Mar., 1917
T H E JOURNAL OF INDUSTRIAL A N D ENGINEERING CHEMISTRY
Repeated physical examinations of t h e older employees a n d careful inquiry have failed t o discover a symptomcomplex t h a t could be attributed t o chronic picric poisoning. If t h e digestive disturbances above mentioned are evidences of such poisoning, t h e n we must admit t h a t such a condition is very easily a n d rapidly acquired, as many of t h e men with these complaints reported shortly after being employed. T h e men working with this substance for t h e longest time show no predisposition. This is without question a dangerous trade a n d many accidents occur as a natural result. Even though a company makes every effort t o protect its men, trouble will still follow gross carelessness on t h e p a r t of employees; a n d it is entirely proper t o attribute a very large percentage of accidents t o this cause. Also, because i t is a dangerous occupation, a n d t h e men are working with something t h a t is more or less a mystery t o them, they are prone t o find in their work a cause for all their bodily ills, regardless of how absurd may b e t h e relation of cause t o effect. WOBURh'. hIASSACHUSBTTS
A NEW DIRECT READING PRECISION REFRACTOMETER
WlTH UNIFORMLY DIVIDED SCALE By G. W. MOFFITT Received December 18, 1916 1-1
N T R 0 D U C T I 0 iX
I t has long been knomm t h a t t h e value of t h e index of refraction frequently serves as a valuable criterion of t h e qualities of a liquid. T h a t t h e means for testing t h u s afforded is not in more general use seems t o be d u e t o t h e lack of satisfactory means for easily determining t h e index of refraction rather t h a n t o a n y inherent weakness in t h e method itself. If some dependable instrument combining ease of operation with accuracy of results were a t hand i t is probable t h a t there are many who would avail themselves of i t s possibilities. While there are several good refractometers which may be obtained, their use involves a great deal of care a n d skill if results are t o be obtained showing t h e necessary high degree of accuracy. I n some of t h e m t h e operation is long and t h e result is not available without more or less calculation a n d reference t o tables. There seems, therefore, t o be a real demand i n t h e field of food a n d industrial chemistry for a simple, accurate refractometer so simple in operation t h a t one without any special knowledge of optics could obtain accurate results easily a n d with certainty. Such a n instrument has been recently designed by t h e writer1 and a brief description of t h e refractometer and a discussion of its theory are here given for t h e purpose of placing t h e instrument before those who have need of i t in their work. T h e good points of t h e instrument will appear in t h e discussion, a n d may be briefly summarized as follows: I--.\ linear scale calibrated directly in terms of t h e index of refraction of t h e liquid under examination. 1
Physical Review, December, 1916.
305
2-The possibility of so constructing t h e instrument t h a t white light may be used when i t is desired t o determine t h e mean index, t h e instrument still retaining approximate achromatization in many cases. 3-Simplicity, and ease of manipulation. 4-Few adjustments other t h a n those fixed permanently in t h e construction of t h e instrument. 5-Settings obtained by comparing t h e dimensions of a n image with those of a n eye-piece scale-an accurate means of determining t h e proper adjustment. 6-Adequate means for temperature control whenever required. 7-Small amount of t h e liquid required for a determination, a single small drop being sufficient. 8-Ability t o determine t h e index t o one or t w o points in t h e third decimal place-a degree of precision equal to, if not better, t h a n t h a t of t h e t o t a l reflection instruments. T h e entire operation of determining t h e index of refraction of a liquid consists in placing a drop of t h e liquid at t h e proper place on a convex surface, bringing t h e nose of t h e microscope down upon i t , and focusing t h e eye-piece. T h e value of t h e index is then read off directly from t h e uniformly divided scale on t h e focusing t u b e of t h e instrument. I n a n instrument of convenient size t h e change in setting for a change of index from 1.000 t o I.jO0 may be more t h a n I O cm. With a n eye-piece of fairly high power t h e uncertainty in a setting need not be more t h a n 0 . 0 2 cm. I n most cases i t will be less. T h e sensitiveness will, therefore, compare favorably with t h a t of t h e best total reflection instruments. 11-THEORY
CASE 1-Consider t h e arrangement shown in Fig. I. Let a point source of light be placed at C, distant R below t h e surface of t h e liquid. I t s image, due t o t h e refraction a t t h e surface of t h e liquid, will be a t S, so t h a t ST = R/lz, where n is t h e index of refraction of t h e liquid. Let S act as a virtual object at distance K R / n from a converging lens L of focus f , a n d let t h e image of S formed b y this lens be at I, distant fi from t h e lens. T h e n
+
Clearing of fractions, npj knf R j = pkrt Rp. This equation becomes linear in n and p when
+
+
+
n p j = n p k , or when k Equation z then becomes n
R =
f2
P
R
- j'
=
j.
