Light sources. The sun. The sun naturally comes first in consideration of light sources. Its use is recommended for many experiments because of its brightness and because in the Fraunhofer lines it contains numerous convenient wave-length landmarks. The Fraunhofer lines, which are conspicuous in the spectrum exhibited by a good pocket spectroscope, are shown in Fig. 1.

The energy distribution in the solar spectrum, as observed through the atmosphere, is closely approximated by that of a black body at 5400°K. The luminous efficiency of the sun is about 80 lumens/watt. As will be seen in Fig. 2, this is nearly as high an efficiency as it is possible to attain with a heated body.

A heliostat or coelostat is required if a beam of sunlight is to be maintained in a fixed direction in the laboratory. Heliostats are obtainable from scientific supply companies. Their mirrors, which are usually silvered on the back, should be recoated on the front surface with aluminum if it is desired to obtain in the reflected sunlight the full range of solar spectrum down to the atmospheric cutoff at approximately 3000 Angströms.

The details of construction for a home-made coelostat are: shown in Figs. 3 and 4. This coelostat may be driven by the works of an alarm clock as shown; it may also be driven by a Telechron clock. The secondary mirror of the coelostat has controls operated by cords for making adjustments.

Tungsten lamps. Tungsten lamps are the most convenient laboratory source of white light. Their efficiency is about 11 lumens/watt for the nitrogen-coiled filament type.

The differences of spectral energy distribution of various tungsten-filament lamps are illustrated in Fig. 6, Chapter XI. The spectrum of emission of the filament is limited in the ultraviolet and infrared by the transmission of glass. With glass bulbs 1/4 mm in thickness, the spectrum extends from about 3100 Angströms in the ultraviolet to 3 in the infrared. Two tungsten lights convenient for many purposes in the laboratory are shown in Fig. 5. The one shown on the left is a projection lamp. It requires 6 volts and 18 amperes. An autotransformer or high-capacity storage battery serves as power source. The battery is, of course, preferred when constancy and steadiness of the emission are important.¹ The lamp shown at the right has a straight filament. It is useful as a galvanometer lamp. Both of these lamps are obtainable commercially.²

A trade-mark on the end of a tungsten lamp bulb, when it interferes with 'he light emission of the filament, may be removed by polishing with rouge and felt or with wet crocus cloth.

A lamp³ with a quartz bulb for absorption spectra is shown in Fig. 6. The bulb contains argon at 1-1/2 atmospheres pressure. The tungsten operates at about3100°C. and gives a continuous emission spectrum extending into the ultraviolet to 2500 Angströms. At the operating temperature, the vapor pressure of tungsten is appreciable, and it would normally blacken the quartz part of the bulb. However, vertical convection currents of argon gas carry the evaporated tungsten molecules upward from the filament, so that they are not deposited on the quartz but rather on the upper glass part of the bulb, where they do not impair the usefulness of the lamp.

Welsbach mantle.⁴ This refractory mantle was formerly used extensively for house illumination and is now used in gasoline lamps. It is brought to incandescence in the outer hot surface zone of a Bunsen burner type of flame, where it assumes a temperature nearly as high as the Bunsen flame temperature. The mantle is composed of thorium oxide with 0.75 to 2.5 per cent cerium oxide added to increase its visible emissivity. This addition of cerium oxide plays much the same role as the sensitizer for a photographic plate; that is, it introduces an absorption band in a desired spectral region without materially affecting the optical properties elsewhere. The effect of the cerium oxide is to make the emission in the green 30 percent greater than that of a black body at 1800°C., whereas the emissions in the red and blue correspond closely to 1800°C. color temperature.⁵ The near infrared emissivity is less than 1 per cent from 0.7 to about 6, and the incapacity of the mantle to radiate heat in this important region accounts for its high temperature. For the spectrum beyond 10 the mantle again has an emissivity greater than 75 per cent. The mantle is an excellent laboratory source for those long wave-length infrared radiations.⁶

Barnes suggests heating the mantle with a sharp oxygen flame striking it at a grazing angle.⁷ This gives it a higher temperature, and also the elongated heated section produced is properly shaped for illuminating the slit of a spectrometer. More recently, Pfund has devised an arrangement to combine both electric and flame heating, allowing the attainment of even higher temperatures.⁸

Nernst glower. Nernst filaments are composed of zirconium dioxide powder with about 15 per cent yttrium oxide powder.⁹ For operation on alternating current, flexible platinum lead wires are later cemented to each end of the refractory tube with a mixture of the oxide powders and zirconium chloride as a binder. For operation on direct current, the manner of attaching the electrodes is more complicated. The Nernst lamp normally operates at around 2000°K. Its spectrum extends well into the ultraviolet and infrared. However, beyond 15 its emission is said to be inferior to the emission of the Globar heater.

At one time the Nernst glower offered great promise for commercial lighting, owing to a luminous efficiency of 6 lumens/watt as compared with 3 lumens/watt for the carbon filament. However, the modern incandescent lamp with a coiled tungsten filament in an atmosphere of nitrogen, having an efficiency of 11 lumens/watt, entirely changed matters. The use of the Nernst light is now confined to the laboratory. Here its usefulness depends upon the fact that it is operated in air and has a convenient form (cylinder 0.4 to 0.6 mm in diameter and 1 to 2 cm long) for focusing on the slit of a spectrometer. Griffith has described details of construction for making Nernst filaments.¹⁰

Since the Nernst lamp has a negative temperature coefficient of resistance, it must be stabilized with external resistance or, better, with a ballast lamp having an iron-wire filament mounted in hydrogen.¹¹ The iron wire of this lamp runs at a faint red glow; its remarkable current-stabilizing effect in an atmosphere of hydrogen at 30 to 100 millimeters pressure is shown in Fig. 7. Such a ballast lamp consumes 10 or 15 per cent of the total power needed for operating the Nernst filament.

