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148      POLARIZATION MICROSCOPY

                                compensator mounting) is oriented parallel to the north-south transmission axis of the
                                analyzer and corresponds to the 0° position on the compensator dial. A linear birefrin-
                                gent specimen, such as a bundle of actin filaments or microtubules, is first oriented at a
                                45° angle with respect to the transmission axis of the analyzer by rotating the stage of
                                the microscope to give maximum brightness. Because the maximum optical path differ-
                                ence of the compensator is small (  /20), the background appears dark and remains rel-
                                atively dark through different angles of rotation of the compensator. The compensator is
                                then rotated counterclockwise from its 0° position until light from the specimen is
                                extinguished, matching the dark background. The angle of rotation from the zero posi-
                                tion on the compensator is used to calculate the relative retardation between the O and
                                E rays using the equation

                                                             obj      comp  sin 2 ,

                                where   is the angle of rotation of the compensator and   comp  is the maximum optical
                                path difference of the compensator (  /20). The precise value of   comp  must be deter-
                                mined by calibration and is a constant in the equation. Depending on the particular com-
                                pensator, retardations of   /2000 can be measured under optimal conditions.



                                       Exercise: Determination of Molecular Organization in
                                    Biological Structures Using a Full Wave Plate Compensator

                                   First prepare the microscope for polarization microscopy. The analyzer and polar-
                                   izer might already be installed in the microscope, in which case it is only neces-
                                   sary to bring them into position as described in the text. If not, strips of dichroic
                                   polarizing film can be used in the vicinity of the specimen slide, although this is
                                   not standard practice for a research grade instrument. The polarizer is mounted
                                   between the specimen slide and the condenser lens with its transmission axis ori-
                                   ented east-west. The analyzer is placed between the specimen slide and the objec-
                                   tive lens with its transmission axis oriented north-south. The analyzer is rotated
                                   slightly until the background is maximally dark (extinction). If a red-I plate is
                                   used, it is inserted between the crossed polars with its slow and fast axes oriented
                                   at a 45° angle with respect to the transmission axes of the polars. (See Appendices
                                   II and III for sources and instructions on how to prepare red-I plates for this exer-
                                   cise.) The blackened edge of the red-I plate marks the direction of the slow axis
                                   of the wavefront ellipsoid.
                                      For orientation, examine several birefringent materials between crossed
                                   polars without the red plate, including grains of corn starch, plant cell crystal-
                                   loids, insect leg and flight muscle, and prepared slides of striated muscle, butter-
                                   cup root, and pine wood. Notice that linear birefringent structures such as
                                   myofibrils in striated muscle and plant cell walls are brightest when their long
                                   axes are oriented at 45° with respect to the transmission axes of the crossed
                                   polars. Spherical particles like starch grains are bright and exhibit a dark upright
                                   extinction cross through their centers. Re-examine the specimens after inserting
                                   the red plate. If the waveplate is a red-I plate, the background has a bright
                                   magenta-red (first order red) interference color. (Note: Other interference colors
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