A POLARISCOPE is an instrument that polarizes light, that is, it alters the orientation of the planes in which light waves vibrate. One effect of optical polarization is the disappearance of reflected glare when one dons Polaroid sunglasses. With a simple polariscope one can also detect stresses in transparent substances and the concentration of chemicals in solution and can create objects of art that have the quality of stained-glass windows.

A polariscope for doing such experiments can be made at home for about the cost of an inexpensive camera. According to Leslie Holliday (The Knoll, Cley, Norfolk, England), the instrument can display phenomena of sufficient variety to fascinate every member of the family, including people more interested in art than in optical effects. Holliday describes the construction of the polariscope and some of his experiments.

"A polariscope consists of a light source, a diffuser plate, a polarizer, an analyzer and a framework to support these parts in alignment [see illustration at left]. The polarizer and the analyzer are optically identical. They are made with sheets of Polaroid or an equivalent material. The light source is an incandescent bulb of from 25 to 40 watts. It is installed in an enclosure designed to provide natural convective cooling. Rays from the lamp are diffused by a sheet of opalescent glass or acrylic plastic.

"Both the polarizer and the analyzer are preferably formed with sheets of Polaroid Type HN-22, a high-extinction material that polarizes transmitted light strongly. In the U.S. the material is available from the Polaroid Corporation (549 Technology Square, Cambridge, Mass. 02139) and from the Marks Polarized Corporation (153-I6 Tenth Avenue, Whitestone, N.Y. 11357). It comes in sheets 12 inches square and .03 inch thick. The sheets transmit about 22 percent of the incident light. The material costs about $20 per square foot.

"Material of another type transmits more than 30 percent of the incident light but polarizes less strongly. It is available from the Edmund Scientific Co. (300 Edscorp Building, Barrington, N.J. 08007). Sheets 20 inches square are currently priced at $15.50 each. For protection and mechanical support both the polarizer and the analyzer should be sandwiched between thicker sheets of clear plastic or glass.

"The dimensions of the instrument can be altered according to preference. Other features of the design can also be modified. For example, some experimenters may prefer to enclose the lamp in a lighttight box. If so, care must be taken to provide ventilation ports fitted with light shields that do not seriously restrict the flow of cooling air.

"Objects are placed for examination in polarized light in the space between the polarizer and the analyzer, which I shall call the working space. This space should be at least two inches thick and six inches or more square. In general the versatility of the instrument increases with the size of the working space. The main limitations on the size are the maximum area of commercially available Polaroid and the budget of the experimenter.

"Polariscopes of the most versatile type, which can make quantitative measurements, are built in a cylindrical form that enables the experimenter to rotate the analyzer in its plane relative to the -fixed polarizer and to read the angle of rotation through at least a quarter of a turn by reference to a dial calibrated in degrees of arc. Square instruments should be made so that the analyzer can be removed easily from its supporting frame and rotated as desired through a quarter of a turn. The importance of adjusting the relative angle between the polarizer and the analyzer can be appreciated by considering the nature of the polarizing phenomenon.

"In theory one can imagine a ray of unpolarized light as consisting of myriad photons moving in a slender beam. If the finest details of the unpolarized beam could be observed end on, photons would be found vibrating parallel to every radial plane. Photons in a beam of polarized light vibrate in a single ribbon-like plane. The orientation of the vibrations can be vertical, horizontal or at any intermediate plane.

"Ordinary light, which vibrates in all planes simultaneously, can be polarized by several methods. The simplest method employs selective absorption. It is based on the discovery in 1852 by the British physician William B. Herapath that synthetic crystals made from a salt of quinine tend to absorb light increasingly as the plane in which the light waves vibrate departs from the optical axis of the crystals. Herapath attempted unsuccessfully to grow large crystals for polarizing wide beams of light. In 1932 Edwin H. Land packed Herapath's needlelike crystals into a soft sheet of nitrocellulose, stretched the plastic to align the needles in a gridlike array and let the plastic harden. He named the product Polaroid. It absorbs light waves vibrating in planes that make an angle with respect to the optical axes of the crystals and transmits waves that vibrate in the plane of the optical axes.