Globars. The Globar is a rod of bonded silicon carbide about 5/16 inch in diameter and about 10 inches long. The ends fit into aluminum cup electrodes. A potential of 100 volts across the rod brings it to an orange or yellow heat. It can be operated in air at a temperature above 1000°C., although at temperatures around 2000°C. the carbide dissociates and carbon is vaporized or oxidized, leaving silicon, or, in the presence of air, silicon dioxide. A protective layer of thorium dioxide sintered to the outside of the Globar with thorium chloride as binder will allow of temperatures in excess of 2000°C.¹² A suitable mounting for the Globar is shown in Fig. 8.

Carbon arcs. The carbon arc is useful as a laboratory light source. Ordinarily, the positive carbon is mounted horizontally. An 8-mm positive carbon is consumed at the same rate as a 6-mm vertical negative carbon. Accordingly, if carbons of this size are used, they may be fed into the arc automatically by clockwork.

The carbon arc requires at least 40 volts to operate it. Higher voltage increases the size of the positive crater without materially affecting its surface temperature.

The character of the light emission from the ordinary carbon arc may be influenced by the addition of metallic salts as cores in the carbons. (Magnesium fluoride is often used to get a white arc.) The spectral distribution of the carbon arc with cored carbons is illustrated in Fig. 9. This is a curve of galvanometer deflections against wave length, as determined with a quartz monochromator (shown in Fig. 32) and cesium oxide photocell. (See Chapter X.) The slit widths were the same for all wave lengths. This curve does not correct for the transmission of the image-forming lens (shown in Fig. 5, Chapter XI) which was used to focus the light. Without this lens the spectrum would have extended well into the ultraviolet.

The ordinary carbon arc has a crater brightness of about 13,000 candles/cm² and an efficiency of about 35 lumens/watt. The Sperry Gyroscope Company has produced an arc that uses special shields to confine the current to a definite boundary around the rotating crater.¹³ This arc is about six times as bright as the ordinary arc.

Lummer has succeeded in obtaining extreme temperatures in the carbon arc by operating it in an inert atmosphere under high pressure. Under a pressure of 22 atmospheres he was able to obtain temperatures of 7600°K., considerably in excess of the solar surface temperature. The surface brightness reported for this temperature was 280,000 candles/cm². The attainment of such temperatures and brightness is difficult.

A technique of measuring. For the preliminary study of a spectrum plate, a technique of measuring and recording data which is neat and avoids confusion is illustrated in Fig. 10. This procedure employs an enlarged print of the original spectrum plate to identify the iron or other reference lines appearing in the eyepiece of the comparator. To facilitate this identification, the wave lengths of the iron lines are written in the margin of the print. Also, the print serves as a permanent record of the appearance of the spectrum as well as a record of the data of measurement.

First, the wave lengths of conspicuous iron comparison lines, which are to be used as reference lines in the measurement, are written in the margin. The original plate has the same appearance in the eyepiece of the comparator as the enlarged print; thus it easily serves to identify the comparison lines. After the wave length of each unknown line is determined by interpolation, it is recorded on the clear margin of the print as shown at the left in Fig. 10. Notes may also be added in this margin when the wave lengths are later identified by reference to Kayser's tables.¹⁴

Iron arcs. The iron arc is used in the laboratory by the spectroscopist as a source of ultraviolet light and also as a standard comparison source. Its spectrum has been thoroughly studied, and the wave lengths of the lines, as well as the influence of pole and pressure effects on them, are well known.¹⁵

An iron arc developed by Pfund¹⁶ suitable for use in the laboratory is shown in Fig. 11. An iron oxide bead is placed on the lower electrode for stabilizing the arc. If the upper electrode is a graphite rod, the arc is even more stable than it is with an iron electrode.¹⁷ The arc can be started by rubbing a carbon across the gap.

Low-pressure mercury arcs. The low-pressure mercury arc is a convenient laboratory light source.¹⁸ It gives several strong lines in the visible, ultraviolet, and near infrared spectra. These lines are far enough apart to be separated with filters. (See Table XI.)

The ultraviolet spectrum of the arc in a fused quartz tube extends to about 2000 Angströms.The energy at the extreme short wave-length limit produces ozone in the air. The ozone formation, however, becomes weaker and weaker as the lamp is burned, owing to changes in the transmission limit of the quartz. Finally the ozone formation practically ceases. Baly has found that such changed quartz will emit a green phosphorescence and will regain its original transparency if it is heated in the blast burner.¹⁹

The Cooper-Hewitt type of mercury light has a brightness of about 2.3 candles/cm². The ordinary Cooper-Hewitt illuminating lamp has a tube 4 feet long and about 1 inch in diameter. It is a convenient light source for many experiments when an extended source is desired, as for observing Haidinger's and Newton's fringes. To get uniform illumination over an extended area, drafting linen is hung below the lamp.

In glass the Cooper-Hewitt lamp does not, of course, emit all of the ultraviolet spectrum. Recently this arc has been put on the market, made with a tube of Corex red-purple glass which suppresses the visible radiation (except 4046) and transmits the near ultraviolet. In this form it is excellent for therapeutic use.

The commercial hot quartz vacuum arc is much more brilliant (350 candles/cm²) than the Cooper-Hewitt lamp discussed above. The ordinary hot quartz lamp is not of a convenient form for use in the laboratory, but it is now available in the form of a vertical straight quartz tube constructed especially for laboratory use.²⁰ These laboratory arcs are equipped with rectifiers, so that they may be operated on either alternating or direct current.

