133 222 .THS. THE USE. OF LIGHT WAVES IN PRECISiAN MEASUREMENTS Thesis for the Degree of M. S. SAMUEL HAROLD DW1GHT I929 ITY LIBRARIES Ilfliiiflijiiiflmfflillwllllmlflllll 93 01689 5470 PLACE IN RETURN Box to remove this checkout from your record. TO AVOID FINE return on or before date due. MAY BE RECALLED with earlier due date If requested. THE} USE OF L on": 1";sz3 IN PEECISIAI‘I LEASUEEZLEIITS . 'mnesis for Degree of 1,-1.8. Samuel Harold Dwight 1929 For the personal interest and assistance so freely given by Dr. C. W. Chamberlain, under whose supervision I have worked, I wish here to express my appreciation. Also I am very grateful to Professor C. W. Chapman for his splendid co- operation thruout my course, and to Professor N. E. Laycock for the hotosra hic work in connection with this thesis. P o P 10552.12 CONSEH‘PS Page. Introduction. 1. ?art I. A “rief History of Interferometry. 4- “ert II. A How and Improved “ethod of Using Interference. *henomena for “aking Accurate fleasurements- 13. Part III. fixvarimental Tork~ . 32. Fart IV. fireposod Commercial Instrument. 45- INTRODUCTION The necessity for accurate standards of measurement, and their preservation, has long been recognized. In spite of wars and natural catastrophes that have destroyed peoples and civilizations, records have been left that would be of great value had the standards of measurement which were used been preserved. Data concerning engineering structures, athletic events and astronomical observations would now be of great use were not the units of measur- ment employed in the records unintelligible to us because of the loss of the original standards. Shortly after the French Revolution the French Government undertook the correction of this long standing difficulty. A terrestrial standard of length was chosen as the one least liable to change or be destroyed. The French engineers, with great care, determined the length of a quadrant of the earth along the meridian passing through Paris. One ten millionth of this quadrant constituted a length corresponding somewhat closely to the English yard. The French scientists very carefully constructed a bar of platinum - iridium having a gold plug near each end. A line was ruled on each gold plug so that the distance between them was exactly equal to the one ten millionth of the earths quadrant passing through Paris. This standard, having been established, it was called the meter and extraordinary care was taken that it might not be de- stroyed. A vault :as constructed in a woods near Paris; the ground -1- on which the vault stood was alienated from France and dedicated to the nations of the earth in the hope that in case of war it might be inviolate. In this vault the Meter of the Archives is deposited. The vault is Opened once in ten years and then only for the examination of the Meter. Copies of the Meter of the Archives have been made and deposited with the principal governments of the world. It has been accepted as the international standard of length by practically all governments except Great Britain and the United States. Few things are more certain than, that with the passage of time the Meter of the Archives will change in length. Scientists have therefore endeavored to find a standard of length that does not depend on the loose molecular structure of metals or other materials. A proposal was made that the Meter of the Archives be measured in terms of a wave length of light, since that is a natural constant that will not change unless the nature of matter itself changes; thus making it possible to replace the Meter of the Archives, should it be des- troyed. The wave length of light is an ideal standard of length in many respects. It may be conveniently produced in the laboratory,.and should it change in length there would be no further need of a stan- dard, since life itself would be destroyed by the accompanying change in the nature and behavior of matter. The minuteness of the light wave makes its use possible for measuring very small magnitudes. This very minuteness of the light wave makes it impossible to ever see it. In fact mathematical theory demonstrates that no microscope can ever be constructed that will make visible, objects smaller than one half wave of light. The frequency of vibration of light is enormous. It is possible for the human eye to detect waves which vary in frequency over approximately a single octave. The frequency in this octave 14 14 varies from about 8.3 X 10 to about 3.9 X 10 vibrations per second. The frequency of light vibrations is therefore a million million times too great to be perceived by the eye. In order to use the light wave as a standard of length it is necessary to devise something which will make it visible and magnify it so it may be observed with ease and accuracy. Inter- ference phenomena are employed for this purpose. FART I A BRIEF HISTORY OF INISRFLROKLTRY YCUUG'S EXPERIKLNT. Interference bands mere first produced and explained by Young. His lectures describing the experiments were published in 1307. His method was to let light that had passed through a very arrow slit fall upon two pinholes very close toyether in a screen, and receiving the light that passed through these holes, and spread out, on another screen. Interference bands were seen on ~ this screen where the two pencils of light overlapped. In this region there was a series of bright and dark bands if monochromatic light was used; bright where the two pencils were in the same phase, thus adding their intensities and dark where they were in opposite phase, thus destroying each other. The bands thus produced were very dim and difficult to observe, due to lack of intensity, since the light was first passed through a very narrow slit and then only a small part of that light passed through the two pinholes. FRESNEL'S EKPERIXENT. Fresnel later produced interference bands that were considerably brighter by a slightly different method. He let light from a slit fall upon two plans mirrors making an angle 0 slightly less than 180 with each other. The two reflected beams were thus made to converge slightly and at a certain distance one was entirely superimposed upon the other, without having to be further reduced in intensity by passing through pinholes. He still later -4- accomplished the same result by passing the light from the slit through 0 a biprism with a very obtuse refracting angle ( nearly 130 ) placed base to base and with their refracting edge parallel to the slit. In this way the lisht from the slit was divided into two beams which at a certain distance are exactly superimposed, the same as with the mirrors. The biprism was much more easily adjusted than the mirrors. These experiments were performed for the purpose of sub- stantiating the wave theory of light. While any one of the three experiments proves definitely that light is a wave phenomenon and miay be used to accurately determine its wave length, none of them could ever be used as practical instruments for making the light wave avail- able as a standard of length. LOYD'S MIRROR. About 1834 a much simpler form of apparatus for producing interference was devised by Lloyd and since known as Lloyd's Mirror. It consisted simply of a silvered piece of glass upon which light fell at nearly grazing incidence; the slit being parallel to the reflecting surface. Interference between the reflected beams and a direct beam was observed through an eye piece. However Lloyd's Mirror produced a one-sided system of interference fringes, since only one half of the system of fringes could be seen. All of the methods, so far described, for producing inter- ference with the exception of Fresnel's fiirrors, suffered the limitation that the relative lenghts of the pawn; of the interfering beams could not be altered, consequently they could not be used as measuring instruments. In the case of Fresnel's Lirrors one path could be altered with reSpect to the other by moving one of the v? mirrors in a direction perpendicular to its face. however , in tii instrument the two beams of light follow too closely the same path to allow it to be successfully used as a measuring instrument. In order that any interference apparatus may be successfully used as a practical measuring instrument the two paths must be entirely seperate, thus making it possible to introduce objects in one pa h WitJOUt are fecting the other. CCIDITIOBS FOR INTERFgREhCE. From these experiments the conditions for interference may be deduced as follows: Light must be taken from a single source, divided into two parts, preferably equal, and these two parts must be led over different paths and then reunited at=a small angle.v The interference is caused by the retardation of one beam (or a part of it) over the other beam thus making them reunite in various phase relations. If monochromatic light is used the interference system will be alternate light and dark bands and many of them may be seen. If white light is used, only a few (a dozen or so) of the central fringes of the system can be seen and they will consist of the Spectral colors arranged in order and repeating. As they get farther from the center of the system they overlap more and more until they finally blend to produce white light again, and so do not Show as fringes at all. The angle be- ween the interfering beams must be very small as the greater this -6- angle the closer together the fringes will be. In fact they will be too close to be readily distinguished if the angle exceeds one one hundredth part of a degree. Jn"‘r“Tlr‘j T"r'1"'?wfi-°~w *" 1"11 a. .L ‘Y. , 2' .L‘. Akin e inlsnrun L_-hn. nany of the d :4- fficu ties met up to this time were obviated by Jamin in his apparatus. It consisted of two nearly parallel plates of rather thick glass placed as shown in fl 1‘ igure 1. If the plates were exactly parallel, of the same thickness, and of the same glass the two paths would be equal. 