If the specimen is composed of negatively birefringent material that is tangentially arranged, the specimen will appear yellowish-orange in the regions where the physical axis of the negatively birefringent material (and consequently its fast axis) is parallel to the slow axis of the compensator; and bluish in the regions where the physical axis of the negatively birefringent material is perpendicular to the slow axis of the compensator. It will have the same appearance as a specimen composed of radially arranged positively birefringent material.Therefore, if we know, from independent experiments (e.g. electron microscopy), the orientation of the material that makes up the specimen, we can determine the sign of birefringence of the material that makes up the specimen, from the pattern of colors that appear ina polarizing microscope equipped with a first order red plate. Alternatively, if we know the sign of birefringence of the material that makes up the specimen from independent experiments (e.g. by knowing its chemical structure), we can determine the orientation of those molecules in the specimen.Molecules, like amylose (in starch), cellulose or fatty acyl-containing lipids, where the majority of the electrons vibrate parallel to the long axis of the molecule are considered positivelybirefringent. Molecules, like DNA, where the majority of the electrons vibrate perpendicular to the long axis of the molecule are considered negatively birefringent.229In biological specimens, we often do not know where the optic axis of a given specimen is. Thus we have to make an operational definition of ne and no. We usually assume that ne is parallel to the physical axis of the specimen and no is perpendicular to the physical axis of the specimen. For example, when looking at a cell wall, the long axis is the cellulose microfibrils themselves; in mitotic spindles, the long axis is the spindle itself; in asters of a mitotic apparatus, the long axis is the radius; for starch grains, the long axis is the radius from the hilum; for membranes, the long axis is the tangent to the membrane; in the A band of muscles, the long axis is the long axis of the myofibril.As I mentioned above, if a specimen placed on a microscope between crossed polars has a great enough retardation to eliminate one visible wavelength, the specimen will appear colored and we can determine its retardation directly by comparing the color of the specimen with the Newton colors that appear on a Michel-Levy chart. If we know the thickness of the specimen by independent means (e.g. interference microscopy), we can read the magnitude of birefringence of the specimen from the chart. However, the retardations caused by most biological specimens are 230too small to give interference colors without a compensator. We can determine the retardation of these specimens by comparing the color of the specimen viewed with a first order red plate, with the Newton colors that appear on a Michel-Levy chart. We can read the retardation of the specimen and the first order red plate directly from the Michel-Levy chart and then subtract from this value the retardation of the compensator. The retardation of the specimen is equal to the absolute value of this difference. If we know the thickness of the specimen by independent means, we can determine the magnitude of birefringence of the specimen from the following equation:BR = ne-no = /t.The magnitude of retardation can also be rapidly estimated and the sign of birefringence determined with the aid of a quartz wedge compensator. Quartz is a positively birefringent crystalwith ne = 1.553 and no = 1.544 (BR = + 0.009). Since the retardation is equal to the product of birefringence and thickness, and since the thickness varies along the compensator, the retardation varies from zero to about 2000 nm. We place the quartz wedge in the microscope so that the slow axis of the compensator is ±45 relative to the polarizer. The specimen is placed on the stage so itis ±45 relative to the polarizer. In order to get complete extinction, the aperture diaphragm must be closed all the way. When the slow axis of the specimen and compensator are perpendicular, there will one position of the compensator where the retardation of the compensator equals the retardation of the specimen. At this position, there will be no difference between the phase of the linearly polarized light that goes through the slow axis of the specimen and the fast axis of the compensator, and the linearly polarized light that goes through the fast axis of the specimen and the slow axis of the compensator. Therefore the specimen will appear black. We also say that at this position, the specimen has been brought to extinction or that the specimen has been compensated.We find this position by gradually sliding the quartz wedge into the compensator slot. As this is done the color of the specimen changes from its initial color toward the “subtractive colors” of the Michel-Levy color chart. When the specimen is brought to extinction, we look at the color of the background produced by the quartz wedge and match this color with the colors onthe Michel-Levy color chart and read the retardation of the compensator directly from the color chart. Since, at extinction, the retardation of the compensator is equal to the retardation of the specimen, we can estimate the retardation of the specimen.The quartz wedge will only bring the specimen to extinction if the slow axis of the compensator is perpendicular to the slow axis of the specimen. Therefore, we can use this methodto determine the direction of the slow axis of the specimen relative to its principle axis. If the slow axis of the specimen is parallel to the principle axis, we say that the specimen is positively birefringent. If the slow axis is perpendicular to the principle axis of the specimen, we say that thespecimen is negatively birefringent. The quartz wedge is able to compensate specimens with retardations less than about 2000 nm. Double wedge or Babinet compensators work the same wayas the quartz wedge compensators, but are more accurate for estimating smaller retardations.231Another method of estimating the retardation and sign of birefringence of a specimen is to use a tilting compensator, also known as a Berek or Ehringhaus compensator. The Berek compensator consist of a MgF2 plate, which is cut with its plane surfaces perpendicular to its optic axis. Therefore, when the