High-pressure mercury arcs. Harries and Hippel²¹ have described a high-pressure mercury lamp which is now commercially available.²² This is illustrated by Fig. 12. The lamp is mounted in a nearly light-tight case, a very convenient construction for use in the laboratory. The lamp is made of uviol glass or quartz, with or without added cadmium to obtain the red cadmium 6438 Angströms line. Schott glass filters are also supplied for isolating the yellow, green, blue, violet, or ultraviolet lines.

The spectrum of the high-pressure lamp exhibits considerable continuous background. Accordingly, the spectral purity obtainable with it by the use of filters is not as great as it is with the low-pressure arc. The emission, however, is very steady, especially when the lamp is operated on storage batteries.

Cornelius Bol of Stanford University (formerly of the Philips Laboratory, Eindhoven, Holland) has developed a so-called super-high-pressure mercury arc.²³ The discharge which produces the high pressure is started, however, by argon at a pressure of 2 or 3 cm of mercury. The operating potential for the lamp is around 500 volts. Heat generated e by the argon discharge volatilizes the liquid mercury exposed in the lamp until a pressure of mercury gas of about 200 atmospheres is attained. On account of the high ultimate pressure, the lamp must be made of a thick-walled capillary tube as shown in Fig. 13. The tungsten electrodes project beyond the reserve mercury in order to guide the discharge down the central part of the tube. In the center, temperatures of 8600°C. and brightness values several times greater than the brightness of molten tungsten are attained. For example, a lamp operating on 640 volts at a pressure of 200 atmospheres has a brightness of 180,000 candles/cm² and a luminous efficiency of 79 lumens/watt. The emission of a Bol lamp is shown in Fig. 9. (See also Table II.)

The inside surface of the quartz capillary probably attains a temperature in excess of the critical temperature of mercury, so that no liquid mercury can condense. The mercury gas envelope around the hot central core of the arc absorbs the resonance line emitted in the core, and at the obtaining pressure and temperature the resonance line is so broad that its absorption extends over the major part of the ultraviolet spectrum (to 2700 Angströms).

The electrodes are sealed in the Bol lamp with a new glass. A lamp of convenient size for use in the laboratory has the electrodes spaced 1 cm apart. It is first filled with 2 cm pressure of gaseous argon and then with liquid mercury until the 30-mil tungsten wires project about 1/2 mm beyond the mercury at each end. A 640-volt transformer is suitable for operating the light. It is connected in series with the arc and a suitable choke coil. When the arc is shorted out, the choke will draw about 3.4 amperes from the transformer.²⁴

A "cold," low-pressure mercury-vapor lamp is shown in Fig. 14.²⁵ This lamp employs a few millimeters pressure of hydrogen, argon, or one of the other noble gases as a starting gas. Heat developed by the discharge in the noble gas soon distills mercury vapor from small globules of the liquid metal. The potential for operating the lamp is obtained from a sign transformer or from a storage battery and spark coil. This lamp is only about one tenth as brilliant in the visible as the Harries and Hippel lamp, but its emission at 2536 Angströms is many-fold greater. In fact, about 80 per cent of its total emission is in the resonance line.

The resonance line from the mercury lamp shown in Fig. 14 is so strong that the mercury vapors, rising from a globule of liquid mercury held in the hand, cast a strong shadow on a fluorescent screen.²⁶ With a 3-mm Corex red-purple filter to suppress the visible spectrum, this lamp is ideal for exciting the fluorescence of minerals.

This type of mercury light is very useful in the laboratory. When neon is used instead of argon as the starting gas, this single source yields a series of strong lines well distributed over the spectral range from 2536 to 10,140 Angströms. The gap in the mercury spectrum between 6907 and 10,140 Angströms is filled by a series of neon lines around 8300 Angströms.²⁷

Filters for use with the various mercury arcs to yield monochromatic light are discussed in a later section.

Other gaseous discharges. Commercial sodium arcs are now available. They are confined in a special glass container that is not attacked by the metal vapor.²⁸ These arcs operate inside a clear Dewar flask and afford a large-area source of monochromatic light which is particularly suited to many laboratory tests and demonstrations. The characteristics of this and the Bol lamp are given in Table II.

Pyrex is not attacked by sodium as readily as are soft glasses, and by fusing borax or boric acid to the inside surface, its resistance to the alkali metal can be further increased.²⁹ Magnesia crystals are not attacked by vapors of the alkali metal, and they may be used for experiments in which sodium, at higher temperatures and pressures, is to be confined behind windows transparent to both the ultraviolet spectrum and the infrared spectrum.³⁰

The ultraviolet spectrum obtained from a hydrogen discharge tube- is continuous, extending from the short wavelength emission limit of incandescent tungsten toward shorter wave lengths to the limit of transmission of quartz. This hydrogen continuum is most effectively excited by sources of the type developed by Duffendack and Manley, Smith and Fowler, Munch, and Jacobi.³¹ These sources excite the spectrum with thermoelectrons emitted from a hot cathode.

Capillary discharge tubes filled with many different elementary gases are now available commercially.³²

Sparks. To obtain the spark spectrum characteristic of the materials composing the electrodes, it is necessary to use a condenser of sufficient capacity to give an explosively noisy spark. Either a transformer or an induction coil can be used as the source of potential. A spark between magnesium electrodes, especially if it is confined between glass plates, is very brilliant. Such a light source, shown in Fig. 15, is useful for shadow photographs of bullets in motion, and so forth, and for the photography of sound waves by the Schlieren-methode.³³ The duration of the illumination from the magnesium spark can be made extremely short.