(2)
(3)
(4)
T h a t is, if Equation 3 is satisfied, t h e position of t h e image depends directly on t h e index of t h e liquid. CASE a-Consider t h e arrangement shown in Fig. 11. Let t h e point source be placed a t C, t h e center of curvature of a spherical lens having concentric surfaces, a n d let a drop of t h e liquid be placed between t h e lens
T H E J O U R N A L OF I N D U S T R I A L A N D ENGINEERING C H E M I S T R Y
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Vol. 9 , No. 3
be brought t o a focus a t t h e plane surface of t h e liquid. CASE 3-Consider t h e case when t h e source is not a t t h e center of curvature of t h e concentric lens, or when t h e lens is of some other form, b u t a t a distance from it such t h a t its apparent distance from t h e curved liquid surface is u. The image by refraction of t h e liquid lens into t h e plane parallel plate is according to t h e equation for t h e plano-concave lens bounded on t h e plane side by a medium of index n‘.
L
?E‘ ~
-I
- I = -n -
C’T
u
R
, or,
C’T =
uRn’ R +-u(n-
(IO) I)
The refraction a t T‘ may be expressed as follows:
The object distance for lens L is
Applying t h e equation for t h e converging lens,
‘C
FlGJ
F I G Z
a n d a plane parallel glass plate placed-in contact with t h e lens. T h e treatment differs from t h a t of Case I i n t h a t t h e effect of t h e plane parallel glass plate must be considered. Beginning with C as a point source t o locate its image C’ by refraction a t t h e surface T we have t h e following equation:
where n’ is t h e index of refraction of t h e plane parallel plate. I n t h e same way t h e refraction a t T’ may be expressed. I R ~ ST’ = (CT’ t)- = -LIZ‘ n n‘
+
+
where t is t h e thickness of t h e plane parallel glass plate. From t h e equation of t h e converging lens, I -
I
I
= -- + z + k +z+k j*
pP + R n n
1
(7)
The condition t h a t this equation be linear in n and
p is
Differentiating with respect t o n, M2Rn‘2f2 dP= - (14) dn (uRn’ (t ? ~ ’ k - - n’j) [R +%-(n - I ) ] } ~ ‘
+ +
When t h e condition expressed in Equation 8 holds t n’k - n’f = 0, (15) and t h e slope is a constant, Equation 13 taking t h e simpler form
+
When k is too large t h e second term in t h e denominator is positive and increases with n. Therefore, t h e slope decreases as n becomes greater and t h e curve is concave toward the axis of n. If k is too small t h e reverse is t r u e and t h e curve is concave towards t h e axis of p . If u be set equal t o R, Equation 16 becomes identical with Equation 9 , t h a t equation being a special case of t h e general equation just derived. RELATIONS
BETWEEN DINENSIONS
OF
OBJECT
AND
IMAGE-Let c represent t h e size of t h e object in Fig. 11, and let C’, S and I represent t h e size of t h e images formed a t these respective points. Then
t
- + k = j . n‘ Making this substitution a n d clearing of fractions we have n = -Rp - - R
f*
f’
It will be noticed t h a t Equation
(9)
since no change in size of image is produced by t h e refraction a t T’. By refraction at t h e converging lens L. (18)
g is identical with
Equation 4, b u t t h a t t h e conditions for linearity of scale stated in Equations 3 and 8 are slightly different, owing t o t h e effect of t h e plane parallel glass plate. It will be seen t h a t in both cases t h e adjustment for linearity of scale is such t h a t if parallel rays were incident upon t h e upper face of t h e lens L they would
Combining 17 and 18,
Substituting t h e values of C’T, p , and SO from Equa-. tions IO, 1 2 and 16, and simplifying,
Mar., 1917
T H E JOURNAL OF INDUSTRIAL A Y D ENGINEERING CHEMISTRY
I
= f-
(20)
c u' T h e image is of constant size for a fixed value of u , a property of t h e system utilized in a method for precise focusing t o be described in a later paragraph. 111-ABERRATIOKS
DISTORTION-With t h e direct illumination t h a t may be used in this instrument it is possible t o use a stop of rather small diameter and still have a well-lighted field of view. Since only a small portion of each lens is used in forming t h e image of any point in t h e object t h e effect of spherical aberration in blurring t h e image is very small. Therefore, i t seems unnecessary t o take particular precautions t o eliminate spherical aberration. Curvature of t h e image, however, may affect t h e performance of t h e instrument t o a slight extent. The curvature of t h e virtual image formed by t h e liquid lens is concave towards t h e eye-piece. The effect of t h e converging lens L in forming t h e image a t t h e eyepiece is t o diminish t h e curvature. The curvatures of t h e surfaces a n d t h e position of t h e stop should be so chosen t h a t t h e resulting image will be as nearly plane as possible over t h e area covered by t h e image a t t h e eye-piece. Even if t h e radius of curvature of t h e image were so small as 5 cm. in a n instrument whose image were 0 . 5 cm. in extent, t h e periphery of t h e image would be out of t h e plane of t h e center by SPHERICAL A B E R R A T I O N A N D
