refractive index of the medium.

Temperature affects the refractive index and therefore refractive index is usually measured at a standard temperature of 25˚C in the United States and 20˚C in Europe. There are a variety of other methods to measure the refractive index of glass in forensic examinations (SWGMAT, 2004). 

The Becke Line Method to determine Refractive Index

If an unknown substance does not disappear and one isn’t able to find a matching refractive index liquid, the refractive index can still be estimated using a microscope and the Becke line method.

A Becke line is a bright halo near the edge of translucent particles or fibers immersed in a medium. The Beck line method can be performed using bright light or phase contrast microscopy. The line is not always easy to see, it helps to reduce the light intensity and close down the condenser diaphragm.  Sometimes using a green or orange filter may help. The Becke line moves towards and into the substance of higher refractive index when one increases the focal distance – i.e. moves the objective further away from focus. On modern microscopes, this means moving the stage down with fine focus.  See below.

Becke line method photographed with the Motic BA310 microscope using phase contrast while viewing a human scalp hair. The three small arrows point to the Becke line. As the stage was lowered (A to F) and the focal distance increased the Becke line can be seen to move inside the hair indicating it has a higher refractive index than that of the surrounding solution (water RI = 1.33). I repeated this with oil immersion fluid (RI = 1. 5810) and the Becke line moved outward into the medium. From these photos, I was able to determine the refractive index of my scalp hair was between RI= 1.333 (water) and R= 1.5810 (oil immersion fluid). To determine the value more accurately would require a series of solutions between these two refractive indices.

A study of the Refractive index of hair based on samples from 92 people and 25,000 measurements using the Becke line and oblique light method reported a mean RI for hair to be 1.548  (M.D. Greenwell et al. 1941). These researchers made a series of standard solutions of varying refractive index by mixing clove oil and nitrobenzene to create standards between  RI= 1.541 to RI=1.553.  The standards were calibrated using an Abbé refractometer and they reported their measurements are accurate to ± 0.001 and the values represent the refractive index of the cuticle of the hair, not the cortex (middle). This data is of value in Forensic science. 

Determining whether a Mineral is opaque or Transparent

Some minerals exhibit varying degrees of transparency. All minerals with a metallic luster are opaque. Transparency isn’t normally used to identify minerals; however, it can eliminate some mineral possibilities. Some minerals may appear transparent with a Polarizing microscope but may be clouded by opaque inclusions (Friedman 1997).

Mineral Section in Bright Field Microscopy
A) mineral section viewed by bright field microscopy showing an opaque region (black) and B) the same section in crossed polarized light, 40X.

Determining Pleochroism with a Polarizing Microscope

Pleochroism is visible as a change in color of anisotropic (double refractive) substances when viewed in white light from different directions and plane polarized light. When polarized light enters crystals that exhibit Pleochroism it is split into two rays that are perpendicularly polarized.  Each of the two rays travels at different speeds and are differentially absorbed as they travel through the material, thus the mineral exhibits different shades of color when rotated in plane polarized light (no analyzer is used).

To study pleochroism only white light or a single polarizer is used. You place the mineral e.g. Tourmaline on a microscope slide on a circular rotating stage. When the stage is rotated and the crystal is viewed at different angles the substance appears in different shades of color.


Pleochroism is a property where some minerals appear to be a different color depending on the direction in which they are observed (Diagram: University of Granada Spain.)

Pleochroism two plates cut from same mineral

In the above diagram, we can see how when two plates are cut from the same mineral but in a different direction (A and B), the color may appear different. When the incident white light (1), composed of the six principle colors (2), reaches the crystal, the orange (A) or green (B) component are absorbed (3), allowing the rest (4) to pass through, but as the complementary pairs of colors using white light (5), we see only the color whose complementary pair is absent (6). (Diagram: University of Granada.)

The situation above occurs when the mineral or fiber is viewed by natural light, but if we use polarized light, we introduce an additional factor apart from the cut of the crystal, the direction of vibration of the light will also intervene (see diagram below).