3y slightly ro- tating one of the plates around a vertical axis the paths may be made unequal. Also tranSparent objects may be placed in one of the paths, since they are entirely sepirated between the two plates, and thus indices of refraction may be measured with this instrument. This could properly be given the ame of a measuring instrument. Later it was called Jamin's refractometer or Jamin's interferometer. A1 EIGH'S INTLRFEROKETER. Much credit should also be given to Lord Rayleigh, whose real name was Sir Hilliam Strut and who vas head of the Cavendish Laboratory at Cambridge University, as as early worker in the field of interferometry. Figure 2 shows a dia- gram of his instrument. Light from the slit at the focus of the first lens is made parallel by that lens. The Optical paths of the light coming through the two halves of the lens can be made to differ by placing tranSparent substances of different indices of refraction in the two paths. The two beam were reunited by the secend lens. It is especially well adapted to measuring the index of refraction of -7- gases under varying conditions of temperature and pressure. Its chief limitation is the fact that the two paths cannot be uidely sogdr- ated without using large and very expensive lenses. Another limitation is that the actual length of the two pathscannot be changed relative to each other so the instrument is of no se for making linear measurements. MICHELSONYS llelFEROXLTLR. hichelson's Interferometer which is perhaps the one most often seen and is shown in Figure 3 and Plate 1. It was originally designed to measure the relative motion of the earth and ether. For this purpose interfering beams at right angles to each other were needed. Later this arrangement proved to be very useful for the solution of many physical problems. Since it is the instrument used in the experiment, in conjunction with a Spectrometer, a detailed explanation follows. As shown in the diagramthe light, which may be a broad beam, falls first on a half silvered mirror, i. 6. one having a coat of silver that till reflect about as much as it transmits, set at an an- o gle of 45 to each of two other fully silvered mirrors at right an- gles to each other. Part of the light is reflected to one mirror and part transmitted to the other. Each beam is reflected back Upon its own path to the half silveredmirror where each is again divided. About half of each beam will go to E, the other half going back to the source. The compensating plate, which must be a companion plate to the half silvered one, is introduced to make the thickness of glass -8- in 3a . in the two paths the same. It can readily be seen that all of the requirements for interference have been met,(except having the beams meet at a small angle, which can be done by very slightly rotating one mirror) and either path can be altered by moving its mirror on suitable ways. An eye placed at B sees the mirror M directly and sees an image of h' apparently superimposed upon n. In discussing the instru- ment it is much simpler to consider h and the image of M' as the two reflecting surfaces and that the paths are changed by moving the image of H' in front of or behind H. In Figure 4 H and M' represent horizontal sections through these two reflecting surfaces crossing at O and making a very small angle a. Let us suppose a radium light is before the instrument. All the light coming to the eye from O evidently passes over the same length of path so should be in phase and produce a vertical bright band there. At a point X where 29, the difference in path is-% a wave length of the light used, the two beams will be in opposite phase giving a dark band there. At double that distance from 0, 2e will be one wave length so the two beams will come to the eye in phase giving another bright band or maximum, and beyond that where 2 6 equals 3/3 wave length there will be another dark band or minimum. Thus the field will appear to be crossed by alternate bright and dark bands and the distance from one maximum to the next will be-fi L/sin a,vhoro a is the angle between the two t.) -9- reflecting surfaces and L is the wave length of the ligat used. In practice th;re is a minimum at O and all the others are similarly re- versed owing to the fact that one beam is reflected from silver to air whereas the other is reflected from silver to glass thus intro- ducing a change of one half phase. This is of no consequence, however. It can be readily seen that any movement of one of the mirrors forward or backward on accurate ways such that the angle ”a" does not changewill make the crossing point 0 move to the rigit or left and the entire system of fringes will move with 0 always Peeping the same distance apart as long as the angle of intersection does not change. Every time a fringe passes a given point in the field it means that 2e has changed one wave length of the light employed or the movable mirror has moved half that far. In that way, by counting the fringes very accurate measurements may be made. A more rigorous treatment will show that only the central fringe at O is a straight line, the others being conic sections convex toward 0. This is of great assistance in locating the center of the system which is the only place where fringes can be seen in white light as previously explained.“ Such fringes as have been des- cribed can be seen by the unaided eye and appear to be on the surface of the mirror. They cannot be seen by a telescope focused for infin- ity but may be seen at the focus of its objective if the eye piece is removed. Hichelson used such fringes produced by cadmium light to measure the Meter of the Archives in light waves. -.) As the angle "a" is made smaller the fringes spread out and it would seem that when H and 2' are parallel no fringes could be seen, but that the entire field would be either dark or light. However, the fact that the eye gathers a converging pencil of light alters circumstances so the above condition would be true only when the eye is at an infinite distance or a telesc0pe focused for infin- ity is used. Figure 5 shows that with the eye at a short distance away, the fringes will be concentric circles with their centers at the foot of the perpendicular from the eye to the mirror, since the difference in path varies with the distance from the foot of this perpendicular of the points that send the rays to the eye. COUPOUfiD INTERFEROKETER. The compound interferometer, shown in Plates II and III, was designed by Dr. C. W. Chamberlain at Columbia University in 1313. In measuring the Radius of Kolec- ular Attraction it was necessary to determine the thickness of a silver film which was far beyond the resolving power of the most perfect microsc0pe built. It was for this purpose that the com- pound interferometer was designed. It was awarded a medal at the Jamestown Exposition. The paths of the two beams in the compound interferometer are shown in Figure 6. The fringes seen in this instrument are very similar to those in the Hichelson type and are governed by nearly the same equations, but by properly adjusting the angles of the mirrors the beams of light may be reflected back and forth as many times as desired before finally meeting one mirror normally -1l— NNWKTVR KemegskuethQN. \uNSQKE ow L i as «his... QuwusoKMKKQNQN \etmeRSoQ \bWLm>.qt\.V. I'm, and being returned upon its path. Thus the difference in path, which may be the thickness of a film, may be multiplied and the fringe systems corresponding to all of the magnifications are vis- ible at the same time. It is practical to use fringe systems up to the twentieth order. The instrument may be likened to a com- pound micrOSCOpe with twenty objectives all in focus at the same time. It is especially adapted to the