A PRECISION DETERMINATION OF THE VELOCITY OF LIGHT BY A BAND SPECTRUM METHOD

57 Pages·1.877 MB·English

by  RUTH, RALPH POWERS

The Pennsylvania State College
The Graduate School
Department of Physics
A Precision Determination of the Velocity
of Light t>y a Band Spectrum Method
A Dissertation
ty
Ralph Powers Ruth
and
Kenneth Leroy Vander Sluis
Submitted in partial fulfillment
of the requirements
for the degree of
Doctor of Philosophy
June 1952
Approved:
Department ox Physics
Head of the Department
ACKNOWLEDGMENTS
The work described herein was the result of a suggestion made
by Dr* A. E. Douglas of the National Research Council (Canada)*
Dr. Douglas also aided the work by furnishing some of his unpublished
data for the HCK bands investigated here.
The authors wish to express their gratitude to the personnel
of the Spectroscopy Laboratory for their aid in this investigation.
In particular, they desire to thank Dr. D. H. Rank and Dr. R. S. Kagarise,
who nude the mirrors for the long path absorption tube* and E. R. Shull,
who prepared the sample of HCN and did much of the glass-blowing.
The precision realized in this work has been due in a large
part to the use of the Tuxedo grating loaned to Dr. D. H. Rank by
Dr. G. E. Dieke of Johns Eopkins University.
The determination of the value of the velocity of light desoribed
here required knowledge of the microwave value of the rotational
constant Bqqq for HCN. The authors are indebted to Dr. C. H. Townes
end his coworkers at Columbia University, and to Dr. IV. Gordy and
his collaborators at Duke University, who furnished their pre­
publication results for Bqqq of HCN.
The authors are grateful to Dr. D. H. Rank for his close super­
vision throughout this investigation, which was supported in part by
Contract N6onr-269» Task V of the Office of Naval Research.
3 7 G 2 3 S
ABSTRACT
The rotational constant Bqqq ^or 2CN has been measured using
the 004 and 103 infrared vibration-rotation bands. A Pabry-Perot
etalon was crossed on a high-resolution plane grating spectrograph,
used in conjunction with a multiple reflection absorption tube. The
value of B000 obtained is 1*47830 ^ 0*00002 cm“*. This same con­
stant has been measured in pure frequency units in the microwave
region by Townes and his coworkers and by Gordy and his collabo­
rators. The weighted mean of their values for this constant is
44f3l5*96 ± 0.13 mc/sec. The ratio of these two values gives
directly the velocity of light in vacuo. The value so obtained is
c ■ 299t776 — 5 km/sec. An improved procedure for precision
determination of molecular constants, which makes better use of
the experimental data, is described*
TABLE OF CONTENTS
SECTION PAGE
INTRODUCTION............................................ 1
Early measurements.................................... 1
Fizeau-type measurements ............................... 2
Foucault-type measurements............................. 1*
Microwave measurements................................ 6
Indirect measurements................................ 7
PAND SPECTRUM METHOD OF MEASURING c ..................... 8
EXPERIMENTAL PROCEDURE AND APPARATUS..................... 13
DETERMINATION OF THE MOLECULAR CONSTANTS................. 23
RESULTS AND DISCUSSION .................................. 28
P1RLIOGRAPHY.............................................. 32
A?; END I X .................................................. 36
LIST OF TABLES
TABLE PAGE
I. V.reighted Means of the Functions....................... 38
II. Rejection Data....................................... 39
III. HCN Band Rotational Constants........................ UO
IV. Fourth Power Coefficients ............................. Ul
V. Principal Experimental Valueso f the Velocity of Light in
Vacuo Since 1900 U2
LIST OF FIGURES
FIGURE PAGE
1. Optical Layout of Interferometer System................ 15
2a. Fabry-Peret Pattern on a Standard Neon Line............ 17
2b. Second Order OOU Band of HCN with Second and Fourth Order
Interferometer Fringes ............................. 17
3a. First- Order 103 Band of HCN with Superimposed
Interferometer Fringes ............................. 20
3b. Second Order COU Band of HCN with Fourth Order Iron
Standards.......................................... 20
Lt. A 2F1' Function OCU Banc HCN........................... ii3
5. A oF1 Function Band HCN......................... UIi
6. Function OQu BandH CN........................... UB
7. Function 00 u. Band HCN'........................... U6
3.^ 2^'' Function 103 BandH CN . ....................... U7
c. Z^F* Function 103 BandH CN........................... U8
10. V. V Function 103 BandH CN .................... U9
11. ^ Function ln3 BandH CN .................. 50
12. Detail of Band-Fringe Intersections .................... 51
INTRODUCTION
Since all electromagnetic radiations travel through free space with
the same velocity, the magnitude of this constant c is of great theoret­
ical importance. As a consequence, many attempts have been made to
determine precisely the magnitude of the velocity of light in vacuo.
Early Measurements
The first recorded attempt to measure the velocity of light was that
of Galileo. He tried to time the transit of a pulse of light travelling
between two observers a few miles apart. The pulse was produced by
manually shuttering a lantern. The eiiort was unsuccessful because of
the extremely short time interval involved.
The first successful measurement was a consequence of astronomical
observations of the period of the inner satellite of Juoiter made by
