SOLUTIONS CONTAINING OPTICALLY active compounds such as sugar rotate the polarization of light passing through them. The rotation reveals asymmetries in the construction of the compounds. This phenomenon also has practical applications, such as controlling the concentration of sugar in food products and sugar refining. Sam Epstein of Los Angeles has designed an inexpensive polarimeter that measures optical activity.

A classical model of light describes it as a moving wave of oscillating electric fields. Often the light is depicted as a ray in order to indicate its direction of travel. Superposed on the ray are vectors representing the direction and strength of the associated electric field. The vectors are always perpendicular to the ray, and they vary in direction and strength in such a way that the composite resembles a wave. The electric field appears to oscillate as the light moves past a given point.

When the light is not polarized, the field can oscillate in any direction perpendicular to the ray. If the light passes through a polarizing filter, the oscillations are restricted in such a way as to be parallel to a single axis perpendicular to the ray. The light is said to be polarized. Its polarization is represented by a double-arrow vector. An imaginary line (the polarization axis) parallel to the polarization of the light represents the effect of the filter.

If a second polarizing filter is placed in the path of the beam, the intensity of the light that passes through it depends on the filter's orientation. If its polarization axis is parallel to the oscillations of the incident light, the light is fully transmitted. If the axis is perpendicular to the oscillations, the light is fully blocked. Intermediate orientations of the filter pass intermediate intensities of light.

The filter closest to the light source is called the polarizer, the other filter is the analyzer. What you see in using the instrument is the light emerging from the analyzer as it is rotated about the original ray. When the axes of the two filters are parallel, you see the brightest light. After a 90-degree rotation of the analyzer you see no light. This position of the analyzer is called the endpoint.

Solutions of optically active compounds such as lactic acid, tartaric acid, nicotine, turpentine, amino acids, and vitamins rotate the polarization of light passing through them. They are distinguished from other compounds by their three-dimensional structure. An optically active compound has one or more carbon atoms, each of which is attached to one of four different types of atoms or groups of atoms. As light passes a carbon atom and its attachments, the electric field of the light interacts with the atoms in a way -that rotates the polarization of the light about the ray.

Suppose a cell that contains a solution of an optically active compound is placed between the filters. When the polarized light passes through the solution, its polarization is rotated about the ray. Hence when it reaches the analyzer, it has an orientation different from the one it had before the cell was introduced. To block the light the analyzer must be rotated to a new endpoint. You study the optical activity of solutions by measuring the angle through which the analyzer must be turned to block the light.

The direction of rotation of the light's polarization is specified from the perspective of the observer. The solution is said to be dextrorotatory if the rotation is clockwise and levorotatory if it is counterclockwise. The extent of the rotation is determined by how many of the optically active molecules the light passes on its way through the cell. Longer cells and higher concentrations of molecules increase the rotation of the polarization. The rotation also varies with the wavelength of the light.

In order to describe how much a certain compound rotates the polarization of light, one speaks of "specific rotation." In Epstein's work this measure is the angle through which the polarization rotates when the light passes through one decimeter (.1 meter) of a solution in which the concentration is 100 grams per 100 cubic centimeters. (Some references define specific rotation in terms of other units.) The wavelength of the light is usually taken to be 589 nanometers, that of the yellow emission line of sodium. The temperature of the solution is usually 20 degrees Celsius.

Epstein's polarimeter operates on light from a 60-watt bulb. The light passes through a color filter and a collimating lens and then into a housing, where it is reflected upward from a mirror. In the housing it travels through a polarizer and a cell holding the solution of interest. Thereafter the light proceeds through a condensing lens and an analyzer, finally reaching an eyepiece through which the endpoint is determined.

The bulb and its socket are mounted on a wood support and covered with an inverted fruit can. The can is mounted about an inch above the support so that air can flow into the can. Holes in the top of the can allow air heated by the bulb to escape. Extending from a hole punched in one side of the can is a length of polyvinyl chloride (PVC) pipe of one-inch internal diameter. The outer end of the PVC tube is covered with a thin plate of ground glass.

Since most data on specific rotation for optically active compounds are listed for the yellow emission line of sodium, Epstein filters the white light emitted by the bulb. He avoided the cost of a professional color filter by making a filter. His rig is made with two microscope slides that serve as windows in a rectangular cell. The top of the cell is made of plastic fitted snugly into place to reduce evaporation. The rest of the cell is glued together with epoxy. The cell contains a water solution of potassium dichromate at a 10 percent concentration (10 grams per 100 milliliters of solution). The cell is placed in a protective covering made of sheet metal or quarter-inch Masonite, and the assembly is mounted on a wood pillar so that the windows are at the proper height to intercept the light.