observation of changing magnitudes as the magnification desired can be quickly selected- The thinning of a liquid film under the action of gravity may be continuously observed and accurately measured. INThnFERENCE SPECTROSCOFBS- Besides its use as a measuring instrument the interferometer is frequently used as a Spectrosc0pe to separate lines in the spectrum too close to be resolved by the best prism or grating. Two instruments which may be called interference spectroscopes have been especially designed for this kind of work, although they are in reality interferometers. They are the Faory and Perot (Plate IV ) and the Lummer and Gehrcke (Plate V) instruments. The hichelson instrument is not well adapted to be used as a Spectroscope as the fringes are too broad and the only way the relative wave lengths of two lines very close together can be determined is by counting the beats produced by the interference between them. This cannot be accurately done- I Fabry and Perot devised an instrument that produces -12- PA/ITEZJZ sharply defined, narrow maxina and broad minima- It is tell known that in the case of a grating, increasing the number of lines increases the resolving power by crowding the maxima up into nar- r wer regions. All the interferometers so far described may be regarded as gratings with two lines, and hence produce wide max— ina. Fabry and Perot used two parallel plates silvered uitd au 80 i or 90 3 film. Thus they produced multiple reflections and each additional reflection has the same effect as adding another line to a grating. It crowds the maxima up into narrower spaces. Otherwise the fringes are just like those seen in the hichelson instrument when there is no angle between the two interfering beams i.e. they are concentric circles- if the two sets of frin;es, produced by the two spectral lines to be resolved, are not sepa- rated with the plates close together, a place ma“ be found where they will be separated by increasing the distance between the plates. Ty making the distance between the two plates several centimeters the resolving power of the instrument may be carried to an incredibly nigh pOint. bummer and Gehrcke made use of the same principle for crowding the maximum into a narrower band, but use multiple in— ternal reflections between the parallel faces of an accurately ground plate of rlass as shown in the diagram. It thus has a fixed resolving power and corresponds to Tahry and Perot's etelon, multiple reflecting pittes of fixed distance apart. -i3- Laminar anGc/fifckc [flier/ceramgr 406/ F46ry 4/71 pct-at [Stale/7, PAH 75 I Tigure 7 is a diagram showing the path of the light in a hummer and Gehrcke plate. Lhili it appears to be much simjler than the etelon, the two faces have to be ground p ane an parallel to an enormous degree of accura.y, and so constitutes a very expensive instrument. liTERFLmENCE 13 ”IlTE LIGHT. in 1909 Dr. C. I. Chamberlain announced before the American Physical Society and the British Association for the Advancement of Science at its meeting in Uinnipeg, a method of producing interference in thite light. The principle employed was a combination of interference and diffraction. 3r. Chamberlain called his instrument a diffract- ometer. It could be employed either with a slit and collimator or with a broad source of light as used in the types of interfer- ometer previously described. The combination of interferometer and diffraction, or refraction as first announced by Dr. Chamberlain, is now universally employed as a quick means of adjusting interfer- ence apparatus. Previous to this work it was exceedingly difficult to find fringes in white light, and as the central white fringe is the only one that can be identified, adjustment for white light fringes is absolutely essential in interferometery. Dr. Chamber- J. lain's method enables the observer, as it were, to look around the corner on both sides of the center of the system and locate the white light fringes even though they may be, virtually, hundreds of feet away. Having once located these fringes the adjustment of the —14- instrument may be altered and the fringes brought into the center of the field. Hours of labor are thus saved in the adjustment of the interferometer. Lr. Chamberlain, in 1910 prOpOScd the method of using a diffractometer for attacking the problem of the relative motion of the earth and ether, as the instrument constituted an exceedingly delicate method of measuring small angles or distances with great accuracy. The combination of an interference system with a refracting system consisting of a prism, either of the dis— persion variety or achromatic, makes it possible to use an inter- ferometer of exceedingly high sensitiveness, and which is at the sam time practically free from disturbance- BARUS 1RATTY% IKTRRVZROIJCJR. in 1910 an instrument called the grating interferometer vas constructed and described by C. éarus and P. fiarus- As shown in Figures 5 and 9, the interfer— ing beans in this instrument result from the combined effect of a grating and a mirrcr, placed close behind the grating, on light from a collimator incident at an angle on the grating. The diagram (Figure 9) shoe that light leaving this combination at a given point and in a given direction may have passed over any one of three different paths. It may have been immediately reflected from the grating and diffracted at the same time, just as in a reflecting tin 2 it ma"r have ,assed directlv throufih the cratins, been re- ; J .. .> \J a t '1 :2 cr 0 flected at the mirror, and then diffracted on passing through the grating the second time; or it may have been diffracted on first passage through the grating, reflected aid then passed directly through the grating. All three of these paths differ in leangth so each pair of rays may interfere, and thus yroduce three sepa- rate systems of fringes, all of which are in the field at the same time. ‘ Q "Shite light may be used with this instrument, since light of one color only emerges in any given direction. This is a distinct advantage. By the use of proper formulas movements of the mirror in a direction perpendicular to its face can be calculated from the shift of the fringes, but the formulas are more complicated than those for any of the instruments previously described. ;ach system of fringes is governed by a different formula. They are: Ae" :1/3 cos i ( l) Ae':L/2cos€3‘ (2) Ale : L/Z (cos 9 - cos i ) ( 3 ) vhereAe", Ae' , andAe are movements of the mirror- i = angle of incidence 6 = angle of diffraction L = wave length The Barus Grating Interferometer has been described because of a seeming similarity between some of the fringes pro- duced and the type of interference used in the present experiment. *Jhite light is used with both ypes of interferometer. One of the three sets of fringes in the 3arus Interferometer is formed by -15- bands crossing the Spectrum where certain wave lengths are absent. Upon this set of fringes is superimposed two other sets. The rave ler”ths that are absent are determined by the difference in phase between paths of the interfering beams. In the type of instrument employed in the present experiment the relation between the fringes used and the difference in path, as will be shown later, is an exceedingly-simple one. -17.. "'1 AR? II A HUB AND ITIROV.LD KETLOD 03 LSIHC IHTEHFE.ZK.CE IHEXOLUXA FOR LAKIHG ACCUHAJE KIM YR'TT"‘" EDSEK A33 BUT HE‘S NETKOD O: CALIB itACEUG A JFLc-nCXETnn. A very accurate method of calibrating a spectrometer mas devised by Kessrs. Edser and Eutler e? rly in the present century. It consist- ed in placing before the slit of a Spectrometer an air film of fixed thickness. In practice the air film was produced by silverin; tWo plane parallel plates of 31'” Us with approximately a 75 fl film, placinr the silvered surfaces face to face and spa c1 ing them with three balls of wax ( very small ). 3y pressing these plates to- gether with the fingers and at the same time viewing a distant source of lirht through them, it was possible to make the many vise ible multiple reflections coincide, and thus produce an air film with plane parallel sides. This film would only be a few wave lengths thick. ’ Let the thickness of the air film be represented by "e”. Then the difference in path between a light ray passing 5 raight through and one reflected twice, as shown in Figure 13, will be 2 e. If 3 o happens to an odd number of half wave lengths, [3 e - ( n + 5-) L] , the two beams will inter fere destructively, thus greatly cutting down the intensity for that particular wave length. There will also be other wave lengths for which 2 e i (.0 exactly some odd number of half wave lengths and which will be similarly lessened in intensity. then this film is placed before the slit of a Spectrometer it causes vertical dark bands to cross the spectrum whereever the wave length is such that 2 e = ( n - fi-wL .4 I where 'n is any integer. If the wave lengths corresponding to any two of these bands are known the wave lengths of all the rest of them can be calculated by use of the Edser and Rutler formula, which is developed as follows: Let L' and L" represent the two known wave lengths; L the one to be calculated; and let n', n", and n be the corresponding integers in the formula. He knew that 2 e = ( n' +-§ ) L' or 2 e/L' = n' + %- (4) and 2 e = ( n" + fi-) L" or 2 e/L" - n" +-§ (3) Subtracting (5) from (4) 2 e( l/L' - l/L" ) = n' - n" (6) Similarly we can derive an equation 2 e( l/L - l/L" ) = n - n" (7) Dividing (7) by (6) 1/1. - 1/1-." _ n - n" Simplifying l/L( n'— n“' ) = l/L"( n'- n) + 1/1.'