The Diffuse Reflection of Light by Milk1

THE DIFFUSE

REFLECTION

O F L I G H T B Y lVHLK 1

w. H. BURGESS 2 AND B. L. HERRINGTON Department of Dairy Industry, Cornell University, Ithaca, N. Y.

Much of the light striking the surface of a layer of milk is reflected. The total reflection is made up of a specular reflection f r o m the surface, which is independent of the thickness of layer, and a diffuse reflection f r o m the interior, which depends upon the thickness of layer. Diffuse reflection data are of value because they provide a basis for calculating the amount of light absorbed by milk and for estimating the effective depth of penetration of light into milk. Hence such data are presented in this paper. APPARATUS

AND PROCEDURE

F i g u r e 1 shows the m a j o r components of the reflectance apparatus. They were: a hollow sphere coated on the inside with magnesium oxide, a reflectance cell, and a multiplier photometer. The incident monochromatic light traveled diametrically through the sphere and struck the reflectance cell. Practically SPHERE ~,~-MONC~HROMATIG LIGHT RL~

R~FLECTANCE

S~JTOMULTIPUE R PROBE

FIG. 1. A schematic diagram of the reflectance apparatus. all of the light diffusely reflected by the milk particles was t r a p p e d in the sphere and its intensity was measured by the photometer. The reflectance cell consisted essentially of a hollow cylinder fitted at the top with a glass window (Corning Vycor 7910) and at the bottom with a black disk. B y changing the distance between the window and the black disk, it was possible to v a r y the thickness of the milk layer in the cell f r o m zero to 25 mm. An aluminum disk with a l-ram. coating of magnesium oxide on its surface was used as the reflectance standard. The coating was p r e p a r e d b y allowing the smoke particles formed b y b u r n i n g reagent-grade magnesium turnings to deposit on the disk. Received for publication September 20, 1954. 1Based in part on material taken from a thesis presented by the senior author to the faculty of the Graduate School of Cornell University in partial fulfillment of the requirement for the degree of Doctor of Philosophy, February, 1954. 2 Present address: Department of Chemical Engineering, University of Toronto, Toronto, Ontario. 250

251

REFLECTION OF LIGHT BY MILK

Reflectance data were obtained for commercial samples of skim, whole, and homogenized milk at the following wave lengths: 5780, 5460, 4360, 4050, 3650, 3340, 3130, and 2540 A. When collecting data in the ultraviolet, filters were placed between the sphere and the photometer in an attempt to exclude fluorescent rays. Except at 2540 A, the effect of fluorescence was small, most likely amounting to less than 4% of the light diffusely reflected. At 2540 A the fluorescence appeared to be much stronger. It was impossible to make an exact evaluation of the strength of the fluorescence because the fluorescence was not monochromatic and the photometer was not uniformly sensitive to light of different wave lengths. The filters employed to exclude fluorescence were the same as those used in the transmission measurements (2). Also, the same source of monochromatic light and the same photomultiplier were used. RESULTS AND DISCUSSION

The reflectance data are given in Figures 2, 3, and 4. The data represent the percentage of light diffusely reflected, taking the light entering the milk layer as 100%. In order to obtain these data it was necessary to apply corrections for the light absorbed by the magnesium oxide o f the reflectance standard, for . . . . I

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FIG. 2. R e f l e c t a n c e d a t a of a typical sample of skimmilk. Composition by the Mojonnier method: total solids 9 . 0 3 % ; f a t 0.59%. I I

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FIG. 3. Reflectance d a t a of a typical sample of whole milk. Composition by the Mojonnier method: total solids 1 1 . 8 7 % ; f a t 3.39%.

252

W . H . BURGESS AND B. L. HERRINGTON

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FIG. 4. I~eflectance d a t a of a t y p i c a l s a m p l e of h o m o g e n i z e d milk. M o j o n n i e r m e t h o d : total solids 1 1 . 9 5 % ; f a t 3.63%.