The potassium dichromate solution acts as a filter because it transmits a narrow range of wavelengths close to the yellow emission line of sodium. Therefore Epstein's combination of a white-light source and a color filter yields approximately the same light as a professional's sodium emission lamp. (The color filter can also be made from a square of orange No. 22 Kodak Wratten gelatin filter.)

The housing for the rest of the apparatus is made from quarter-inch plywood or Masonite to form a rigid support. The interior is painted flat black to eliminate stray light. A door on one side of the housing provides access to the sample cell.

The distance between the color filter and the collimator lens is equal to the focal length of the lens, so that the light from the filter passes through the rest of the apparatus approximately as a beam. The lens is mounted in a section of PVC pipe that shades the lens from extraneous light. The light shines on a front-surface mirror glued with epoxy to a wood support. The mirror is mounted at an angle of 45 degrees with respect to the horizontal. Epstein cautions that proper alignment of the optical path is essential.

Just above the mirror is a partition made from quarter-inch plywood or from Masonite. The mirror directs light through a hole five-eighths of an inch in diameter cut into the partition. The polarizer is glued to the bottom of the partition.

Epstein made the polarizer by sandwiching a one-inch square of polarizing filter between two microscope slides. The position of the square is maintained by two sections of file-card stock. The edges of the two microscope slides are covered with transparent tape that extends one-eighth of an inch inward to keep the polarizing filter from sliding out of position. A spot of epoxy is put on both sides of each piece of file-card stock to glue the sandwich together.

A microscope slide is glued across the hole in the partition to protect the polarizer sandwich and the mirror against leaks of the solution being tested. On top of the slide is a one-by-two inch Masonite pad. A hole in the pad matches the hole in the partition. The sample cell containing the test solution rests on the pad and is held in the path of the light by a six-inch length of PVC pipe, sawed so that the cross section of the top five inches is a half circle. The pipe is attached to the housing of the apparatus with two 10-32 brass bolts.

A sample cell must have a flat bottom to avoid distorting the light beam. Epstein uses 50-milliliter color-comparison tubes (Type EXAX, low form) that are available from most laboratory-supply houses. The tubes slide into the PVC holder and rest on the Masonite pad.

Because the tubes cost about $8 each, Epstein suggests that you build your own cell from a transparent plastic tube that is one inch in diameter and has a wall 1/16 inch thick. Cut off a six-inch length of the tube and grind one end flat. Glue a 1 1/2-inch length of microscope slide to the flat end. The f slide should be centered on the tube. The glue should be epoxy and must provide a watertight seal.

This design has two drawbacks. You will need to modify the PVC holder so that the cell fits into place. A more serious problem is that the cell may be ruined if you do experiments with some types of organic solvents.

Above the sample-cell holder is a condensing lens that directs light from the cell through the analyzer and the eyepiece. The analyzer is a sandwich made in the same way as the polarizer is made with one important difference: the filters are skewed. Begin with a 1 1/4-inch square of polarizing filter. Cut a five-degree triangular segment out of the center. Slide the remaining parts of the filter together. Trim them so that they form a one-inch square. Sandwich this arrangement between the microscope slides.

The skewed arrangement of filters in the analyzer makes the determination of the endpoint easier. Otherwise you must guess what position of the analyzer best eliminates the light passed by the test solution. With the skewed filters you merely compare the relative brightness of the light passing through each part of the filter arrangement. The endpoint is achieved when the two parts are equally bright. If you rotate the analyzer in either direction from the endpoint, one part brightens and the other part darkens. Hence the skewed arrangement of filters enables you to fine-tune the determination of the endpoint.

The analyzer sandwich is glued to the bottom of a holder for the eyepiece. The holder passes through a hole in the housing. It is held in place with two flanges but is still free to turn in the hole. The eyepiece can be a single lens or a low-power compound-lens system. A scale marked in degrees surrounds the holder.

To set a pointer on the scale switch on the light bulb and turn the eyepiece holder (and thus the analyzer), monitoring the brightness of the light as you look through the eyepiece. Find the position where the two parts of the analyzer are equally bright. Then attach a pointer to the eyepiece holder so that it points to zero on the rotation scale.