This value is less t h a n t h e error of a setting. And since t h e focusing is always done on t h e peripheral portions of t h e image the effect would be t o change slightly t h e position of t h e zero point of the scale. C H R O M A T I C ABERRATION-In considering t h e chromatic properties of t h e system two distinct cases arise. If t h e converging lens L be strictly achromatic t h e adjustment for k is correct for all wave-lengths. The instrument will not give an achromatic image a t the eye-piece, b u t t h e various colored images will be distributed along t h e axis according t o t h e dispersion of t h e particular liquid in t h e apparatus. Such would be t h e construction of t h e refractometer if it is desired t o measure t h e value of t h e index for different wavelengths in order t o determine the dispersion of t h e liquid. I n this case monochromatic illumination is, of course, necessary. Lens L must be thoroughly achromatized in order t h a t t h e adjustment of k shall be correct for all t h e values of wave-length with which t h e instrument is t o be used. T h e other case arises when t h e lens L is of t h e simple uncorrected type. This leaas t o a construction which may be approximately achromatized for liquids. of ordinary dispersion, a n d which when illuminated with white light will give t h e index for some particular value of t h e wave-length for which t h e instrument has been calculated. Considering t h e positions of the red a n d t h e blue images formed by t h e liquid alone, we find t h a t t h e blue image lies nearer t h e lens L t h a n
3Oi
does t h e red image. If t h e chromatic properties of this lens are such t h a t its images of t h e images formed by t h e liquid lens fall a t t h e same point t h e system will be achromatic in t h e sense t h a t t h e different colored images will be a t t h e same point in t h e eyepiece. This condition can be realized only for liquids whose dispersion bears a certain relation t o t h e index of refraction for some intermediate wave-length. Since no such relation is general it will be seen t h a t it is not possible t o achromatize t h e instrument completely, although a n approximation may be realized which will be satisfactory for many liquids. Whenever it is desired t o use t h e instrument with a liquid which gives chromatic effects detrimental t o accurate focusing it would be necessary t o use t h e monochromatic light for which t h e instrument was designed t o give accurate readings. T h e condition for approximate achromatization may be derived as follows: For t h e convergent lens L, assumed bi-convex,
where V'p and V'C are t h e virtual object distances for t h e lens L for t h e same value of 9 , and where d' = n'p - n'c for t h e lens, and r is t h e radius of curvature of t h e lens faces. For the plano-concave liquid lens,
where Vc and Vp are the distances from t h e liquid t o t h e corresponding images for a given value of u. R is t h e radius of curvature for the curved surface of the liquid 'and d = nF - nc. The condition for achromatization is vc - VF = V'c - V'p. (23) Dividing
(21)
by
(22)
and substituting ( 2 3 ) ,
This reduces t o
U R ~ ~ ~ D ( ? Z 'i)d D-= lzDfDUdZR&'+ (UR+ f ~ R - - f ~ u ) d a R d ' ,
(25)
which shows t h a t i t is possible t o achromatize the system for any liquid whose mean index bears a certain relation t o t h e square root of its dispersion. This relation is determined b y t h e constants of t h e optical sys te m. IV-THE
INSTRUMENT
The refractometer may be set up in a convenient form resembling an ordinary microscope in appearance. Instead of t h e usual state a heating t a n k may be provided, through t h e center of which passes a springmounted t u b e carrying t h e object scale a t the lower end and t h e lens on which t h e liquid is placed a t the upper end. The spring mounting lifts this tube so t h a t t h e lens comes above the top of the heating jacket when the microscope is raised. I n this position i t is easy of access for cleaning and for placing the drop
3 08
T H E J O U R N A L OF I N D U S T R I A L A N D ENGINEERING C H E M I S T R Y
of liquid in position. At t h e lower end of the microscope t u b e is placed t h e plane parallel plate, and up in t h e t u b e a t t h e proper distance is placed t h e converging lens L. The microscope tube is arranged so t h a t i t may be lowered into position and t h e two lenses brought into contact, and in contact with t h e liquid, a n d lowered into t h e heating jacket. The eye-piece should be mounted in t h e end of a t u b e telescoping into t h e microscope tube with rack and pinion adjustment for ease of focusing. The focusing t u b e should also be provided with a scale, read with a vernier, whose divisions are in accord with Equation 16, if t h e instrument is t o be direct reading. The eye-piece should be of fairly high power and should be mounted in such manner t h a t it and t h e eye-piece scale may be moved laterally a short distance in order t o enable t h e user t o bring t h e image and t h e scale into coincidence.