"Land later developed high-extinction Polaroid by similarly aligning organic molecules impregnated with iodine in a matrix of polyvinyl alcohol. Other varieties of polarizing materials have since been compounded. To visualize the mechanism of polarization it is convenient to imagine that grids of molecular particles filter out light waves that make angles with respect to the direction of the grids, much as only vertical waves can propagate along a rope stretched through a picket fence.

"The polariscope transmits maximum light when the optical axis (the imaginary grid) of the analyzer is rotated into parallel alignment with the polarizer. In general the intensity of the light transmitted by the combination varies in proportion to the trigonometric cosine of the angle between the optical axes of the analyzer and the polarizer. The addition of a protractor enables the experimenter to read the angle directly and thus transforms the device into a quantitative instrument. A diameter of eight inches is recommended for circular polariscopes. A shaded lamp is helpful in instruments designed primarily to demonstrate colorful effects of polarization.

"In my opinion the most interesting effects are observed when the optical axis of the analyzer is adjusted to make a right angle with respect to the optical axis of the polarizer. With the analyzer and polarizer so crossed the instrument transmits minimum light (1 percent or less, depending on the kind of polarizing material). Many transparent substances polarize transmitted light more or less, depending on their nature, and polarize reflected light more or less, depending on the angle at which unpolarized rays fall on the reflecting surface.

"Light that is reflected upward from a wet surface at an angle of about 37 degrees becomes polarized. The reflected rays vibrate most strongly in the horizontal plane. For this reason Polaroid sunglasses are assembled with the optical axes of the crystals in the vertical plane. It is in this 'crossed' orientation that they tend to absorb the polarized glare.

"The effect can be demonstrated by examining with Polaroid sunglasses light reflected at various angles from ordinary window glass. The reflections from ordinary glass will be absorbed most strongly when the rays make an angle of about 33 degrees with respect to the surface of the glass. The angle of reflection at which the polarization is strongest is related to the refractive index of the transparent reflector (glass, water or some other substance).

"It is possible to make a rough estimate of the unknown refractive index of a substance with a pair of sunglasses and a protractor. Measure the angle at which reflected rays are absorbed most strongly. Subtract the angle from 90 degrees. The trigonometric tangent of the resulting angle is equal to the index of refraction.

"With ordinary glass the rays reflected at an angle of about 33 degrees are the ones most strongly absorbed by the Polaroid. The complement of this angle is 90 - 33, or 57, degrees. The tangent of 57 degrees is 1.539, which is the refractive index of ordinary glass. The refractive index of water ranges from 1.333 at a temperature of 14 degrees Celsius to 1.317 at the boiling point.

"Many substances have no effect on the polarization of light. Well-annealed glass is an example. A sheet of this glass vanishes (except possibly for the edges) when it is put between the polarizer and the analyzer. Many other substances put in the same place appear brightly lighted and many take on patterns of dazzling color.

"All materials of this type are said to be birefringent. They transmit light in two distinct planes at velocities that are ¢ unique and characteristic of each plane but less than the velocity of light in a~ vacuum. In other words, such materials have two indexes of refraction.

"The phenomenon can be observed by placing on the polarizer of the polariscope a glass microscope slide and a strip of cellophane. The microscope slide will not be seen through the analyzer, but the cellophane will appear brightly lighted and possibly colored. The glass slide will remain invisible at any orientation, but various regions of the cellophane brighten, darken and change color when the strip is rotated.

"Cellophane is one of the more active of the readily available birefringent materials. Its appearance in the polariscope ranges from white through the hues of the rainbow, including both saturated and pastel colors, depending on the thickness of the specimen (or the number of layers) and on its birefringent property. All colors are present as a mixture in the white light of the lamp.

"After polarization the cellophane splits the white mixture into two parts that vibrate in planes at right angles to each other and that travel at different velocities. Having passed through the cellophane, the rays combine to form a single white beam. Because of the relative difference in velocity, however, the waves in the two planes emerge more or less out of step. The resulting effect is equivalent to rotating the planes in which waves of each color vibrate.