Polarized light passing through minerals

The image above shows what occurs when plane polarized light is passed through some minerals and then they are rotated. In case (1), the light arrives vibrating horizontally and the mineral is seen as red because for this direction the green wavelengths are absorbed.  In case (2), the direction of vibration of the polarizer is rotated 90º the crystal is seen as blue (the light corresponding to yellow-orange have been absorbed. Normally, the polarizer remains fixed in the microscope and the mineral is turned on a rotating stage, case 3. The result is the same when the polarizer has been turned (case 2). Source - University of Granada.

Polaroid polarizing filters were originally made of microscopic herapathite crystals. Its current H-sheet form is made from polyvinyl alcohol (PVA) plastic with an iodine doping (iodine is incorporated into the crystal lattice). Stretching of the sheet during manufacture causes the PVA chains to align in one particular direction. So incident light polarized parallel to the chains is absorbed by the sheet and only light polarized perpendicularly to the chains is transmitted (Polarizers Wikipedia). Thus Polaroid polarizing filters use Pleochroism to create polarized light. A modern type of absorptive polarizer is made of elongated silver nanoparticles embedded in thin (≤ 0.5 mm) glass plates and they produce more efficient polarizing filters.

Some uniaxial minerals exhibit two colors called dichroism. Dichroic crystals are hexagonal, trigonal, or tetragonal. Biaxial crystals may be associated with three colors called trichroism and are associated with orthorhombic, monoclinic, or triclinic crystals. Pleochroism is found in some synthetic textile fibers, chemicals, food ingredients, biological agents, drugs, minerals, and gemstones.

Minerals that exhibit Pleochroism


exhibits violet and orange when rotated in plane polarized light.


exhibits light purple and purple when rotated in plane polarized light.


exhibits light purple to very light purple when rotated in plane polarized light.


blue asbestos – appears gray-blue when rotated in plane polarized light.


Isotropic versus Anisotropic Substances

When a polarizing microscope is used with the polarizer and analyzer in the crossed orientation so that no light travels through both filters the background will appear black. You may see some stray or refracted light if your microscope objectives and condenser are not strain free, but it can still be used to identify anisotropic materials. Isotropic substances will appear transparent when rotated between the crossed polarizers. Glass for instance is isotropic and so is table salt. Glass is a material that has hardened without crystallizing, making it amorphous and isotropic.  Crown glass has a single refractive index 1.517. Table salt has a single refractive index of 1.544 and has a cubic crystal structure.

A) Table salt (sodium chloride) crystal by bright field microscopy B) salt viewed under crossed polarizers and C) salt viewed by crossed polarizers and full-wave retardation plate - 50X. Salt is isotropic and clear in polarized light and adding a (550 nm) retardation plate into the light path will not add additional colors as it would for anisotropic substances.

Anisotropic substances include minerals, crystals, synthetic fibers, biological fibers such as microtubules, actin filaments, wood, plant material, or molecules in a liquid oriented in a particular direction.  Other substances which are anisotropic include ceramics, mineral fibers (e.g. asbestos), starch grains, urea, collagen fibers, and muscle fibers.  Plastics and other polymers can also exhibit strain-induced birefringence.


Birefringence indicates that a substance (mineral or biological) exhibits molecular or atomic asymmetry. Birefringence can be due to atomic structure (intrinsic), tensions induced within the structure (strain birefringence), supra-molecular assembly (form birefringence), and a logs-in-a-stream effect of rod-shaped molecules in a suspension (flow birefringence) that sometimes occurs in liquid crystals. You can also have specimens that contain both intrinsic and form birefringence (e.g. human hair).

Birefringence measurements are used in forensic science and the pharmaceutical industry to identify fibers, crystalline chemicals and determine the purity of substances like illicit drugs (Watanbe et al. 1985). It is also used to identify gemstones and minerals. 