Flames. Flames such as the Bunsen flame, which are almost colorless, give characteristic emission spectra when volatile metallic vapors are introduced. The metals most commonly used to obtain monochromatic or nearly monochromatic light are given in Table III.

Filters for the ultraviolet. Thin metal films are among the most interesting filters for the ultraviolet. The transmission band exhibited by silver and the alkali metals is associated with a gap lying between the region where the reflection is ascribed to the effect of free electrons (on the long wave-length side of the gap), and the region where reflection is ascribed to bound electrons (on the short wavelength side). In silver, this gap at 3160 Angströms is approximately 100 Angströms wide. It is much wider than this for the alkali metal films.

Potassium films may be used as a filter for isolating ultraviolet radiations. The full transmission of potassium in the ultraviolet begins at 3000 Angströms for films of a thickness just sufficient to be opaque in the visible to sunlight. R. W. Wood has studied this phenomenon and describes how these films can be formed on a quartz-glass bulb cooled to liquid air temperatures.³⁵ Unfortunately, films prepared as he describes are only permanent at temperatures considerably below room temperature. O'Bryan, however, has shown how potassium may be deposited between quartz-glass plates to give films permanent even at the elevated temperature of boiling water.³⁶ The transmission of these thicker films begins at about 3350 Angströms, becomes about 25 per cent at 2500 Angströms, and decreases to a little below this value as the wave length 2000 Angströms is approached. The transmission of such a potassium film is illustrated by Fig. 17.

Bromine vapor can also be used as a filter. It is transparent to the ultraviolet rays. A layer of saturated bromine vapor 5 cm thick at room temperature is opaque to blue light and nearly opaque to green light, as one can readily see by interposing a bottle containing a little liquid bromine between a mercury lamp and a pocket spectroscope. The ultraviolet transmission of bromine begins at 3800 Angströms, and the vapor is quite transparent to the spectrum from wave length 3500 Angströms down to at least 2345 Angströms.

A 5-mm layer of a solution of nitrosodimethylanalin (10 mg to 100 cc water) has about the same transparency as the bromine vapor.³⁷

A filter of 14 g pure, iron-free nickel sulphate crystals and 10 g pure cobalt sulphate crystals dissolved in 100 cc distilled water is opaque to the visible spectrum but transparent in the ultraviolet below 3300 Angströms. In layers 3 cm thick this filter transmits 3.5 per cent of the 3342 Angströms mercury line and 96 per cent of 3126 Angströms line, and it is transparent as far down in the ultraviolet as 2300 Angströms.³⁸

The ultraviolet transmission limit for mica is at about 2800 Angströms for 0.01 mm thickness. Mica of this thickness is completely opaque at wave lengths below 2600 Angströms.

The transmissions in the ultraviolet of some other materials are illustrated in Figs. 18 and 19.

Polarization of the ultraviolet. The new sheet polarizers³⁹ made of herapathite are opaque to ultraviolet light. (See Fig. 38.) Although the calcite of Nicol prisms is transparent to 2000 Angströms, the Canada balsam used for cementing them is not transparent in the ultraviolet at wave lengths below about 3000 Angströms. For cementing optical surfaces to be used in the ultraviolet, glycerin, castor oil, or dextrose sugar should be used. A Wollaston prism may be used to polarize light in the ultraviolet when its parts are properly cemented.

The infrared. The infrared spectrum extends from 7600 Angströms, or 0.76, to about 400. A thermopile or radiometer is generally used for measuring infrared radiation. As the operation of these instruments depends on thermal effects produced by the radiation, the infrared spectrum is often referred to as the heat spectrum. The infrared radiations are emitted by heated bodies. Ordinarily, heated bodies are used as laboratory sources for the infrared spectrum.

It is convenient to divide the heat spectrum into three regions: The near infrared, from 1.1 to 20; the intermediate infrared, from 20 to 40; and the far infrared, from 40 to 400. The spectroscopic significance of the near infrared is that the characteristic frequencies of gases which fall in this region generally arise from molecular oscillations, whereas the characteristic frequencies which fall in the visible and ultraviolet regions arise in general from electronic oscillations. On the other hand, in the far infrared the characteristic frequencies of gases arise from molecular rotation and molecular bending. In the case of crystals the characteristic frequencies in the near infrared are generally interatomic oscillations within the chemical radicals that exist as units in the crystal, while frequencies in the far infrared are due to oscillations of the positive ions (or radicals) of the crystals relative to the negative ones.

The intermediate infrared spectral region from 20 to 40 was formerly closed to investigation on account of the lack of transparent substances to be used for making windows and prisms. There are now available, however, a transparent paraffin of high melting point,⁴⁰ and large synthetic crystals of the alkali halides which are transparent in the range 20 to 40.⁴¹

Prisms, windows, lenses, and mirrors for the infrared. The important prism materials for the infrared are listed in Table VII. These materials are not ordinarily combined to form achromatic lenses for focusing the infrared rays; mirrors which are much more satisfactory are used. Even spherical mirrors are useful for the less exacting work, since the slits in infrared spectroscopy can never be set as fine as they can in the other spectral regions, in which photography can be applied.⁴²

Materials useful for windows on absorption cells and vacuum radiometric devices are listed in Table I, Chapter VIII. (See also Figs. 20, 21, 22.) Of these materials the high-melting-point paraffin is of special interest, since it is one of the few materials opaque to the near infrared spectrum and transparent to the long wave lengths. Soot is another such material. Although it is quite opaque in the visible, soot is translucent for the heat spectrum.