Homer in 1676. Discrepancies between observed and predicted times of
eclipse of the satellite were attribute^ by Romer to the varying distance
between Juoiter and the earth and to a finite velocity of light. A
second astronomical determination mace by Eradley in 1728 involved the
aooarent angular displacement of the fixed stars when viewed in a direc­
tion perpendicular to the orbit of the earth. This aberration is due
to the motion of the earth in its orbit, and the resulting forward
angular displacement is equal to tan-1v/c, where v is the velocity of
the ^arth in its orbit.
2
Fiaeau-type Measurements
In the mid-nineteenth century (I8U9), Fizeau devised the first
successful terrestrial method for direct measurement of the velocity of
light. For this determination a beam of light was interrupted periodically
by a rotating toothed wheel. The resulting light pulses traversed a
distance of 8.633 kilometers to a mirror and retraced the path to the
toothed wheel. The phase of any given pulse with respect to the rotating
wheel was determined by the total optical path and by t-he frequency of
rotation. For a oarticular frequency the phase of a returning pulse was
such that it was eclicsed by the too+.h adjacent to the ODening through
which the nulse emerged. For odd multiples of this frequency the eclipse
was '■reduce'' by teeth farther removed from the exit slot. From observa­
tions of these frequencies and from the known distance the velocity of
light in air was determined.
The chief difficulty in Fizeau1s experiment was the production and
accurate measurement of a constant frequency of rotation. This difficulty
was minimized by several investigators who replaced the toothed wheel of
the Fizeau method by other oulsing devices. The first of these were
Kerolus and hittelstaedt^ who, in 1926, reporte' the use of two Kerr
cells instead of a toothed wheel. The pulsing frequency with the Kerr
cell is several hundre~ times that obtainable with a rotating tooth-wheel.
This makes it uossible to use shorter path lengths, but as a result the
1 0. Mittelstae:t anc. A. Karolus, Phys. Zeits. 2£, 6?8 (1928);
C. Mittelstaedt, Phys. Zeits. 30, 165 (1929); Ann. d. Fhys. 2, 288 (1-29).
3
measurement of path length becomes the principal source of error.
Anderson'- further modified the Fizeau method by employing only one Kerr
cell and dividing the outgoing beam try means of a half-silvered mirror.
The two components of the beam travelled different distances before
being recombined; the relative phase of the two components, upon reaching
a photocell detector, was dependent uoon the relative path lengths and the
frequency of the Kerr cell modulation. Here the chief source of error
involved the difficulty in recombining the two beams at the same point
in the ohotocell. This source of error was eliminated by Eergstrand,3
who used a single beam modulated by a Kerr cell. The sensitivity of
the phototube detector was modulated by the oscillator that modulated
the light source; thus, for certain path lengths, the modulated return
beam and the phototube sensitivity were in phase, producing maximum tube
output. In contrast to the other Kerr cell measurements, which were
made indoors with relatively short path lengths, Bergstrand's determina­
tions were made with long oath lengths outdoors and thus include atmospheric
uncertainties.
Another variation of the Fizeau method was used by Houstoun,^ who
replaced the toothed wheel by a quartz crystal in an alternating electric
field of freauency equal to one of the natubal frequencies of the crystal.
2 7*. C. Anderson, Rev. Sci. Inst. 8, 239 (1937); J. Opt. Soc. Am.
31, 187 (I9I4I) •
3 L. E. Bergstrand, Nature lo3, 333 (19U9); 165, H05 (1950);
Ark. Fys. 3» b79 (1951)•
U R. A. Houstoun, Nature 1U2, 833 (1938); 16H, 1,00U (I9U9);
Proc. Roy. Soc. Edinb. A63 (Pt. 1), 95 (1950).
k
Under these conditions a quartz crystal acts as a periodically intermit­
tent diffraction grating, transmitting a modulated monochromatic light
beam in a given direction. Upon reflection by a mirror the beam retraced
its Dath to the crystal where it was transmitted only if its phase and
that of the crystal grating agreed. For different mirror distances suc­
cessive maxima and minima were observed in the return beam, and from
these observations and knowledge of the modulation frequency the velocity
of light in air was found. A similar technicme was resorted by McKinley,5
who utilized the electric double refraction in quartz for purposes of
modulation only. The light beam was divided into two parts of different
oath lengths; these were recombined at a tuned photocell detector, their
relative phase denuding on the position of a reflecting mirror in the
longer path. Although McKinley's largest error was in the measurement
of the actual path lengths, the most serious uncertainty inherent in both
of these methods was in the determination of the mirror positions which
oroauced mini-rum intensity at the detector.
Foucault-type Measurements
A second terrestrial method for obtaining c was suggested by Arago
in 1838 and carried out by Foucault in 1862. In this measurement a light
beam nassed through a clear parallel plate inclined to the beam and was
reflected by a olsne mirror and focused on a concave mirror 20 meters
from the plane mirror. Tne center of curvature of the concave mirror was
at a ooint on an axis about which the plane mirror could be rotated. Thus
5 D. '.V. R. McKinley, J. Roy. Astron. Soc., Canada Uli, 89 (19?0)