( n - n") 1/L=_}'_1.' 'n_.1. + 11"”...1. (8) n'— n”L” n'— n” L' In applying this formula the ( n' - n ) is obtained by -19- counting the bands between L‘axfi L ; ( n - n" ) is obtained by counting the bands between L and L"; similarly ( n' - n” ) is the total number of bands between L' and L". This constitutes a very accurate method of calibrating a spectrometer. A careful study of these bands and the formulas gov- erning them led to the conclusion that they might be useful for mak- ing accurate measurements. However, for that purpose they must be produced by a different means, since the air film as produced be hdser and Butler can never be reduced to zero thickness, nor can it be made to have a negative value, i.e. one reflecting surface moved through the other. Also when produced in this may, owing to the multiple reflections that take place and the consequent interference between different pairs of emerging rays, the bands present a very complex striated appearance, especially when the air film is very thin. This makes it exceedingly difficult to locate the center of a fringe. THE SPECTRO-INTLRFEROKETXR- It will be remembered that in discussing the Xichelson Interferometer it was found advisable to consider the instrument as acting exactly as though it were an air film inclosed between the mirror seen directly by the eye and the virtual image of the other mirror. Therefore, if the Michel- son or Chamberlain Interferometers are carefully adjusted so that this hypothetical air film has parallel sides, and placed so that white light passing through it enters the slit of a spectrometer, dark bands will cross the white light spectrum just as when the -20- hdser and Butler film is used. However, with this set up, no multi- ple reflections are possible, there being only the two paths. Hence the bands will be simple, the objectionable striation being done away with. Furthermore, the thickness of the air film may be altered at will, and since the virtual image of the one mirror may be passed right through the other mirror, the air film can be changed from what may be called a positive thickness, through zero, to a negative thickness. As will be shown later this doubles the range of the instrument. Suppose the interferometer has been adjusted, by the usual method, using sodium light, then in white light by use of a grating the white light fringes are located and brought nearly into the field thus aking the two paths nearly equal, correSponding tOEl very thin air film, and finally carefully adjusted for circular, Fizeau, fringes ( making the sides of the air film parallel ) and placed before the slit of a spectrometer. When white light is passed through this combination an observer looking into the tele- scope of the spectrometer will see the white light spectrum, which really is a multitude of images of the slit each in a different 0010?: crossed by a few black bands, caused by the absence of the images of the slit in these colors where twice the thickness of the, air film is equal to any odd number of half wave lengths. These bands will be very black in the center ( not simply a lessening of in- tensity ) because the two interfering beams are equal strength and -21.. so entirely destroy one another when in opposite phase. If, now, the moveable mirror of the interferometer is moved so as to increase the thickness of the air film, the black bands will travel across the spectrum from blue to red, some pass- ing out at the red end but m2§g_entering at the blue end, thus in- creasing the total number of bands in the spectrum. If the mirror is moved in the opposite direction, decreasing the thickness of the air film, the reverse will take place; the bands will move across the Spectrum from red to blue but going out at the blue end faster than they come in at the red end until finally there are no bands in the spectrum. This is the point of zero thickness of air film. On continuing to move the mirror in the same direction the bands will begin coming in again at the blue end, moving across the spectrum, leaving at the red end, and increasing in number. This corresponds to what I have previously referred to as a negative thickness of air film. Of course it is negative only in that it_ is on the other side of the zero point from its initial position. It is to be especially noticed that these bands move across the spectrum with varying speeds. The always move fastest in the violet and the Speed gradually diminishes toward the red- Consider a length of white light spectrum one octave long ( say 4,000 A.U. to 8,000 A.U. ). For any movement of the mirror it will be noticed that exactly twice as many bands move by a fiducial point at the violet end of this octave ( 4,000 A.U. ) -29- as go by a point at the red end ( 3,000 J.U. ). This can also be demonstrated mathematically. Thus whenever two hands come in ( or go out ) at the violet end, one band goes out ( or comes in ) at the red end, leaving one extra ( or less ) band in the octave. This corresponds to a movement of the mirror of a distance equal to one wave length for the violet or one half of the red wave length. Rule 1. In general vhenever the mirror is moved a distance "s" one band passes the line in the Spectrum having a wave length of 2 s, and two bands pass the line in the spectrum whose wave length is ”s”- Rule 2. Another general rule easily deduced from the above is that for a given movement of the mirror, the product of the number of bands passing any point in the Spectrum, times the :ave length for that point, is a constant. 3y the application of these two generalizations it is possible to calculate the extremities of a section of the white light Spectrum in which the addition of an extra band, or the dis- appearance of one band in this portion of the Spectrum, will cor- respond to a movement of the mirror as eXpressed by an even decimal part of an inch, centimeter, or any other unit of length desired. I will term such a portion of the spectrum as a range. Thus a range may be calculated in which each band represents a -23- movement of the mirror of one ten thousandth of a centimeter. Also a range may be calculated in which the addition of a band means a movement of the mirror of five hundred-thousandths of an inch. KATKEIATICAL DLVEL TILHT. The range used for the meas - urements in the present experiment was one in which each band had a value of 0-0001 centimeter. In order that the range may be most satisfactory it must include only that part of the spectrum to which the eye is most sensitive, so that the bands can be distinct— ly seen and counted even when the slit is very narrow. The above condition is satisfied by that part of the Spectrum from blue—green to red inclusive, or from about 4,800 A.U. to 7,000 A.U. There is a distinct advantage in having one end of the range at some wave length which is an even decimal part of the unit used, as then, if desired, short distances can be measured by counting bands as the go by that end of the range, then dividing by two. This number multiplied by the wave length gives the distance moved. That method is essentially the same as the procedure necessary when making measurements with the interferometer alone. It is apparent, therefore, that the line in the Spectrum where "L" equals 5,000 A.U. or 0.00005 cm. would be very convenient as one end of the range, when using the metric system. CALCULATION OF THE R fiGE. It is desired to determine a range in which each band represents a movement of the mirror of 0.0001 cm. flaking use of Rule 1, it is easily determined that -34- whenever the mirror moves 0.0031 cm., two sands v.0uld go by the line in_the spectrum where ”L" equals 0.0001 cm. or 10,000 A.U., and that for every movement of that amount, one band would appear, or disappear, in the octave 10,0003.U. to 20,0 00 A.U. This octave is entirely in the infra-red so could not be used. By Rule 2, the number of bands pa ssing any given point in the Spectrum times ”L” for that point, is always 20,000 for this movement of the mirror, when ”L" is eXpressed in A.U. Therefore {‘0 0 ,000 5, 000 H" H , or 4, bands