The reflection of most metals such as silver, speculum, and aluminum is high in the infrared. The reflectivity for wave lengths longer than about 10 can be calculated from the electrical conductivity of the metal by the expression

(1)

where is in ohms mm²/m and is in microns.

Reflection of crystals. Residual rays. Crystals exhibit so-called bands of "metallic" reflection at certain wave lengths where the reflection coefficient, usually of the order of 5 per cent, approaches 100 per cent. This property of crystals was first observed by E. F. Nichols.⁴³ The bands of high reflectivity exhibited by quartz, for example, are shown in Fig. 23 Quartz (for the ordinary ray) exhibits two strong bands, one at 8.9 and one at 20.8. Rock salt has only one band, at 52.

Multiple reflections from crystals are employed to isolate narrow bands of monochromatic radiation from the heat spectrum. For example, if the spectrum from a heated body is reflected once from a rock-salt crystal surface, the energy at wave lengths about 52 are reflected while those radiations elsewhere, especially in the short-wave spectrum, where the reflection is nonmetallic, are attenuated about twenty times. In spite of this attenuation by a single reflection, the energy in the 52 band may still be much less than the integrated energy reflected at other wave lengths. After a second reflection, however, the short-wave spectrum is again attenuated about twenty times, or four hundred times altogether, while the energy in the band of waves around 52 is little affected. Accordingly, after four or five reflections the only radiations remaining, the so-called residual rays, are those of the 52 band.

The use of these successive reflections is a standard procedure for obtaining monochromatic bands of radiation in the far infrared. The crystals used for obtaining various wave lengths are listed in Table VIII. We shall describe the apparatus used for obtaining residual rays in a later part of this chapter.

Special absorbers for the near infrared. Water is transparent from wave lengths greater than 0.2 in the ultraviolet throughout the visible spectrum. (See Fig. 24.) However, it is opaque in the heat spectrum for all rays beyond the limits for thickness , as given in Table IX.

A water filter is often used to absorb the heat rays that are emitted when a carbon arc, the sun, or a tungsten lamp is used as a light source. The use of a water filter prevents the cracking of lantern slides with heat, burning of photographic film, overheating of microscope objectives, or excessive heating of polarizing Nicols.

The addition of cupric salts to water results in increased absorption of the infrared. The absorption for the infrared is illustrated in Fig. 24 for a 2-cm cell containing cupric chloride.⁴⁴

Manufactured glass filters such as Aklo glass and the Schott filters BG17 and BG19 are designed to remove the heat spectrum.⁴⁵ (See Table X and also Jena Colored Optical Filter Glasses, obtainable from Fish-Schurman Corporation, 250 East 43rd Street, New York City.) The transmission of BG17, 1 mm thick, and BG19, 4 mm thick, is about the same as that of 2-cm of a nearly saturated copper sulphate solution.

Visible spectrum. Glass and gelatin filters are used for isolation of the mercury lines They are easier to handle and much more permanent than water solutions. The transmissions of some of the glass and gelatin filters commercially available in this country are illustrated in Figs. 25 and 26. A list of the filter combinations for the separation of various spectrum lines is given in Table XI.

The Christiansen filter. The Christiansen filter consists of a mass of solid particles immersed in a liquid medium, as, for example, particles of borosilicate glass immersed in carbon disulphide and bezene.⁴⁶ Fig. 27 shows the dispersion for a borosilicate crown glass and for a 10 per cent solution (by volume) of carbon disulphidein benzene (both anhydrous) at 20°C. The filter composed of these two transmits freely the color for which the indices of refraction of the liquid and solid phases are identical, that is, where the two lines in Fig. 27 cross. For this color the medium is optically homogenous. The filter is a nonhomogenous optical medium for all wave lenghths. Accordingly, they are scattered. By means of the arrangement shown in Fig. 28, the scattered waves are isolated from the freely transmitted color. The individual transmissions of five filters are shown in Fig. 29. These filters are 18 mm thick and were made up from borosilicate glass using different concentrations of carbon disulphide and bezene.

One limitation of the Christiansen filter lies in its lack of complete opacity to wave lengths on either side of the transmitted band.

This limitation is a serious one. For example, when the filter is to be used in conjunction with a highly selective receiver, such as a photocell, the response of the receiver for rays weakly transmitted by the filter but for which the receiver is exceptionally sensitive (or for which the emission of the source is especially strong) may seriously interfere with the interpretation of the results obtained. Another limitation of this filter is its sensitivity to temperature changes. The filter cannot be used effectively in an intense beam of light such as sunlight, owing to temperature gradients set up in the cell.

However, the dependence of the transmitted wave length upon temperature may be put to use. F. Weigert and collaborators have found, for example, that a cell made of particles of crown glass immersed in liquid methyl benzoate transmitted red light at 18°C. (64°F.) and blue light at 50°C. (122°F.).⁴⁷

A very interesting Christiansen filter effect is exhibited by the infrared transmission of thin powder films.⁴⁸ Their maximum of transmission occurs at the wave length at which the index of the powder is unity or equal to the index of the surrounding medium. For magnesia this transmission maximum in air is at 12.2, and if the filter is immersed in carbon tetrachloride, the maximum shifts to wave length 9, at which both the carbon tetrachloride and the magnesia have the same index.

Reflection of metals. Of the metals useful in the visible spectrum for reflection of light, the three most important are aluminum, speculum, and silver. Their reflectivities are shown in Fig. 30. It is to be noted that aluminum is superior to newly deposited silver for all wave lengths less than 4100 Angströms. In the visible spectrum the use of aluminum instead of silver is recommended. Although new silver has a better reflectivity in the visible spectrum than aluminum, it soon tarnishes.