Ascorbic Acid crystals Polarized light
Anisotropic Ascorbic Acid crystals by polarized light and full-wave retardation plate 100X © Robert Berdan
Quartz fragments of various sizes viewed by  A) crossed polarizers B) crossed polarizers and ¼ wave retardation plate C) cross polarizers and full-wave (550 nm) retardation plate. 100X Retardation plates are discussed in  Part II of this article.
Tardigrade Milnesium tardigradum in polarized light and a full-wave retardation plate showing yellow and blue birefringent muscles.  The gut is also full of anisotropic granules - 100X. © Robert Berdan
Plastic showing strain birefringence – Photo by Nevit Dilmen CC BY-SA 3.0,

The colors seen between crossed polarizers are produced by destructive interference of specific wavelengths.  If the green light is removed from white light the substance or background appears pink- magenta the complementary color of green. If blue is eliminated you see yellow, and if red is eliminated you see cyan and vice versa.  Manipulation of complementary colors is a process that was used while making color prints in a darkroom to correct color during printing – today color correction is done using a computer and image editing program.

The above graphic shows the RGB color model with red (R), green (G), and blue (B) the three primary colors that combine to make white. If green wavelengths are removed from white light by destructive interference the resulting color will be magenta its compliment. A full-wave retardation plate inserted between crossed polarizers removes green light which is why the background appears magenta (reddish-violet).

Michel-Lévy Interference Chart used to estimate Birefringence

The Michel-Lévy chart, named after a French geologist was first published in 1888 and shows interference colors for several orders of wavelength. The area between 0 and 550 nanometers is known as the first order of colors, and the magenta color that occurs in the 550-nanometer region is called first-order red.  Interference colors are grouped into orders (1st order 0 to 550 nm, 2nd order 551 to 1102nm, 3rd order 1103-1653 nm and 4th order 1654-2204 nm, etc., each order is separated by a red-colored band). The colors become muted at higher orders and gradually approximate white.  1st order colors between 0 to 250 nm include shades of black and grey which are difficult to determine accurately as are high order colors above 1400 nm. Some colors have wide bands making it difficult to choose the correct horizontal position within a color band on the Michel-Lévy chart.

When a specimen is placed between crossed polarizers and rotated such that it provides the brightest interference color (usually at 45 degrees to the crossed polars), one chooses the brightest interference color of the specimen and finds the same color on the Interference chart.  It can be challenging to determine which order of interference color you are viewing. Yellow first order and Yellow 2nd order look similar. Fixed retardation plates (full-wave, quarter-wave) can help identify the interference order by moving the interference color up or down the order after insertion into the light path.  A quartz wedge contains 4-6 orders and can also help identify the correct order. Once you select the color you note the wavelength in nm. Some interference bands are 100 nm wide and small errors in your choice can result in different birefringence values so keep this in mind and remember the values are estimates. More accurate birefringence values require the use of compensators (retardation plates) discussed in Part II.

Above is a new more accurate calculated Michel-Lévy Interference chart showing 5 orders (I – V) of interference colors by Sorensen (2013). To use the chart you first identify the interference color of the specimen seen by polarized light microscopy (e.g. 450 nm 1st order yellow) then if the specimen is 30 microns thick at the intersection of 450 nm and 30 microns you follow the diagonal line up and read off the birefringence value = 0.15 in the example above. Knowing the birefringence you can look up the substance in reference books or scientific publications.

If you compare different Michel-Lévy charts you may notice that the colors appear different shades and/or more spread out.  Furthermore, because most Michel-Lévy charts are limited to specimens 50 microns thick for specimens thicker than this you will need to calculate the birefringence value as shown below.

When examining anisotropic fibers you can sometimes determine the interference order by counting the number of red bands between the center and edge of the fiber but you have to be careful because the colors become very close together near the edge of the fiber cylinder.

Calculating Birefringence

Birefringence can be calculated using the formula below which you will need to use if the thickness of the specimen exceeds the chart’s maximum value.


Retardation = thickness of specimen x (optical path difference – i.e. birefringence)

R = t (n2 – n1)        n2-n1 difference between two anisotropic refractive indices


If t = is the fiber thickness of 15 microns in diameter and the maximum interference color is 2nd order yellow – the retardation = 900 nm from the Michel-Lévy chart and knowing two values you can calculate the third.

 (n2-n1) birefringence = R/t         900 nm/ 15 microns x 1000 (to convert µm to nm) = O.06


A birefringence value of 0.06 identifies the fiber as being nylon.