The bottom of a sample cell often has optical imperfections that alter the polarization of light. To eliminate this possibility fill each cell with 50 milliliters of water and mount it in the apparatus. Rotate the cell in its holder, monitoring the light through the eyepiece, until you get the best overall image and endpoint. Permanently mark the side of the cell holder. Make a corresponding mark on the cell. Whenever you use that cell, place it in the holder with the marks aligned. Repeat this procedure for each cell.

Epstein suggests testing the optical activity of a solution of sucrose (ordinary sugar). Begin with a sample cell containing 50 milliliters of water. Place the cell in the polarimeter with the mark on its side aligned with the mark on the cell holder. Rotate the eyepiece to find the endpoint. Note where the pointer lies on the circular scale of degrees.

Exchange the water for 50 milliliters of sugar solution at a concentration of 20 grams per 100 milliliters. Again check for the endpoint. Epstein finds that it is rotated clockwise by about 17 degrees from its position on the scale when only water is examined.

The rotation can also be ascertained by a calculation. The specific rotation for sugar is 66.5 degrees clockwise. In Epstein's experiment the length of the light path is 1.3 decimeters. To compute the expected rotation multiply the specific rotation, the concentration (grams per milliliter) and the length (decimeters). The expected rotation is clockwise by about 17 degrees. You might like to determine how the rotation depends on the sugar concentration. Begin with the strongest solution and gradually dilute it as you measure the rotation.

Epstein also investigated a wellknown reaction in which sucrose is broken down into two simpler sugars, dextrose and levulose. (The process is called inversion.) Dissolve 20 grams of sucrose in 50 milliliters of water in a 100-milliliter flask. Mix it well. Prepare 10 milliliters of a mixture of hydrochloric acid in the ratio of one part acid to three parts water. Add the mixture to the flask and again mix the solution. Put a thermometer into the flask and place the flask in a water bath at 70 degrees C. Monitor the temperature of the solution until it reaches 67 degrees. Keep it in the bath for five more minutes. (Do not let the temperature of the solution exceed 69.5 degrees.)

Transfer the flask to another water bath at 20 degrees C. Remove the flask from the bath when the temperature of the solution falls to 35 degrees. When the temperature of the solution reaches 20 degrees, rinse the thermometer with about 25 milliliters of water, letting the water run into the flask. Add enough water to bring the volume in the flask to 100 milliliters. Again mix the contents.

Place the flask in the 20-degree bath for another 15 minutes. If necessary, again add enough water to the flask to bring the volume to 100 milliliters. Mix the contents and pour 50 milliliters of it into a sample cell. Position the cell in the polarimeter and measure how much the solution rotates the polarization of the light. Epstein measures a rotation of about 2.8 degrees counterclockwise.

The breakdown of sucrose is catalyzed by the hydrochloric acid, producing 10.5 grams each of dextrose and levulose. The specific rotation of dextrose is 52.5 degrees clockwise, the specific rotation of levulose 93 degrees counterclockwise. Calculate the rotations created by the two products in the sample cell. The dextrose should 9 rotate the polarization of light by about 7.16 degrees clockwise and the levulose should rotate it by about 12.7 degrees counterclockwise. Since the rotations are in opposite directions, the calculation of the average rotation amounts to subtracting the two numbers and dividing by two. The result is about 2.8 degrees counterclockwise, just as Epstein measured.

You might also enjoy studying the optical activity of such substances as corn syrup, maple syrup and pancake syrup. Add 25 milliliters of the syrup to a 100-milliliter volumetric flask, along with about 25 milliliters of rinse water to ensure the complete transfer of the syrup. Add two drops of concentrated ammonium hydroxide to serve as a catalyst. Mix the contents well, add enough water to bring the volume to 100 milliliters and mix again. Pour 50 milliliters into a sample cell and measure the rotation of polarization. The molecules of the sugars in the syrup rearrange themselves in a process called mutarotation until an equilibrium is reached. Before equilibrium the optical activity of the solution varies.

Epstein suggests that you take readings on the polarization rotation about every 15 minutes until the variations disappear.

With a similar procedure you might also study the optical activity of different types of honey. The procedure for sugar inversion can also be employed to study the optical activity of gelatin, soft drinks and other liquids containing sugar. If the gelatin is flavored, make sure it is the orange variety in order to obtain a color close to that of the sodium yellow light. You might also compare the polarization rotations of both pure and sweetened fruit juices.