Vol. 9, No. 3
I-When t h e stop is between t h e object and t h e liquid lens the chief image ra'ys are slightly convergent a n d t h e image increases in size as t h e eye-piece is racked in. This convergence is never very great. A rather large aperture for t h e liquid lens is also required. For these reasons this position of t h e stop is not good. 2-When t h e stop is in t h e plane of t h e liquid lens it is a t t h e principal focus of t h e lens L a n d t h e chief image rays are parallel. No change in the size of t h e image results on moving t h e eye-piece toward or away from t h e lens. Accurate focusing cannot be done with the stop in tliis position. 3-When the stop is a t t h e converging lens the chief image rays diverge from a point approximately coincident with t h e optical center of t h e lens. Their slope decreases with increase of t h e index of the liquid, thus decreasing the accuracy of a setting for the higher
ADJUSTMENTS-The adjustments of t h e instrument are few and simple. T h e converging lens and t h e plane parallel plate must be carefully fixed with respect t o each other. On this adjustment depends t h e linearity of scale. It will be seen t h a t t h e proper adjustment is such t h a t parallel light incident on t h e lens from above is brought t o a focus on t h e lower surface of t h e plate. If t h e system be lined up with a telescope focused for parallel light by t h e auto-collimation method, t h e adjustment may be made by eliminating parallax between t h e cross wire of t h e telescope and t h e images of fine dust particles on t h e lower surface of t h e plate. If t h e lens is not achromatic this adjustment should be made with monochromatic light of t h e same wave-length for which t h e instrument is t o read correctly. FOCUSING-In t h e development of t h e equations i t was shown t h a t t h e image in t h e eye-piece is of a fixed size whenever t h e instrument is in proper focus. The ratio of t h e image size t o t h e object size is given in Equation 2 0 . Therefore, if two scales be ruled with divisions in t h e ratio off t o u t h e one may be used as a n eye-piece scale and t h e other as a n object whose image is formed a t t h e eye-piece. When focusing is complete, image and eye-piece scale will be of t h e same size and coincident. POSITION OF STOPS: EFFECT O N FOCUSING-The rays usually used when locating t h e position of a n image graphically are seldom those t h a t actually form t h e image. The position of t h e stop t h a t limits t h e apert u r e of t h e instrument determines t h e rays t h a t actually form each part of t h e image. This would seem t o be of small importance here in its effect on spherical aberration and curvature of field b u t it plays a n important p a r t in focusing by comparison of image with eye-piece scale. While t h e eye-piece is moved outward throughout t h e range of clear focus we may have t h e image increasing, decreasing, or remaining of cons t a n t size, depending on t h e position of t h e stop. And t h e steeper t h e slope of t h e chief image rays with t h e axis of t h e instrument t h e greater will be t h e accuracy with which t h e focusing may be done. Several cases arise.
IT I I
i-.