will go by the line in the Spectrum where n equals 5,000 A.U. In order to deterrIine the other end of tr e range we must find where one more or one less band will pass for movement of the mirror. The place where one less band, i.e. 3 bands will so b" for ever 4 bands "oing by the line ”L" e uals 5,000 A.1. J 5 C1 0 H. s at gigggm. which is 6,066.67 A.U. which is the other end of the a desired range. It includes that part of the spectrum which has maximum visibility The range could lie between 5,000 A.U. and 4,000 A.U.; EQJQ:9.; just as well if the human eye was as sensitive to that on of the spectrum as it is to the other. This range could be used for making photographic records of measurements. . The range having once been calculated and set up, the determination of a movement of the mirror consists in simply counting the number of bands_in the range before and after the movement. The difference between these two numbers is the o:- distance the mirror moved expressed in the unit for which the range was calculated. One must remember that if the movement of the .irror is such as to make the thickness of air film pass through zero, the second number is negative with respect to the first, so the sum of the two numbers ( which is the algebraic difference ) is the desired reading. To show that this last statement is true, consider five positions of the mirror, namely, where the thickness of the air film ”e" is 20,000A.U., 10,000 A.U., zero, -10,000 A.U-, and -Z0,000 A.U. reSpectively. (‘1 D ‘ 9 7 0 since 2 e - ( n +~g ) L or L = .:_ET~ ( n being 1’1 1’ "r: 1 I some whole number ) gives the positions of the dark bands, the positions of dark bands when "c" has the above values are as follow: Uhen "e" is fiands will be where "L” equals 20,000 A-V. 40000 . 4:000 , 400-0 , 40000 . 4LOJC . \ . _.""" a 77" .(""' a ‘" 7'" a ”7.4"— : 7'12"“ 9 CT O'CT 0.3 cm. 1. .3 :5 ¢ -. l3 '7] (,1, ~/ 13 A. . 55;? . £53332. . .9 “C 9 ., h , , fl - , 9 “ ' r/I 10,4 1a,. 17/» 10,000 A.U. 30000 , 9 00' . 20000 '\ "\ ”‘7‘." 7 1 I o o o o "7: , -"- q 0 0 I O C o 0 or 0-00 1 on. 1/. I 3 9/4 0 O O C n I o o o o o -13:000 A.U. - 0000 . ... "ROUJO .-23000 .‘ u {*a... O -..4,.‘ . -..:...;-_. 0...... or -0.000l cm. 1?3 7/3 ; 3 -20.000 A.U. ~50000 , 40030 ~40000 ‘ —-'-r 5*- , O O c O O O O --0.-- r ; “twfif— O 0 I r 0 c or -o.oooz cm. 1/2 13,4 13,5 Only those values of "L” enclosed in parentheses are -26- J I within the measuring ranje calculated. They are symetrically placed in that range. The above table shows that, wuen ” e” : 0.0052 cm. thera; are 2 bands in the range; then "e" . 0.0001 cm there is 1 band in the range; none vhen "e” is O; 1 when "e" 3 -0.0001 cm; and 2 when "e" I —0,2303 cm. Therefore if the mirror yes moved from 0.0002 cm.thickness to -0.0002 cm.thictness, a distance of 0.0004 cm., the difference in the number of bands betreen the two positions would be. 2 ”(-2 : 4 4 x 0.0001 cm. gives 0.0004 cm. thedistance actually moved by the mirror. In making measurements it is best to pass through the zero point, as illustrated above, since it necessitates counting fever bands than when both readings are taken on the same side of the zero point. Also the distance between bands will be greater thus making for greater accuracy. In this way distance of one twentieth of a mi limeter can be quickly measured and tenths of a band space estimated quite accurately. In other words the measurment can be made accurate to 0.00001 cm. very guickly. By using an eye piece of greater magnification in the telesc0pe, measurements of equal accuracy over a much greater range could be made, for the bands become more sharply defined as ,hey get closer together. They can be clearly seen as seporate bands even when there are hundreds of them in the range, but of course are difficult to count, unless highly magnified. LOCATITG THE RACGE. A great deal of experimental work and calculating was done in attempting to determine the best method of locating the range on the spectrum after it had been calculated. This must be done exactly as the accuracy of every measurement de- pends upon it. Finally it was discovered that, for measurements in the metric system, nature has provided a standard for setting up the range, that is convenient beyond all previous hopes, in the form of the light from a helium vacuum tube. It produces, besides seve‘al lines in the blue end of the spectrum, and one very bright yellow line, lines whose wave lengths are 5016 AU. and 6678 AU.reSpectively. It will be noticed that these lines come almost exactly at the two extremities of the ideal range as calculated, and that both lines are shifted in the same direction from the ideal thus making the error extremely small. For short measurements, for which this instrument was primarily designed, the error is negligible, and for longer measurements such as were made in this GXperiment to test the method, multiplication by a correction factor in5 an exact 8 result. The yellow line proved very useful for making adjustments as will be described in Part I l. Tefore discovering the sufiability of the helium tube for this work, another method was developed for locating the range. This method could be applied to the setting up of any range and so will be described here. Take any source of light that gives a line spectrum, but not so many lines that they could not be easily identified, two of the lines being in the bright part of the spectrum somewhere near the ends of the desired range. These two lines should be fairly well separated to give accuracy. By use of the formula used in calibrat- ing a spectrometer by the Edser and Butler method, Formula (8) Page (19), it is possible to determine a number of bands to be placed be- tween these lines such that, if one of the lines is considered as one end of the range the other end of the range may be located by counting a certain number of bands from the other line, estimating .tenths if necessary. Of course it is first necessary to calculate the other end of the range by the method previously described. For example the hydrogen veéfim tube produces lines at L : 4861 AU. and L ; 6563 AU. If the latter line is used as one end of the range the other end should be at L = 4941.8 AU. If 16 bands are placed between the two hydrogen lines let us determine where the band next to the blue line toward the red will come. In Formula (3). n' — n = 1 L' 2 4861. n - n": 15 and L" n 6563. nl _ n"- 16 .1..=._.1... , L 16 6563 16 4801 Solving for L L 3 4941.2 which is only 0.6 AU. from the desired position, and can be used as the other end of the range. In order to make use of this plan for locating the range, one must have an eye piece having movable masks, pref- erably transparent with a fine line ruled on each, which may be set at the two ends of the range. Once the range is set it is perman- ent unlessthe adjustment of the spectrometer is changed. ADVANTAGES OF THIS METHOD. The greatest advantage of this method of measuring over the us a1 interferometer method is that the bands record the movement of the mirror. This record may be made permanent by photography if desired. In measuring a dist— ance with the ordinary interferometer it is necessary to count each fringe as it goes by a point in the field. Any jarring such as is caused by the passing of an automobile outside will cause the fringes to vibrate and an observer may easily lose count, in which case the entire measurement must be started over. However, with the combination of interference and refraction just described, the bands are stationary while being counted, and the count may be made as many times as desired to be sure no mistake has been made. If, in making a long measurement ( which must necessarily be done a short distance at a time ), the interferometer gets slightly out of adjustment due to sl';ht inaccuracy of the ways, it may be readjusted Without in the least affecting the measurement. -30- This cannot be done when the interferometer alone is used. Short measurements may be with the interferometer alone since magnitude directly in whatever unit measure. lflis method is eSpecially between lengths that are nearly the made much more quickly than it gives the value of the the range is designed to adapted to making comparisons same and the description of an instrument making use of this principle and especially designed for making comparisonsis given in the last chapter of this thesis. PART III EKPERIKEUTAL WORK ARRANGEKENT OF AFFARATUS- In the descriptions of the appa- ratus given heretofore, the interferometer has been considered as placed before the slit of the spectrometer. This was the arrangement first tried out but it has the disadvantage that only a small por- tion of the light that passes through the interferometer, enters the slit of the spectrometer, thus making it necessary to use a very bright source in