Composition by the

the light absorbed by the glass window of the reflectance cell, and for the light reflected from the surface of the glass window. If the incident light rays had been perfectly normal, it would not have been necessary to make the last correction. However, the incident rays were slightly divergent, so most of the light reflected from the surface of the glass window was t r a p p e d in the sphere and measured along with the diffusely reflected light. The equations used in applying the corrections are derived below. Let

light incident on the window of the reflectance cell C = light reflected from the surface of the window and t r a p p e d in the sphere a fraction of the light transmitted by the window b = fraction of the light entering the milk layer which was diffusely reflected f = fraction of the incident light reflected by the magnesium oxide standard R = uncorrected reflectance--i.e., the reading given by the photometer

L

=

Neglecting the reflection at the glass-milk interface, the light entering the milk layer is (L-C)a. Assuming that the fraction of light transmitted by the window is the same for both the incident and reflected light, 3 the light that is diffusely reflected by the milk and travels back through the window is (L-C)a~-b. The light reflected by the magnesium oxide standard equals fL. Combining these terms gives us the equation : R = ( L - C ) a ~ b + C × 100 .............................................................

(1)

TL Strictly s p e a k i n g , this a s s u m p t i o n is n o t justified, b e c a u s e on t h e a v e r a g e t h e reflected r a y s travel a g r e a t e r distance t h r o u g h the g l a s s t h a n t h e i n c i d e n t rays. However, except a t 2540 £ the a b s o r b e n c y of t h e g l a s s is very low a n d hence t h e error i n t r o d u c e d is in g e n e r a l n o t serious.

REFLECTION

OF

LTGHT

BY

253

MILK

Since the photometer was set at 100 with the magnesium oxide standard, we can write : = 100 or L -

fL

100 Substituting - - ~ b =

100

f

for L and solving for b, we get R-C

. 100

C)

........................................................................

2)

a~

f TABLE

1

Correction factors Wave length

f '~

a~

C

0.98 0.98 0.98 0.97 0.94 0.93 0.93 0.95

1.0 1.0 1.0 1.0 0.99 0.98 0.97 0.73

3.5 3.5 3.5 3.5 3.5 3.5 4.0 4.0

¢X) 5780 5460 4360 4050 3650 3340 3130 2540

a The f v a l u e s a t 5780, 5460, a n d 4360 Jr were t a k e n f r o m L u c k i e s h (3); r e m a i n i n g wave l e n g t h s were t a k e n f r o m ]Benford et al. (1).

the values at the

The values of f , a 2, and C used a p p e a r in Table 1. The values of f were taken f r o m the literature. The values of a ' were determined b y measuring the transmission of the glass window and correcting for reflection losses. C was obtained by measuring the reflectance of a layer of milk of zero thickness, in which case b equals zero and equation 2 reduces to R-C

= 0 or R = C

The reflectance data contain one e r r o r in addition to those f o r which corrections were made. When determining the reflectance, an area of about 6 sq. cm. on the Surface of the milk was illuminated. Consider a small, but finite volume of milk n e a r the center of the illuminated area. Most of the light diffusely reflected f r o m this volume originally entered the volume f r o m the glass-milk interface. However, some of the diffusely reflected light entered f r o m neighboring volumes. This means t h a t the volumes of milk at the b o u n d a r y of the illuminated area reflect less light t h a n those at the center because the volumes at the b o u n d a r y did not receive their p r o p e r share of light f r o m neighboring volumes. I t is not known how serious this b o u n d a r y error is, but it is hoped t h a t the area illuminated was large enough to make it u n i m p o r t a n t . The reflectance data show t h a t much of the light entering a layer of milk is diffusely reflected. F o r example over 70% of the green light (5460 A) entering a 10-mm. layer of whole milk was diffusely reflected. I n the n e a r ultraviolet

254

W. H. B U R G E S S

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WAVE LENGTH

I 5000

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FIG. 5. The reflectance of whole milk as a function of wave length. The sample of milk is the same as that in Figure 3. (3650 A) over 60% was diffusely reflected. The homogenized milk reflected the most light, and skimmiik, the least. I n F i g u r e 5 the reflectance is plotted as a function of the wave length for layers of milk of a given thickness. The plot shows t h a t thin layers of milk reflect a relatively greater percentage of light at the shorter wave lengths. This is a fact familiar to anyone who has observed t h a t thin layers of milk have a bluish color. Reflectance data, assuming they are accurate, can be used to estimate the amount of light absorbed b y milk. As an example, consider a layer of whole milk which is at least 1 cm. thick and which is exposed to blue (4360/~) light. U n d e r these conditions the transmission loss is negligible and the diffuse reflection is 57%. Hence the fraction of the incident light absorbed is: 1 -- 0 . 5 9 ' = 0.41 The value 0.59 was used instead of 0.57 to account for an assumed specular reflection of 4%. I t should be r e m e m b e r e d t h a t light absorptions estimated in this way a p p l y only to monochromatic light normal to the surface of the milk. The graphs of the reflectance data provide information on the penetration of light into milk. I n the case of a thin layer of milk, much of the incident light traveled t h r o u g h the layer and was absorbed b y the black disk which served as the bottom of the reflectance cell, before it had a chance to be reflected. T h i s accounts for the low reflectance of the thin layers. As the layer grew thicker, less light p e n e t r a t e d to the disk and more light had an o p p o r t u n i t y to be reflected. E v e n t u a l l y a point was reached where such a small amount of light was absorbed b y the disk t h a t f u r t h e r increases in the thickness of the l a y e r resulted in no measurable increase in the amount of light reflected. Twice the distance to this point was taken as the effective depth of penetration of the light. Twice the distance r a t h e r t h a n the distance itself was used, because the light:

255

REFLECTION OF LIGHT BY MILK

w h i c h was reflected f r o m t h e g r e a t e s t d e p t h m u s t h a v e t r a v e l e d a d i s t a n c e o f t w o t h i c k n e s s e s t h r o u g h t h e m i l k . T h e effective d e p t h r e p r e s e n t s t h e t h i c k n e s s o f t h e l a y e r in w h i c h v i r t u a l l y a l l of t h e l i g h t a b s o r p t i o n t a k e s place. TABLE 2 Effectivedepthofpenetrationoflightinto mil~ Effective depth Wave length

Skim

Whole

}tomogenized

(~) 5780 5460 4360 4050 3650 3340 3130

(m~n.) 28 26 12 11 9 7 5

(m~n.) 24 24 10 9 7 6 4

(~nm.) 18 18 8 7 7 5 3

2540 ~

1

1

1

The effective depth at 2540 A may be in error, because the strong fluorescence made it difficult to determine at what thickness the reflectance reached its maximum value. T h e v a l u e s of t h e effective d e p t h a r e p r e s e n t e d in T a b l e 2. T h e effective d e p t h s v a r y f r o m a b o u t 2 era. f o r y e l l o w l i g h t to a b o u t 0.1 cm. f o r l i g h t i n t h e f a r u l t r a v i o l e t . T h e m a g n i t u d e of t h e effective d e p t h s is a b o u t w h a t one w o u l d e x p e c t on t h e basis of t r a n s m i s s i o n d a t a (2). SUMMARY AND CONCLUSIONS Diffuse r e f l e c t a n c e d a t a were o b t a i n e d f o r t y p i c a l s a m p l e s of skim, whole, a n d h o m o g e n i z e d m i l k a t t h e f o l l o w i n g w a v e l e n g t h s : 5780, 5460, 4360, 4050, 3650, 3340, 3130, a n d 2540 A. The d a t a s h o w e d t h a t m u c h of t h e l i g h t e n t e r i n g a l a y e r of m i l k was d i f f u s e l y reflected. T h e a m o u n t r e f l e c t e d v a r i e d f r o m a b o u t 7 0 % a t 5780 A to a b o u t 9 % a t 2534 A. A n u m e r i c a l e x a m p l e was g i v e n to show h o w r e f l e c t a n c e d a t a c a n b e u s e d t o estimate the light energy absorbed by milk. T h e effective d e p t h of p e n e t r a t i o n of l i g h t i n t o m i l k was e s t i m a t e d f r o m t h e r e f l e c t a n c e d a t a . T h e v a l u e s of t h e effective d e p t h of p e n e t r a t i o n r a n g e d f r o m a b o u t 2 cm. a t 5780 A to 0.1 era. a t 2537 A.

ACKNOWLEDGMENTS This investigation was supported in part by a grant from the Corning Glass Works and in part by funds furnished by the Eli Lilly Company through D. D. Van Slyke. REFERENCES ( 1 ) BENFORD, F., SCHWARZ~ S., AND LLOYD, G. P. Coefficients of Reflection in the Ultraviolet

of Magnesium Carbonate and Oxide. J. Opt. Soc. Amer., 38: 964. 1948. (2) BURGESS, W. II., AND ItER~INGTON, B. L. The Penetration of Light into Milk. J. Dairy Sci., 38 : ....... 1955. (3) LUCKIESt, M. Artificia~ Sunlight. p. 92. D. Van Nostrand Co., New York. 1930.