Last month I examined the optics of kaleidoscopes consisting of either two or three mirrors. In each type one can have a direct view of the objects at the far end of the kaleidoscope and see additional images reflected from the mirrors. In a two-mirror system the images lie in pie-shaped sectors clustered around the vertex at the intersection of the mirrors. In a three-mirror system the entire field of view is filled with images. In both types the images appear to lie in a flat plane called the image field that extends through the direct view.

Most arrangements of three mirrors create image fields that are ambiguous in the sense that the content in any area of the field depends on your angle of view into the kaleidoscope. Suppose you see a red bead at a certain place in the field. If you change your perspective, something else may replace the bead. The image fields in a kaleidoscope whose mirrors form an equilateral triangle or a rectangle are unambiguous in the sense that their content is independent of your angle of view.

What other mirror systems yield unambiguous image fields? Initially I thought the only requirement was that an optical system should fill the image field with nonoverlapping copies of the direct view, much as one might fill a floor with identical tiles. I discovered that I was wrong by considering the hexagonal arrangement of mirrors shown in Figure 6. The direct view and two reflected hexagons appear in each part of the illustration. An easy way to derive the reflected hexagons is to rotate the direct view about an edge until it lies again in the image plane. Then rotate the reflected hexagon about one of its edges to form a second reflected hexagon.

The first part of the illustration indicates that I began with the direct view and proceeded clockwise to find the two reflected hexagons. I rotated the direct view about real mirror A to form the reflected hexagon at the lower left. Then I rotated that hexagon about its top edge to form the hexagon at the upper left.

An edge of a reflected hexagon is called a virtual mirror because it effectively functions as a mirror even though it is only an image of one. Hence the second reflected hexagon arises from an edge serving as a virtual mirror. My procedure results in two reflected hexagons that would be seen by an observer looking into mirror A toward the position of the hexagons in the image field.

The second part of the illustration shows how again I began with the direct view but proceeded counterclockwise to find the reflected hexagons that would be seen by an observer looking into mirror B. Note that the two sets of reflected hexagons differ in content. The image field is ambiguous.

After playing with hexagons and other polygons I finally understood what arrangements of mirrors yield unambiguous image fields. For any arrangement the key is to examine each vertex at which two mirrors meet. Looking into the system, you see a sector of the direct view, around the vertex are reflections of that sector. To determine the reflections imagine rotating the sector of the direct view about one of its sides until it is again in the image field. Then you rotate the new sector about its side. Continue the rotations both clockwise and counterclockwise until the sectors begin to overlap. If their contents overlap precisely, the image field around the vertex is necessarily unambiguous. The only vertex angles that yield such a result are even divisors of 360 degrees. If a mirror system is to yield unambiguous image fields, every vertex in the system must meet this requirement. As I already knew, an equilateral triangle and a rectangle qualify. Surprisingly, there are only two more polygons, both right triangles, that meet the requirement. One of them has angles of 45 degrees and the other has angles of 60 and 30 degrees. I do not know whether these systems have already been discovered.

The four polygons generating unambiguous image fields differ in the types of symmetry that appear in the fields. An equilateral triangle gives rise to clusters that have only sixfold symmetry. Each cluster consists of six images that are either exact or reflected copies of the direct view. The image field from a rectangle of mirrors consists of clusters that have only fourfold symmetry. The right-triangle systems offer clusters displaying more types of symmetry. In one of them the right-angle vertex produces a fourfold symmetry and the 45-degree angle produces an eightfold symmetry.

The system with 60- and 30-degree angles represents the most beautiful kaleidoscope design because it offers three types of symmetry, the maximum in any unambiguous image field. The right angle creates a fourfold symmetry, the 60-degree angle a sixfold symmetry and the 30-degree angle a twelvefold symmetry. A kaleidoscope of this type is easy to construct because the mirrors form a right triangle with a hypotenuse twice the length of the shorter leg.

Bibliography

OPTICAL METHODS OF CHEMICAL ANALYSIS. Thomas R. P. Gibb, Jr. McGraw-Hill Book Company, Inc., 1 942.

FUNDAMENTALS OF OPTICS. Francis A. Jenkins and Harvey E. White. McGraw-Hill Book Company, Inc., 1957.

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