The apparatus shown in Fig. 31 was used for the above reflectivity measurements. This apparatus measures the square of the absolute reflectivity directly (putting the comparison mirror in both the numerator and denominator, so to speak).

Monochromators. The best method of isolating a narrow wave-length band of high spectral purity from a source of white light is to use a double monochromator, that is, two single monochromators built together. High spectral purity is often desirable for highly selective effects, such as, for example, the determination of the long wave-length limit of the photoelectric effect, or in any other case when the slight spectral impurity that one might have with a single monochromator would vitiate the results of the measurement. A step can be made in the direction of high spectral purity by the use of filters in series with a single monochromator. These filters are, however, usually less efficient than a single monochromator. The transmission of a single monochromator is about 45 per cent.

The monochromator may have achromatic lenses, but these are very expensive if they are constructed of materials which will function in the ultraviolet. Generally, monochromators employ quartz lenses. These are brought to focus with a mechanism operated by the wave-length drum. Fig. 32 shows how this is accomplished in the Hilger-Müller double monochromator by the use of a cam bar mounted on the prism table. As the prism table and lens system move as a unit toward the slit system, the lenses are brought into focus for shorter and shorter wave lengths. The cam bar is so constructed that it causes the wave lengths to fall on the exit slits for which the lenses are in focus.

Use of mirrors in monochromators. Parabolic mirrors are often used in monochromators, because an optical system using mirrors is achromatic. However, mirrors have the distinct disadvantage as compared with lenses that the parallel collimated beam is returned in the direction of the entrance slit, a direction which precludes a neat simple arrangement of the other optical parts. To use a mirror on its optical axis requires either an auxiliary flat as in the Pfund⁴⁹ arrangement shown in Fig. 33 (a) or an off-axis mirror as shown in Fig. 33(b). One way to make such an off-axis mirror is to construct a large ordinary paraboloidal mirror and cut out the desired mirror from one side of it.

A mirror system composed of spherical mirrors like the one shown in Fig. 33(c) may be used. This, of course, introduces large distortions in the wave front. It is possible, however, by proper orientation of a similarly imperfect mirror to compensate in a measure for the distortions produced by the collimator and to obtain better definition than would be possible even if a perfect telescope were used. The proper arrangement of the telescope system for achieving this compensation is shown in Fig. 34, with the regular Wadsworth arrangement.⁵⁰

The optical train in monochromators is usually either the Littrow arrangement or the Wadsworth arrangement, both of which use the prism at minimum deviation. These arrangements are shown in Fig. 35.⁵¹

Water monochromator. An ultraviolet monochromator with improvised optics, devised by Harrison,⁵² is shown in Fig. 36. The optical parts consist of a water prism and a spherical aluminized mirror. This monochromator is very simple, and optically it is good enough for isolating the stronger mercury lines (as the illustration of the produced spectrum shows). It has a relatively high aperture, f/6. The dispersions of crystal quartz, fused quartz, and water are related as 25:21:19 at 3000 Angströms. Since water is more transparent to the ultraviolet than quartz, this monochromator can be used for isolating wave lengths as short as 1820 Angströms.

Focal isolation. Fig. 37 shows the method of focal isolation invented by Wood to isolate the far infrared radiations from a Welsbach burner.⁵³ When the first lens is positioned in relation to the light source at a distance equal to twice its focal length for the far infrared rays, where the index of refraction is 2.25, the near infrared rays emerging from the lens are divergent. An opaque spot at the center of the quartz lens prevents the direct transmission of the median near infrared rays through the aperture provided at the focus of the far infrared rays. Usually two lenses are arranged in series of effect complete separation of the far infrared rays.

A focal isolation method has been applied to the isolation of the 1940 A group of aluminum lines with a quartz lens.⁵⁴ And, while there is for quartz no such diversity of index in this part of the spectrum as there is in the infrared, yet these lines are separated from the rest of the aluminum spectrum with a spectral purity of 0.98. The intensity obtained is sevenfold greater than that obtainable from a quartz monochromator. This focal isolation method has also been applied to the 2030 Angströms to 2140 Angströms group of zinc lines.

Residual-ray isolation. Apparatus using the residual-ray method for the isolation of wave lengths in the infrared is illustrated in Fig 38.⁵⁵ The apparatus shown at the top of this figure employs four crystal reflections, while the one at the bottom, placed at the focus of an image-forming mirror, uses only two crystal reflections.

When the two-crystal apparatus is equipped for 6.7 (crystals of calcite) it is useful for measuring humidity, since this region of the spectrum is very sensitive to moisture in the radiation path. On the other hand, with either quartz, Carborundum, or potassium chromate crystals, which give bands of radiation at 8.7, 12, and 11.6, respectively, the instrument is useful as a radiation pyrometer insensitive both to water vapor and to light smoke or haze. In the region from 8 to 13 there is very little absorption by the water in the air even when it is humid; in this region of the spectrum the entire thickness of the atmosphere exhibits a transmission comparable to the transmission of the atmosphere for green and yellow light (T = 85 per cent).

Polarization. There are now new polarizers available for use in the visible spectrum, but they are not as efficient as Nicol prisms.⁵⁶ The transmission of these polarizers, shown in Fig. 39, does not yield as high efficiency as that of a Nicol prism. For plane-polarized light of proper azimuth a Nicol prism transmits about 80 per cent. Two Nicol prisms in series transmit a maximum of about 32 per cent of unpolarized white light. At the other extreme, two Nicol prisms accurately crossed are quite opaque. For example, they will not transmit enough sunlight to make the disk of the sun discernible. However, to obtain this degree of, opacity, the Nicol prisms must be crossed very precisely (to an accuracy of the order of 1 second of arc).