"A striking feature of the phenomenon is that the imagined rotation is not equal for each color. The velocity of short waves is retarded more than the velocity of long waves. This phenomenon ac- t-t counts for the observed colors. One area of a specimen of cellophane may retard by 5,000 angstroms waves that are perceived as green. This retardation would be equivalent to rotating the plane in which these waves vibrate out of alignment with the optical axis of the crystals of the analyzer. Accordingly the analyzer would not transmit wavelengths that are perceived as green. The transmitted portion of the remaining mixture would be perceived as the complementary color: red.

"Still other areas of the specimen might introduce retardations of less than 3,000 angstroms. Waves of this length lie in the ultraviolet region of the optical spectrum, beyond human perception. The eye is also insensitive to total retardations of less than 3,000 angstroms. Hence these areas of the specimen would appear white.

"Rotating the analyzer 90 degrees causes an observed color to be replaced by its complement. A sheet of cellophane can be rotated to positions of maximum and minimum transmission of light. In general colors are observed best when the cellophane occupies an intermediate position between these extremes, being at an angle of about 45 degrees with respect to the optical axes of both the polarizer and the analyzer.

"The characteristic amount by which light must be retarded to display each color has been measured [see illustration lower left]. For example, if the crests and troughs of the waves emerge from the two paths of cellophane within 2,000 angstrom units of the same relative positions at which they entered the material, the specimen will appear white. In areas of the specimen where the waves of the two paths fall out of step by 7,000 angstroms the specimen appears green because the complementary color, red, has been absorbed.

"Retardation up to 7,000 angstroms results in bright, saturated colors. At still larger retardations colors continue to appear, but they are less brilliant. 'Higher order' colors are seen at higher retardations when two hues are extinguished simultaneously. The colors overlap. At a retardation of 14,000 angstroms the second-order red (2 x 7,000 angstroms) and the third-order blue (3 x 4,500 angstroms) are extinguished simultaneously, leaving a pale yellow. At retardations above the third order, which begins at 14,000 angstroms, one observes a repetition of white, pink and green with each succeeding multiple of 7,000 angstroms. The colors become still more dilute with increasing retardation. Ultimately they degenerate into off-white.

"Experiments with the polariscope might begin with clear plastic. As I have mentioned, cellophane (a regenerated cellulose) is an excellent material. Certain other packaging films are birefringent; they include polyester and polypropylene. Before the era of plastics slices of mica and tourmaline were popular for specimens.

"Cellophane of the thickness normally found in packaging causes a relative retardation of about 3,000 angstroms per -layer. In other words, an unstressed layer of the material appears white when it is placed between the polarizer and the analyzer of the polariscope at an angle of about 45 degrees. Some samples exhibit more birefringence than others. Two layers aligned in the same direction appear blue. Three layers show orange as a second-order color.

"Since the amount of retardation introduced by a layer varies from specimen to specimen, combinations that exhibit intermediate colors can be found. For example, a double layer combining 2,000 and 3,000 angstroms of retardation yields a retardation of 5,000 angstroms and appears green. I assembled a reference device by superposing 101ayers of cellophane in the form of a book, so that each lower 'page' of film was somewhat longer than the films above it. The exposed, multilayered edges served as a reference for combining layers of cellophane to display any desired color. For protection the layers are bound between sheets of glass that are hinged with adhesive tape. The sheets measure four by six inches.

"The experimenter will discover that only certain kinds of transparent plastic film exhibit birefringence. The property usually appears when the polymer molecules are aligned to a greater or lesser extent during manufacture. Polyethylene film, which has a soft, waxy feel and does not emit a crackling sound when it is crushed, is not birefringent. It can be made birefringent, however, by stretching.

"Place a strip of polyethylene about eight inches long and an inch wide at an angle of 45 degrees in the polariscope. (Some plastic bags of the kind sold for protecting sandwiches are made of polyethylene.) Grasp the ends and stretch the strip. A reversible color will appear when the material is stretched lightly. A range of first-order colors can be observed by applying additional stress. Permanent molecular orientation and birefringence can be induced by stretching the film beyond its elastic limit.