order to produce a spectrum of sufficient intensity, with a narrow slit. This strong light produced so much heat that it_ caused expansion and distortion of the interferometer parts. Further experimenting showed that the refraction-interference bands in the Spectrum, which hereafter will be called Chamberfiih fringes, may be produced by placing the interferometer anywhere in the path of they. light before it gets to the telescope. The best order of arrangement was found to be, collimator, interferometer, prism, and telescope. In this arrangement the rays of light in the beams are parallel as they go through the interferometer thus conserving intensity to the greatest possible degree. Practically all of this light could be passed through the prism and gathered by the telescope. By this _ means it was found possible to use a very much less intense source, an ordinary 6 volt automobile bulb burning on the dim filament bein: sufficient. This eliminated the trouble from the heatinr. O -32.. rn‘b The object of this experimenting was to solve the prob- lems met with in designing the practical coniercial instrument described in Part IV. For certain reasons it is necessary that the interferometer of that instrument be in a vertical plane rather than horizontal, and it would be much better if the axis of the tele- scope of that instrument could be parallel to the axis of the col- limator, rather than in the awkward position that would result if e an ordinary prism were used in the optical system. A 90 con- stant deviation prism would satisfy the above condition perfectly, but since the Hilger Block is very expensive, a Wadsworth mirror— prism was designed, which would have a constant deviation of 300, and in which an ordinary 60° prism could be used. The Ladsworth mirror-prism is simply a mirror and prism mounted together on a rotating table with the plane of the mirror and the bisector of the refracting angle of the prism intersecting at the axis of rotation of the table. It has the property that the rays passing through the prism at minimum deviation and then falling on the mirror will suffer constant deviation. The amount of deviation depends upon the angle between the base of the prism and the mirror. The angle of minimum deviation of the prism to be used was measured in the spectrometer and found to be 47Ofor sodium light. With this information :E: was a simple matter to calculate the angle between T . . . o the mirror and prism base that would give a deV1ation of 90 - it was found to be 1350. Figure 11 shows the apparatus made from heavy sheet metal to be attatched to an ordinary Spectrometer table and carry the mirror-prism combination. with this combination in place and adjusted any portion of the spectrum could be brought into the center of the field of view by rotating the table carrying the mirror-prism. The Chamberlain fringes moved with the spectrum, and since there was a pointer in the focal plane of the telesc0pe, this provided an excellent means of counting the fringes in the range. CHOICE OF LIGHT SOURCES. The most satisfactory source of white light available was a standard, double filament, 6 volt auto- mobile bulb. The low candle power filament gave sufficient light and was also better than the other filament for the reason that it was a straight coil and could be set parallel to the slit- Flash light bulbs and other low candle power bulbs were tested but none of them were satisfactory because of looped filaments, which caused an unevenly illuminated slit and spectrum. A still better 1 mp than the one used would be one having a perfectly straight filament. The lamp was placed so that the filament was about 4 centimeters from the slit. As previously mentioned the best source found for produc- ing lines in the spectrum was the helium vacuum tube. It was of the type most frequently seen, a capillary tube with a bulb on each end. It was supported so that the capillary tube was as close as possible to the slit and parallel to it. The helium tube was kept before the slit all the time since it seemed to have very -34- little effect on the intensity of the white light which passed through it. It was Operated by a Ford induction coil and was used only momentarily to place the pointer in the telescOpe eyepiece exactly on the end of the range at the beginning and end of a count. The lines produced were very well defined, standing out sharply against the white light spectrum. Other sources were tried for producing lines. A hydrogen vacuum tube was used in the same manner as the helium but the lines were not as bright, and so were difficult to see even when white light was masked off from the lower part of the slit. Also the lines were not as well placed as are the helium lines. The mercury arc was also examined. It had to be placed at some distance to one side and reflected into the slit by a small comparison prism. This made the lines very dim. Furthermore it complicated the electrical system since the mercury arc required 110 volts and the other light only 6 volts. when the vacuum tube was used the induction coil and the white light were both Operated by a small 6 volt transformer. An automobile storage bettery would have served equally well. ADJUSTKEKTS. To secure sharp and distinct C. fringes, the mirrors of the interferometer must be very accurately adjusted for the condition corresponding to a parallel sided air film. At first it was considered necessary to make this adjustment with the interferometer separate from the rest of the apparatus and using sodium light produce Fizeau fringes, but on becoming more familiar with the apparatus it was found possible to quickly adjust the in- strument without any change whatever in the set up, especially when the helium tube was used. The bright yellow line produced by this tube served just as well as a monochromatic source. The procedure for making adjustments is as follows: First, after correct alignment of the Optical parts is obtained, the Spectrometer is adjusted in the usual manner. The telescope is removed, taken to a window and focused on a distant Object. It is then placed in position and the length of the col- limator changed until the lines in the line spectrum ( which are really images of the slit ) are in sharp focus. This is done pith an obstruction in one path of the interferometer. On removing this Obstruction, if the mirrors of the interferometer are in per- fect adjustment, the lines will remain sharply defined. Iowever, this is not likely to be the case, but as soon as the Obstruction is removed each line rill proeably be seen double. The adjustment of the interferometer mirror consisus in making these douole lines match perfectly. it is best to first adjust so the two images are side by side with the two ends exactly even, then adjust the inter- ferometer mirror in a plane at right an; es to the first adjustment so as to bring them together siderise. All this may be done with both the white light and the line source on, in which case, if the interferometer paths have previously been made nearly ( but not -04.)- exactly ) equal in length, the Chamberlain 11 view as the tie sets of li neszre brought accurate adjustment may now be made by into coincidence. turning .; 3“ r'.’\' “-1th swill come into I .‘. " ("1 "u' A‘ '-'rJ the prism table so the yellow line is in the middle of the field, turning out the white li ht, removin" cular Fizeau fringes as described under the eyepiece of t1e telesc01e and ad' the hichels usting for cir- on interferometer. They cannot be secn in the telesCOpe exce t b" removing the eyepiece. Another way to increase the accuracy of the adjustment is to use the white light only and turn the interferometer screw until only a few .strument is not in good :i'justment they 1ill not be vertica slantinj and perhaps curved. Just touching screws one at a time with the tip of the fi effect on the fringe will tell which one to ges vertical. The necessary turning of the Slifrjlt c Q“ LnaoLflIL” TIL ACCLHACY 0? ‘k S 3:)L—Jrno The measuring of the accuracy of U! for trrifr out this method of measurement. v Q the followinr results show. Q factory as The from the scope removed diameter made to into a slab of limes (1 .".'.!‘l I.) CL \ 1 -37- ( 2 or 3 ) Chamberlin fringes are in the field. nger and va micrometer-microsc0pe was dis: carriage, and a steel post about 3 on. the mirror aujustinw tching the turn to make the frin- scrcw will be Varg, very, U"? 0'7 our” ~11 T“ A)“ § UoLALA—n-ao—A.