The new polarizers have the advantage over Nicol prisms that they can polarize a beam of greater aperture (both areal and angular). Two applications of the new polarizers are illustrated in Figs. 40 and 41.

One of these, illustrated in Fig. 40, applies to the measurement of strain in glass. Objects to be tested for strain, as, for example, glass-to-metal seals, are immersed in a jar fitted with parallel glass sides and containing a liquid medium having the same index of refraction as the glass. This medium may, for example, be a mixture of the proper proportions of carbon disulphide and benzene or a mixture of zylene and alcohol. Polarized light obtained from a lamp by reflection off black glass at the polarizing angle (or reflection off the back of an exposed photographic plate which has been developed, fixed, and dried) is viewed through a full-wave mica plate and analyzer. (The construction of the full-wave plate is described below.) When a full-wave plate is placed in front of the analyzer, slight variations of the polarization over the field of view are manifest as variations of color from the purple of the unstressed condition.

Engineering applications of polarized light. The property of isotropic transparent materials that a strain makes them double refracting is used by engineers for studying the magnitude and distribution of stress produced by loading various two-dimensional structures, such as, for example, the shapes represented by the cross section of a dam.⁵⁷ An arrangement for such studies using spherical mirrors and the new polarizers is shown in Fig. 41. The astigmatism (due to using the mirrors off axis) can be balanced out, at least in part, by tipping the camera lens about a horizontal axis by a suitable amount. The model of the shape to be tested is usually made from a clear sheet of Bakelite or Marblette. Table XII gives the coefficient of forced double refraction for various materials suitable for constructing models.

The quarter-wave plates are used in the illustrated arrangement to allow the elimination of the pattern of isoclinics (the lines along which the principal stress in the specimen has a constant inclination) from the pattern of isochromatics (the lines along which the quantity (p-q) has a constant value). Here p and q are the principal stresses produced in the model by the applied loading Methods of determining the magnitude of the quantities p and q from the measured isoclinics and isochromatics cannot be described here, since they are quite complicated.⁵⁸ However, in spite of this, the experimental method of studying the stresses in many structures is easier than the theoretical method, and the experimental method has the advantage over the theoretical method that it carries with it the conviction of a more direct appeal to nature for the information desired.

Quarter-, half-, and full-wave plates. Quarter-, half-, and full-wave plates are made of quartz, selenite, or mica cut or split parallel to the optical axis. The thickness of the plate is made such that the relative retardation of the ordinary and extraordinary ray is 1/4, 1/2, or 1 full wave length. The thickness required for a quarter-wave plate is

(2)

where is the index of the crystal for the extraordinary ray and for the ordinary, and is the wave length in question. For mica the thickness of a quarter-wave plate for the D lines is about 0.036 mm. Although for mica the quantity (-) varies from specimen to specimen,⁵⁹ it can be taken as essentially constant for all wave lengths. Therefore, the thickness of a quarter-wave plate is roughly proportional to the wave length for which it is intended.

The principal directions of mica are determined by interposing it between crossed Nicols. The principal directions are parallel and at right angles to the azimuth of polarization of the incident light when the mica (of any thickness) is so oriented that it does not affect the cutoff of the second Nicol.

Tutton's test⁶⁰ for distinguishing between the two principal directions in a quarter-wave plate is to place the plate between crossed Nicols (with its plane perpendicular to the axis of the beam of incident white polarized light) oriented in an azimuth such that the restored light is a maximum. The principal directions in the plate now make angles of 45° with the azimuth of vibration of the incident polarized light. The mica plate is rotated first about one principal direction and then about the other, so that, in each case, light traverses a thicker layer of mica. In one case the color passes from bluish gray through iron gray to black, and in the other case the color passes from white to yellow and then through colors of a higher order. The latter color sequence corresponds to rotation about the principal direction of slower vibration in the mica and the first case corresponds to the principal direction of faster vibration in the mica.

Splitting of mica. Quarter-wave plates are most easily made from mica, since it is easily split to the thickness required.

The stock sheets are split from clear mica plates.⁶¹ The starting sheet is trimmed to about 3 inches square with sharp tin snips so as to have clean edges. (The exact size of the starting sheet is immaterial.) One corner of the starting sheet is then frayed out by rubbing it, and a clean dissecting needle is introduced to divide the sheet approximately in half. A drop of water is introduced in the cavity so produced.⁶² The mica is then split all around the edges by working the needle along, point first, at an angle of about 30°, so that the first cleavage starts inside the boundary of the sheet. This avoids a terraced cleavage. After the needle has gone around the circumference, a second drop of water is introduced, and the plates are drawn apart. The water so facilitates cleavage that the sheets may be separated almost as easily as the pages of a book. This process is repeated until the thickness is approximately 0.036 mm or as thin as desired. Each time, the sheet is divided so as to give two sheets of approximately the same thickness.

Mica gauges.⁶³ A gauge may be made up as shown in Fig. 42. To make such a gauge the principal directions are first marked on a starting plate. The thinnest possible sheet is then split from the starting plate and cut up into strips about 1/4 inch wide. The strips are cut at an angle of 45° with the principal directions. These strips are then cut to give rectangles with lengths of 2 inches, 1-7/8 inches, 1-3/4 inches, 1-5/8 inches, and so forth. (See Fig. 42.) The strips are next cemented (with balsam) between glass plates as illustrated, care being exercised to see that none of the strips are mounted upside down or rotated end for end. The steps so formed are then indexed.