"Photoelasticity can be demonstrated by a specimen of translucent rubber or glass. I cut a strip one by eight inches in size from a surgical glove of polyvinyl chloride and stretched it in the polariscope at an angle of 45 degrees with respect to the optical axis of the polarizer and the analyzer. Even though I stretched the specimen quite forcefully, it remained white, indicating a retardation of less than 2,000 angstroms.

"I then laid a square of cellophane on the polarizer at the 45-degree orientation From previous experiments I knew that the cellophane introduced a retardation of 3,000 angstroms. I again stretched the strip of polyvinyl chloride. Its color passed from yellow through purple to blue, corresponding to a total retardation of 6,500 angstroms, including the contribution by the specimen of a stress-induced retardation of 3,500 angstroms.

"The coefficients of stress and retardation of plastics are much higher than those of glass. For studying photoelastic effects the space between the polarizer and the analyzer may be limiting. If so, remove the analyzer and view the specimen through a pair of Polaroid sunglasses.

"In engineering circles it is well known that regions of high concentration of stress exist around notches and holes in a structure. The effect can be demonstrated with the polariscope and a strip of translucent rubber. At the center and at one side of a six-inch strip about an inch wide and .03 inch thick I cut a notch with a radius of about .25 inch. Then I put in the polariscope the sheet of cellophane previously employed to introduce a retardation of 3,000 angstroms.

"When I stretched the strip, its color (in combination with the cellophane) was orange, indicating a total retardation of 4,500 angstroms, or a net contribution by the specimen of 1,500 angstroms. At this point the notch just began to show a blue color, indicating a total retardation of 6,500 angstroms, or a net increase of 3,500 angstroms of retardation by the rubber at the site of the notch. Hence a stress concentration of 3,500/1,500, or 2.3, is indicated. That is close to the figure predicted by theory. Higher stress concentrations would be created by sharper or longer notches.

"This experiment raises the question of stresses that are frozen into certain materials, as represented by nonuniform birefringence and color patterns that can be observed in substantially all injection molded objects of transparent plastic. These objects include dishes, medicine vials and the handles of toothbrushes. Nearly all of them display a profusion of colors in the polariscope.

"The point of mold injection can be ascertained by the higher orders of color (pink and green) that usually surround it. The retardation results from stresses that formed when the article cooled in the mold. The stresses can be relieved by immersing the plastic in boiling water for a few minutes and letting it cool in air; the colors then vanish.

"The polariscope holds much fascination for people who are artistically inclined. Many interesting patterns appear when cellophane packets are viewed between the crossed Polaroids. (Cellophane is difficult to buy alone now, but it can be obtained from packaging materials.) Interesting abstract designs can be made by cutting pieces of cellophane to a desired shape and superposing them in layers. During this work the reference device I have mentioned is helpful in compounding colors. It is possible to cement layers together before cutting them and thus prevent slipping.

"This art form has produced some impressive works. A schoolboy in a community near mine based a large picture on the brass figure of a Crusader in a nearby church. The entire figure was made of multilayered cellophane segments carefully executed to create the desired forms and colors. The effect resembles a stained-glass window.

"Large pictures can be illuminated by polarized light from a 35-millimeter slide projector fitted with a Polaroid slide. The pictures are viewed with either Polaroid glasses or a small square of Polaroid held in the hand. Slides of convenient size can be made for larger projectors that can be assembled at home. In this scheme the slide carrier is sandwiched between the polarizer and the analyzer in the optical train. The lamp housing must include a blower to cool the polarizer if the lamp exceeds 100 watts."

Bibliography

FUNDAMENTALS OF OPTICS. Francis A. Jenkins and Harvey E. White. McGraw-Hill Book Company, Inc., 1950.

The Society for Amateur Scientists (SAS) is a nonprofit research and educational organization dedicated to helping people enrich their lives by following their passion to take part in scientific adventures of all kinds.