-u‘.lu a very good micrometer crew, made by Gaertner, was chosen as the most severe test a.ai ails "W" in ne test was very satis— issembled, the micro - in tone and carry the I HATE JZZ \ micrometer frame in a vertical {lane at the same heiqht as the mirrors of the interferometer, when the latter uas placed upon the slab of stone. The stationary mirror of the interferometer was removed and a mirror of somewhat similar dimensions, with a mounting and adjusting soret, attached to the carriage moved by the micrometer screw to be measured. The interferometer was placed so that the mirror would take the place of the one re- moved from it and the other apparatus assembled as already dos- cribed. Flate VIshows this set up. As soon as the adjustments were made and Chamberlain fringes brought into the field it ras discovered that, short and stiff as the post supporting the micrometer screw was, still it vibrated enough to make it impossible to count the fringes when- ever an automobile passed the laboratory. Surrounding the post with a cylinder of paraffin wax did not help matters but the difficulty was finally overcome by bonding the stationary carriage of the interferometer and the frame carrying the ways and microm- eter screw together with a strong rubber band. This led to the con- clusion that both the interferometer and the post vibrated and the remedy consisted in making them vibrate together. The measuring was done as follows: All adjustments having been made the micrometer screw was turned until the mirror moved by it was as close as possible to the interferometer, then, to take out all back lash, the motion 1 — ;)— was reversed and the screw turned until it read an even number of millimeters. The interferometer screw was then turned until approx- inately 25 Chamberlain fringes were in the range between the red and green helium lines, making sure that the setting was such that when the micrometer screw was turned the fringes would decrease in number to zero then increase in a negative sense. The temperature was read on a thermometer placed on the interferometer carriages, and recorded, then the Chamberlain fringes in the range were counted. estimating tenths at each end, and recorded. Then the micrometer screw was turned 5 divisions of the head, or 0.005 cm., making the setting with a hand lens, and the Chamberlain fringes counted again. If there were 25 fringes in the range at the start there should also be about the same number in the range now, but on the other side of the zero point, since the movement was fifty times the value of each fringe, assuming the screw to be absolutely correct. The sum of the two readings ( if the negative sign is not consid- ered ) gave the actual distance moved. text the interferometer screw was turned, reducing the number of fringes to zero and then about 25 on the other side ( any number from 18 to 35 was satisfactory ) and the process repeated. It was found necessary to wait for about one minute after moving the interferometer screw beforecounting the fringes as they tended to drift slowly across the field for a time, as the -39- stresses set up in the metal came to equilibrium. This was due to a rather long post in the interferometer, connecting the nut on_the 'screw with the moveable carriage, and would not be present in the instrument described in Part IV. In order that any error arising from this cause would be eliminated, the initial count was made go— ing from red to green five times, then reversed and made going from green to red an equal number of times, thus balancing the errors- The method of making the count was to set the middle of the red line exactly on the pointer in the eyepiece by turning the tangent screw that rotated the prism table, estimate the tenths of a fringe to the first dark band, then, again using the tangent screw, move the Spectrum slowly across the field, counting the fringes as they passed the pointer until the green line was reached. The helium light was used only momentarily at the beginning and end of each count to exactly locate the end of the range. ‘In this way 5 millimeters of the screw were measured, doing one millimeter at a time and taking the temperature at the beginning and end of each millimeter measured. Then a centimeter of the screw was skiped and another millimeter and a half measured. In making a measurement of this length it is necessar'r to apply a correction factor to correct for the slight variation of the range as shown by the helium lines, from the true range. The calculation of the absolute value of each fringe in this range ( 6673 to SOlS A.U. ) was done as follows: -40- .Elflill A.“. — 3->94 1 OUIJ 4_)n9Q_. = 3.?37241 5016 Tilerefore thenever the mirror moves 0.0031 cm. 2.9943l fringes go by the red line anc 3.937241 fringes C‘o by the green one. The change in the range then is 3.037213 - 2.99491 I L3 . 1- K.— I» o) C») re P” 7 3 o . "' o If 0.'J923 33 fringe represents a movement of the mirror of 0.000l on. 1. fringe represents a movement of ”' ”J3f-, or 0.0001007? cm. inqduJJ‘; For short measurements, then, each fringe may be consid~ ered as having a value of 0.0001 cm., but for long measurements this must be multiplied by 1.0077. RESULTS. The results are shown graphically in Plate VIII which was made by ploting the micrometer readings against the number of fringes corresponding to equal movements of the screw, as measured by the divided head. Following the graph are the results in tabulated form. The term R. I. (standing for refraction—inter— ference ) fringes, as used in the tables, refers to Chamberlain fringes. A sumraary is given here. -41- Readings of Temperatures Cent. Keasured screw length Beginning End '7 - "0 an O n ( 1 9000‘13000 23-0 9901 uOlOJOLG cm. . 9 o qq o ‘1" a 13-00-14-00 ~2ol as. 0.09:013 cm. , o o , i _ le-OO-l5-OO 19-0 20.5 U-O9Ja733 cm. r- P I O . r~ PC I a”. ~' . la-OO-lu-OO 30.5 31.3 0.0v90835 cm. 1" 'W n 0 no we .0 r. m3 “oar -0004’170v0 QOOU a~03 u'ngJuaJ cm- Total 0.49361 cm. 97 mo r33 :3. no 09 C ,x.. -‘ r. u -v -a»~00 QHOJ ~~o5 g-OquQJ cm. The above summary shows that there was no " error of run ” . . . o . H at one definite temperature, aoout 23.0 C. all but one of the readings show a shortage, but it was because the temperatures were lower . t o . , . . than 33.0 C. It Will be noted that there is an approx1mate proportionality between the discrepancies in the lengths and those in the temperatures. error A study of the graph shows that there is a periodic in the screw; i.e. at a certain place in each revolution the advancement is greater than the average and at another place ( about 1300 around on the screw ) the advancement is less than the average. This is probably due to a slight eccentricity of the head, screw or to a slotted master screw having been used to cut this or some of its forerunners. However the graph was purposely constructed so as to -42- greatly magnify this error. In reality it was so small as to be of no consequence since the average variation was only 0.2 fringe, or 0.00002 cm. either way from the correct value, and by estimating tenths of divisions on the screw head it was possible to measure only to 0.o001 cm. It serves, however, to show the extreme accuracy with which measurements may be made by this method. :raph, which shows U One might get the impression from the the readings very scattered, that the method was not accurate, but it must be remembered that the vertical scale on the graph is mag- nified 250 times over the horizontal scale, so these variations are really very small. That the variations are due principally to the inability to set the mark on the screw head exactly even with the index mark, is shown by the fact that the readings integrate to produce a curve with regular variations. Even these slight errors are not present in the final measurement of length ( except the error of setting at the beginning and end of the entire run ), since what was gained at one setting was lost in the next. The experiment also showed that the instrument was very sensitive to changes of temperature, and so must be carefully shielded from sudden changes of even a degree or two. The steam came on in the radiator during one measurement with the result hat the fringes became so erratic that further measurements had to be postponed until the temperatures in the room were equalized. It also proves that the method is highly accurate, the -43- greatest inaccuracy being in estimating tenths of a fringe ( 0.9000l cm ) and while, perhaps, lichelson's method is capable of measuring longer dis.ance, such as the meter, this method is less laborious and far superior for making short measurements and comparing two lengths that diffen y only a short amount. -44- PART IV 7') “h4finfifn nr\1"'117)h75 I T?"