The retardation per step of the gauge is determined as follows: After the analyzer is set for maximum transmission of the light, the gauge is placed on the mirror of the Norremberg doubler (see Fig. 43) either parallel or perpendicular to the azimuth of polarization. A sodium light should be used for illumination. The index number of the step which gives opacity is noted. The step giving opacity is a quarter-wave plate for the D lines. Other steps are proportionately greater and less.

Using the gauge. The gauge is used as follows: First, the analyzing Nicol of the Norremberg doubler is set for extinction. The mica of unknown thickness is placed on the bottom mirror of the doubler, with its principal direction making an angle of 45° with the azimuth of polarization to give maximum transmission. Then the gauge strip is laid on top of the mica so that it is either parallel or perpendicular to the azimuth of polarization. At one of these orientations, the steps show "interference" colors, and at the other, and proper one, opacity is obtained for one or two of the steps. The calibration value of the step which gives opacity corresponds to the retardation of the mica sample. Interpolation may be required to make a delicate measurement.

Magnification of lenses. The transverse magnification of a lens is the ratio of image diameter to object diameter, or, expressed another way, it is the ratio of transverse image displacement to transverse object displacement. For a simple lens the magnification is given by the ratio of image distance to object distance. For a system such as a spectrometer, which has a collimating element (lens or mirror) with the object at or near its focal plane and a telescope element also with the image at or near its focal plane, the magnification produced is the ratio of the focal length of the telescope element to that of the collimating element.

Another case, encountered in a telescope, is that in which parallel light is received by the objective and observed by an eyepiece adjusted so that its focal plane is very near the focus of the objective. Here, the angular magnifying power is the ratio of the focal length of the objective to that of the eyepiece.

The longitudinal magnification of an image-forming system gives the ratio of the displacement of the image along the optical axis to the displacement of the object. In the case of a system composed of two lenses (or mirrors) with the object and image at or near the respective focal planes of these elements, the longitudinal magnification is given by the square of the ratio of the focal lengths.

Other properties of lenses. When a beam of parallel light is focused with a thin lens on the optical axis, its focal length f is given by the expression

(3)

where and are the respective radii of curvature of the two surfaces of the lens, and n is the index of refraction of the material from which the lens is constructed. The r's are taken positive if the curvature acts to converge the light.

If the light is inclined to the optical axis of the lens, it exhibits astigmatism as shown in Fig. 44. For example, the best focus of a distant star, which would be a small hard spot of light on the optical axis, is a soft image when the lens is inclined. The diameter of the smallest image is known as the "circle of least confusion." Within the focal distance giving the smallest off-axis image, the lens gives at one particular distance a rather sharp line focus, which is perpendicular to the plane passing through the image and the optical axis. Also, outside this image another rather sharp line focus is obtained. This line focus is perpendicular to the first line and parallel to the plane referred to above.

The astigmatism of a simple lens is illustrated in Fig. 44. The locus of the inner astigmatic images is a circle, a, having a diameter

(4)

or 0.275 f for n = 1.5, and the locus of the outer astigmatic images is a circle, b, of diameter

(5)

or 0.6 f for n= 1.5.

Properties of mirrors. The mirrors generally used in optics are conic sections of revolution and the flat. They are paraboloidal for focusing parallel light, ellipsoidal for two conjugate real focii, and hyperboloidal for two conjugate focii, one of which is virtual. The spherical mirror is, of course, suited for focusing light from a source at its center of curvature exactly back on the center.

When a spherical mirror of radius R is used to focus parallel light striking it at an angle, the image exhibits astigmatism, and the lines corresponding to the two circles shown in Fig. 44, determined by the positions of the astigmatic images, are a circle of diameter R and a straight line, respectively. (See Fig. 2l, Chapter XI.)

Properties of prisms. Some interesting properties of a right-angle prism are illustrated in Fig. 45.

This prism, viewed through the long face and perpendicular to the vertex of the 90• dihedral angle in one azimuth, has the interesting and often useful property of returning a beam of light back on its path, regardless of the angle of incidence on the long face in the other azimuth. Fig. 46 illustrates the corresponding property for the corner of a cube.

Optical recording systems. Professor Hardy has written an excellent article on recording systems as applied to oscillographs.⁶⁴ We can refer only to his results. He concludes that a simple optical system with a single lens in front of the galvanometer mirror will give as much illumination on the recording film, on a basis of equal resolving power, as any other possible stigmatic system. Furthermore, he points out that the focal length of the simple systems should be chosen so that the limit to the resolving power is set by the photographic material rather than by interference effects. Although 25 lines/mm or more can be resolved by photography, Hardy sets an arbitrary practical limit of 0.1 mm as the resolving power of the photographic material. To obtain maximum illumination and at the same time to conserve on the use of photographic materials, the simple lens should be chosen to give a spot at least 0.1 mm wide.

However, by using an astigmatic optical system such as the one shown in Fig. 47, it is easily possible to obtain nine times as much illumination as with the simple lens. Furthermore, the astigmatic system has the additional advantage that rotation of the galvanometer mirror about a horizontal axis does not produce a vertical deflection of the image on the recording film.

The calculation of the maximum velocity at which the recording spot can traverse the photographic emulsion and still yield a perceptible trace is treated in Chapter XI. This treatment includes the astigmatic case illustrated in Fig. 47. Owing to the recent developments in fast photographic emulsions, the data given in Table VI, Chapter XI, for the various materials may be regarded as being distinctly conservative.

A bibliography of some of the best works on the subjects treated in this chapter is given in a footnote.⁶⁵

¹ The autotransformer is as satisfactory as the battery when it is energized by the output of a Raytheon voltage regulator.

² These lamps may be obtained from the General Electric Company, Nela Park, Cleveland, Ohio.

³⁷ Wood, R. W., Phil. Mag., 6, 257 (1903).