'r III I
FIG.I11
values of t h e index. I t is apparent, however, t h a t t h e decrease in accuracy is less rapid t h a n t h e increase in value of the index so t h a t t h e percentage error decreases with increase of t h e index. It will be noted t h a t t h e center of t h e liquid lens is used t o form t h e center of the image while t h e peripheral rays form t h e edge of t h e image. This arrangement enables one t o focus with a good degree of precision. 4-If t h e stop be placed a t a fixed distance above t h e converging lens, say a t its principal focus, t h e divergence of t h e chief image rays is increased over t h a t of Case 3, and t h e accuracy of a setting thereby increased. Between t h e liquid lens a n d t h e converging lens t h e chief rays are parallel t o t h e principal axis. The effective apertures of both lenses are t h e same and v a r y inversely with t h e index of t h e liquid. The percentage accuracy of t h e settings is a constant because t h e distance from the stop t o t h e image is directly propor-
hIar., 1917
T H E J O U R N A L OF INDUSTRIAL A N D ENGIXEERING CHEMISTRY
tional t o t h e index of t h e liquid. This position of t h e stop seems most likely t o give high precision in t h e readings. Evidently t h e most accurate settings can be made when t h e divergence of t h e chief image rays is as great as is consistent with a good length of image a n d reasonably small apertures of t h e lenses, especially of t h e liquid lens. Since t h e aperture of t h e lenses is increased b y bringing t h e stop nearer t h e eye-piece i t is seen t h a t there is a limit where t h e increase in aberration effects due t o increased aperture of t h e lenses will counterbalance a n y gain in accuracy of focusing due t o increased divergence of t h e chief image rays. A compact instrument with a very open scale, a n d covering a long range, might be constructed in t h e following manner: Let t h e spring-mounted tube carry three object scales instead of one. Let these scales be so ruled a n d placed t h a t when focusing on t h e first scale values of index from 1.000t o 1 . 2 + would cover t h e range of t h e engraved scale of t h e instrument. By focusing on t h e second scale values from 1.2 t o 1.4+ could be read, a n d b y focusing on t h e third scale values from 1.4t o 1.6+ could be determined. Such a n instrument would be of practically t h e same size as one with single scale covering t h e same range with one-third t h e openness of scale. With certain values of index two scales would be in focus in t h e field of view a t t h e same time. Each scale should be given a distinguishing mark a n d t h e three should be placed a t different angles across t h e field of view in order t o prevent confusion of t h e scales. V-E
XP E RI 31E N T A L
After considerable preliminary work a single scale instrument was constructed essentially as described above. T h e lenses, except t h e optical flat, were made b y a local firm of spectacle lens grinders. T h e centering was not all that could be desired a n d for this reason a satisfactory s t u d y of t h e effect of varying t h e position of t h e stop was impossible. The stop was placed a t t h e converging lens L which h a d a focal length of about 8.5 cm. T h e aperture used was somewhat less t h a n a centimeter in diameter. The radius of curvature of t h e upper face of t h e concentric lens was 6.of cm. Actual openness of scale was found t o be 1.282 cm. for a change of 0.1 in t h e index of t h e liquid. T h e value of u was placed equal t o t h a t of f , since t h a t adjustment leads t o t h e shortest t u b e length for t h e instrument. It also leads t o more accurate focusing t h a n when t h e t u b e is longer since t h e chief image rays are more divergent. The length of t h e object a n d t h e image scales was 0 . j cm. T h e approximate adjustment of k was made b y t h e collimation method already described, using sodium light. Careful determinations of t h e index of refraction were then made for several liquids using a spectrometer a n d a hollow 60' prism. Immediately after t h e deviation readings were taken with t h e spectrometer a drop of t h e liquid was removed from t h e prism a n d placed in t h e refractometer. A number of settings were made a n d the reading of t h e centimeter scale on t h e focusing tube of t h e instrument recorded each time. T h e illumination for all readings was furnished b y a Bunsen burner whose flame was colored
309
by a piece of asbestos soaked in a solution of common salt. T h e procedure was carried out for all t h e liquids in t h e table below. Spectrometer Value of n 1.000 (assumed) 1.3318 1.4475 1.4994 1.6209
SUBSTANCE
.... . . . . . . . . . . .. . . . . .. . .
Air ,, ,, Water.. .. , , .., ., . . Kerosene.. . . .. Cedar Oil. . , , , . . . Carbon Bisulfide.. . .
Refractometer Readings cm. 1.42 1.41 1.42 < 4 1 + 5 . 5 7 5.59 5.58 7.02 7 . 0 3 7 . 0 4 7.68 7 . 6 6 7.67 9 . 1 2 9.14
Curve I, Fig. IV, shows t h e results graphically. I t will be noticed t h a t t h e curve deviates somewhat from a straight line, being concave toward t h e axis of index of refraction. If we refer t o Equation 14, which gives t h e slope of this graph as IZ varies, we see IO
I
I
I
8
6
4
2
0 t h a t t h e curve would be concave toward t h e axis of indices when t h e value of k is too great. The value of k was then decreased by 0.03 cm. a n d readings again taken. The results are shown in Curve 11, Fig. IV. The graph is sensibly a straight line. It is obvious t h a t if a uniformly divided scale be placed so t h a t t h e 1.000mark shall coincide with t h e 1.55 cm. mark of t h e centimeter scale on this instrument as used in making t h e above readings, a n d t h e 1.600 mark be made t o coincide with t h e 9.23 cm. mark we shall have a direct reading instrument with a n openness of scale sufficient t o determine t h e index t o t h e third decimal place. This refractometer has been made t h e subject of patent application, a n d its manufacture will be taken u p if sufficient demand arises. WASHINGTON UNIVERSITY S T . LOUIS, MISSOURI