‘rfl". ’7‘YT'W c's A VOA“ '~/UA._..LA.5I'~JJ.A‘J flay-J -4L ¢.W.o L Plate Vllis a drawing of a proposed commercial caliper and m—asureing instrument which makes use of the method of measurement just described for making comparisons of objects of about the same size. The design is primarily the work of Dr. C. I. Chamberlain under whose guidence I have worked. However, some features incor- porated in the present design are the result of investigations carried out in this experiment. The optical system is identical with that used in this experiment except that it lies in a vertical instead of a horizontal plane, and all the parts are designed to fit together as one compact 1 unit, Which is entirely inclosed thus excluding unlesirable air our- The measuring device can be moved up or down the su;port- ing column several inches by means of a rack and pinion movement. A cubical block of glass with plane parallel upper and lower faces, the upper one silvered, constitutes both the moveable interferometer mirror and the upper jaw of the caliper. The lever jaw of the cal- iper is an accurately ground plate in the base of the instrument. 1 he lass block is to be carried in a hollow brass cylinder which 1)“ J slides up and dorn inside another cylinder. The two surfaces in 51: contact ceul be ground to a high degree of accuracy. revision -45- ............ c-' . " I ........... In! ------- ;l ---- 1-5 -. . ...... “at" U... ', z : 2"".10: , I I a". u ' It 0 I ' l u u . I r ' ' n)- , I ; I - u ‘0 ......... C ' - V . - J "":J ‘I". ’ O ............ -;- ----- I I l .. . I r355 l' 1/; [I I I I, I; 1/., 1 (I (I: ." INVENTOR. BY (MK-(Ismér’m ATTDRNEY. :1- would be mwde for raisin he cylinder carrying the glass block, a centimeter or two by turning a knurled nut. The instrument would be used for making comparisons such, for example, as comparing the size of a steel ball with a standard Johanson block of the same thickness as the steel ball was supposed to be. To do this the instrument would be lowered until the Jeaan- son block would just fit between the caliper jaws and hold the up- per jaw and mirror up slightly. The nuuber of Chamberlain fringes in the range would be noted. Then the mirror would be lifted, the Johanson block removed, and the work to be tested put in its place, the mirror lowered and the number of fringes again noted. The difference between these two numbers would be the amount that the work wa "off size" expressed_in the unit for which the range was set up. It will be noticed that there is an extra horizontal mirror just under the telesc0pe and that provision has been made for setting the mirror Opposite the collimator either vertical or at an angle of 45° with the vertical. then in the latter position the light falling on it would be reflected up to the horizontal mirror just below the telescope thus lengthening this path. The same adjustments could be used in this position as in the former and the inetrumen could now be used like the Zeiss instrument for measuring the length of a Johanson block in light waves by making observations on Fizeau fringes formed between the mirror and top of -45- the Johanson block, and the mirror and lower caliper jaw ( the upper caliper jaw being removed for this purpose ), in six different colors of monochromatic light. One of the sets of Prizeau fringes will go half way across the field and the other set the rest of the way thus making a break in the fringes unless the double thickness of the Johanson block is an exact number of wave lengshs. By mak- ing observations in the six different colors it is possible to calculate the length of the Johanson block. -47.. Fig. 1. E! G: fix .E NKTVR . “(UN u 5.~\\.§\ t .q a\ -3 \suxum, tUNquLutk \o mewheok \ ? 3 :95qu 0» y. a, -9 40/ JJ'JDLL/OJD/A/ Uo swag/1.1 p hicrometer R-I. Fringes Difference 3.1. Fringes Temper- Reading in Range in Range ature AFTER hovement BEFOREKovement 12.00 xxxx xxxx 33.6 23.6 C. 12.05 -15.3 48.9 24.2 12.10 -25.0 49.2 29.3 12.15 -20.4 49.7 26.3 12.20 -23.0 49.3 31.5 12.25 -18.4 49.9 27.9 12.30 -21.9 49.6 28.3 12.35 -21.3 49.6 23.0 12.40 -26.5 49.5 29.5 22.0 C. 12.45 ~20.2 49.7 27.7 12.50 -22.1 49.3 19.1 12.55 -30.7 49.8 28.7 12.60 -22.1 49.8 25.3 12.65 -24.2 49.5 25.7 12.70 -24.3 50.0 21.3 12.75 -28.4 49.7 26.6 12.80 -23.1 50.1 22.7 12.85 -26.8 49.5 24.0 12.90 -25.7 49.7 28.4 12.95 -20.9 49.3 24.4 13.00 -24.5 49.9 xxxx 22.1 C. Total number of Fringes 992.5 Length 992.5 x 0.00010077 or 0.100016 cm. hierometer R.I. Fringes Difference R.I. Fringes Temper- Reading in Range in Range ature AFTER hovement BEFORE Movement 13.00 xxxx xxxx 23.2 22-1 C. 13.05 -26.2 49.4 24.7 13.10 -24.7 49.4 29.3 13.15 -19.9 49.2 19.9 13.20 -29.0 48.9 23.6 13.25 -25.9 49.5 23.5 13.30 -26.1 49.6 22.6 13.35 -27.0 49.6 24.9 13.40 -24.9 49.3 29.5 13.45 ~19.7 49.2 26.4 13,50 -24.4 50.8 23.7 13.35 -26.0 49.7 26.5 13.60 -22.1 48.6 33.9 13.65 -15.5 49.4 23.0 13.70 -26.9 49.9 26.3 13.75 -23.3 49.6 24.0 13.80 -25.7 49.7 23.1 13.85 ~26.6 49.7 25.1 13.90 -24.3 49.4 28.2 13.95 -2l.1 49.3 21.7 14.00 —23.1 49.8 xxxx 22.5 C. Total number of Fringes 990.5 Length 990.5 x 0.00010077 or 0.099815 cm. Micrometer R.I. Fringes Difference R.I. Fringes Temper- Reading in Range in Range ature AFTER hovement BEFORE Hovement 14.00 xxxx xxxx 30.9 19.0 Co 14.05 —17.6 48.5 25.8 14.10 —23.4 49.2 24.3 14.15 -25.0 49.3 24.5 14.20 ~24.8 49.3 23.5 14.25 ~25.4 44.1 23.6 14.30 -25.6 49.2 20.7 14.35 -28.9 49.6 25.4 14.40 -24.2 49.6 29.8 14.45 -19.8 49.6 25.6 14.50I -24.1 49.7 37.3 14.55 -11.2 49.3 24.4 14.60 ~25.7 49.9 21.4 14.65 -28.1 49.5 28.6 14.70 -21.0 49.6 17.8 14.75 -31.8 49.6 23.4 14-80 —25.9 49.3 25.0 14.85 —23.9 49.7 22.4 14.90 ~27.2 49.6 26.0 14.95 -23.2 49.2 27.1 15.00 -22.2 49.3 xxxx 20.5 C Total number of Fringes Length 988.1 988-1 x 0.00010077 or 0.0995725 cm. Hicrometer R.I.Fringes Difference R.I. Fringes Temper- Reading in Range in Range ature AFTER hovement BEFORE Movement 15.00 xxxx xxxx 25.9 20.5 C- 15.05 -23.2 49.1 27.2 15.10 -22.0 49.2 25.0 15.15 ~24.6 49.6 27.1 15.20 -21.9 49.0 24.0 15.25 ~24.8 49.4 24.6 15.30 -24.6 49.4 24.2 15.35 —25.2 49.4 21.5 15.40 ~28.0 49.5 33.0 15.45 -l6.2 49.2 25.5 15.50 -24-2 49.7 23.2 15.55 -26.4 49.6 25.3 15.60 ~24.2 49.5 30.4 15.65 ~19.1 49.5 29.6 15.70 -20.3 49.9 ~22.3 15.75 —27.9 50.2 23.4 15.80 -26.1 49.5 23.0 15.85 -26.4 49.4 26.8 15.90 ~22.5 49.3 26.5 15.95 —23.0 49.5 24.7 16.00 ~24.6 49.3 xxxx 22. C. Total number of Fringes 989.2 Length 989.2 x 0-00010077 or 0-0v96323 cm. micrometer R.I. Fringes Difference R.I. Fringes Temper- Reading in Range in Range ature AFTER Hovement JEFORE Movement 16.00 xxxx xxxx 20.8 20.0 Co 16.05 -27.8 48.6 39.0 16.10 -10.0 49.0 23.6 16.15 -25.5 49.1 24.4 16.20 -24.9 49.3 20.8 16.25 ~28.3 49.1 . 25.8 16.30 -23.5 49.3 26.3 16.35 -23.2 49.5 30.1 16.40 ~19.3 49.4 21.4 16.45 -28.3 49.7 26.0 16.50 -23.6 43.6 22.8 16.55 -26.6 49.4 23.9 16.60 ~26.1 50.0 28.2 16.65 -21.1 49.3 23.3 16.70 ~26.4 49.7 20.2 16.75 ~29.5 49.7 23.0 16.80 -26.8 49.8 21.0 21.5 C. The heat came on causing air currents at this time- 16.85 -28.4 49.4 20.2 22.5 C. 16.90 —28.9 49.1 28-6 16.95 -20.8 49.4 29.5 17.00 ~19.7 49.2 xxxx 22.8 C. Total number of Fringos 987.6 Length 987-6 x 0.00010077 or 0.995225 cm. Micrometer R.I. Fringes Difference R.I. Fringes Temper- Reading in Range in Range ature AFTER movement BEFORE Movement 27-00 xxxx xxxx 25-1 22-0 C- 27.05 -24-3 49.4 28.0 27.10 -21-3 49.3 25.7 27.15 —23-2 48.9 29.8 27.20 -19.4 49.2 28.5 27.25 -21.0 49.5 27.3 27.30 «21.9 49.2 26.1 27.35 -23.3 49.4 24.4 27.40 -25.4 49.8 25.4 27.45 -24.1 49.5 22.9 27.50 -26.4 49.3 23.8 27.55 ~26.1 49.9 27.5 27.60 ~22.2 49.7 37.1 27.65 —l2.9 50.0 26.5 27.70 —23.4 49.9 21.2 27.75 -28.9 50.1 29.0 27.80 ~20.6 49.6 23.2 27.85 —26.3 49.5 24.6 27.90 —24-7 49.3 24.3 27.95 —24.3 49.1 27.7 23-00 -21-5 49.2 xxxx 22-5 C- Total number of Fringes 989.8 Length 989-8 x 0.00010077 or 0.099845 cm. hicrometer R.I. Fringes Difference R.I. Fringes Temper- Reading in Range in Range ature AFTER hovement BEFORE hovement 28-00 xxxx xxxx 23.2 22.5 C- 28.05 «21.0 49.2 29.9 28.10 ~18-9 43.8 21.7 28.15 —27.7 49.4 23.9 23.20 -25.3 49.2 27.7 28.25 —22.0 49.7 32-8 28-30 «16.4 49.2 27.2 28.35 —22-1 49.3 24.9 28.40 ~24.o 49.5 21.7 28.45 ~38.1 49.8 18.7 23.50 -20.9 49.6 xxxx 22.5 C. . 'r—yv ‘l‘ \fi'fi w—v—xv 31.3141 «-rrulrni A Treatic on Light R. A- Houston- Fages 134 - 139; 147 - 150; 224 - 245. Physical Review, Vol- 31, Tags 591 ; The Grating Interferometer By C. Zarus and H. Barus. Publication $0- 149, Carnegie Institute of Machington, Part I, Page 53- Interferometry with the Aid of a Crating. C- Zarus- Dictionary of Applied Physics, Vol. III. Glazebrook. Pages 475-477; hichelson's Experiment; Determination of the Keter also Pages 604—605; Errors of Screws- Dictionary of Applied Physics, Vol. IV. Glazebrook- Pages 180—190; Interference of Light also Pages 143-149; Technical Applications of Interference- The Theory of Light Preston. Pages 164-241; Interference. Philosophical Kagazine, Vol-XXIX, Tags 449; Nichelsons Interferometer. Dictionary of Applied Physics, Vol- IV- Glazebrook. Pages 299—303; Kaking Johanson Blocks. :.in. 11.1. Iii-It'll. . . ‘ v g‘gi {.\.t$\1.tl.l.k‘,.Illl.l|'-I’. ..II.vv.Vl til}- . J! 1.: .. tii‘ffgf :1. f in to; err? s l t'l.’£: 9': b-n.l.\!.ul 0 5|]! llHI111IllIll!"INN"llllllflllllllllllll”1111111ll 016895470