To help learn how to use the Michel-Levy chart and check your calculations, there is an easy to use Java tutorial where using an interactive Michel-Levy chart you click on the intersection of the thickness and retardation color and it will automatically calculate the birefringence based on the thickness (K.R. Spring et. al. – note values on the edge of the chart do not appear to be accurate).  I find colors are easier to match on a Michel-Lévy chart viewed on an LCD monitor. To test and view the Java tutorial click here

Above is a human hair A) Polarized light showing 2nd order blue in the center 1250 nm B) addition of 550 nm full wave plate - fast axis over slow results 1250 – 550 nm = 700 nm 1st order blue C) human hair oriented 90 degrees and D) with addition of full 550 nm wave plate 1250 nm + 550 nm = 1800 nm 3rd order red, therefore the hair has a positive sign of elongation.  The arrows point in the direction of the 550 nm wave plate slow axis (maximum RI). Because the hair thickness exceeds the Michel Levy chart the Birefringence value of the hairs cortex must be calculated using a formula   Birefringence = retardation/thickness in microns x 1000 = 0.011. Using the online interactive Michel-Levy chart (K.R. Spring et al) 700 nm retardation provides a birefringence value of 0.015 for a thickness of 50 microns which is close.

Read more about our Moticams here.


When viewing anisotropic specimens with a polarized light microscope many specimens appear beautiful, especially crystals, and polarized light microscopy is a perfect combination of science and art.  The colors, however, provide important information about the specimen, including its thickness and birefringence.  In this regard, a polarizing microscope is a powerful tool used to aid the identification of a wide variety of substances.  In the second part of this article, I will describe how retardation plates and variable compensators are used to provide more accurate measurements of birefringence.

By Robert Berdan Ph.D.


1) J. G. Delly (2017) Essentials of Polarized Light Microscopy and Ancillary Techniques - Hooke College of Applied Sciences. Westmont, Illinois. Available on McCrone's website & Amazon.
2) R. Berdan (2021) Polarization Microscopy - The Motic BA310 Polarizing Microscope a Review.
3) J.G. Delly The Michel-Lévy Interference Color Chart – Microscopy’s Magical Color Key. You can purchase a printed chart from the McCrone website.
4) K. R. Spring, M. J. Parry-Hill and M.W. Davidson Michel Lévy Birefringence Chart. Interactive Java Tutorial where you can select the wavelength and thickness and it will calculate the Birefringence automatically for specimens 60 microns thick or less out to 6 orders.
5) Friedman (1997) The Mineral & Gemstone Kingdom – Mineral Properties: Transparency.
6) SWGMAT (2004) Scientific Working Group for Materials Analysis – Glass Refractive Index Determination.
7) M. D. Greenwell, A. Willner and P. L. Kirk (1941) Human Hair Studies: III Refractive Index of Crown Hair, J. Criminal Law and Criminology. 31: 746-752.
8) Pleochroism (2020) University of Granada – the source of diagrams which are in the public domain.
9) M. Raith, P. Raase and J. Reinhardt (2011)  ISBN 978-3-00-033606-5 PDF. Guide to Thin Section Microscopy (minerals). Determination of thin section thickness pages 27-29. Free download.
10) Watanbe et al. (1985) Study of Crystalline Drugs by Means of a Polarizing Microscope. VI. Polarizing Microscopy of Drugs Acting on the Nervous System and on Individual Organs Listed in the Japanese Pharmacopoeia. Chem. Pharm. Bull 33:1599-1608.
11) Cargille Refractive Index Liquids reference kits.
12) J.A. Reffner, B.W. Kammrath and S. Kaplan (2019) A More Efficient Method for Synthetic Textile Fiber Analysis Using Polarized Light Microscopy. Includes Tables showing birefringence values for Many Synthetic Textile Fibers. J. Forensic Sci.

Free Michel-Levy Charts you can download

McCone’s – available as PDF
Wikipedia – Zeiss Chart
B.E. Sorensen (2013) A Revised Michel-Lévy colour chart based on first principles calculations. Eur. J. Mineral 25, 5-10.


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