Color Effects in the Scattering of White Light by Micron and Submicron Spheres*

M. Kerker; W. A. Farone; R. T. Jacobsen

doi:10.1364/JOSA.56.001248

Journal of the Optical Society of America
Vol. 56,
Issue 9,
pp. 1248-1255
(1966)
•https://doi.org/10.1364/JOSA.56.001248

Color Effects in the Scattering of White Light by Micron and Submicron Spheres

M. Kerker, W. A. Farone, and R. T. Jacobsen

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M. Kerker, W. A. Farone, and R. T. Jacobsen, "Color Effects in the Scattering of White Light by Micron and Submicron Spheres*," J. Opt. Soc. Am. 56, 1248-1255 (1966)

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Abstract

The tristimulus color system is used to describe the colors of the light scattered by spheres with radii a = 0.2, 0.3, 0.4, 0.5, 0.6, 0.8, 1.0, and 1.2 μ for real refractive indices m = 1.31 and 1.46 and by spheres with radii a = 0.1, 0.2, 0.4μ for complex refractive index corresponding to a highly absorbing substance such as vanadium pentoxide. The quantities calculated are the dominant wavelength, purity, the visible intensity, and the intensity for unpolarized incident white light from a 3200°K source as well as for each of the two plane-polarized components.

The angular variation of colors designated as higher-order Tyndall spectra (H.O.T.S.) occurs only for radii comparable to the wavelength. For small particles, the light is blue, corresponding to Rayleigh scattering, while for radii a>0.8 μ, the scattered light is uniformly yellow. At intermediate sizes 0.2 μ≤a≤0.8 μ the H.O.T.S. described by Sinclair and La Mer occur. However, there is no correlation between the appearance of the color bands and the intensity peaks of the scattered light. It is possible to have a polydisperse system in the intermediate size range exhibit H.O.T.S. while a perfectly monodisperse system of larger radius does not exhibit this phenomenon. A visual measure of the polarization ratio at two or three backward directions can serve to determine the particle size.

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Wavelength (mμ)	Refractive index
406	2.13–0.92i
436	2.53–0.62i
489	2.05–0.14i
546	2.04–0.03i
578	1.92–0.02i
659	1.78–0.09i

Wavelength (mμ)	Notation	Hue
400–450	V	Violet
451–500	B	Blue
501–570	G	Green
571–590	Y	Yellow
591–610	O	Orange
611–700	R	Red
<515C	R	Red
>515C	P	Purple

Angle of observation	m = 1.31; 3200°K Source
	Radius (microns)
	a = 0.2	a = 0.3	a = 0.4	a = 0.5	a = 0.6	a = 0.8	a = 1.0	a = 1.2
0	pB	pB	pG	pY	Y	bY	O	pB
2.5	pB	pB	pG	pY	Y	bY	O	pB
5.0	pB	pB	pG	pY	Y	bY	O	pB
7.5	pB	pB	pG	pY	Y	bY	R	pB
10.0	pB	B	pGY	pY	Y	brY	R	pB
12.5	pB	pG	pY	Y	bY	brY	bR	G
15.0	pB	pG	pY	Y	bY	brO	pB	bY
17.5	pB	pG	pY	Y	bY	bO	pG	bOY
20.0	pB	pG	Y	bY	brY	R	bYG	bR
22.5	pB	pY	Y	bY	brY	pB	brY	R
25.0	pB	pY	Y	bY	brO	pG	brY	O
27.5	pG	pY	bY	BrY	R	pG	bO	bG
30.0	pG	Y	bY	bOY	pP	bY	R	bYG
32.5	pG	Y	bY	bO	pB	brY	pOY	bY
35.0	pG	Y	bY	R	pB	bO	G	bO
37.5	pG	Y	bY	P	pG	R	bG	O
40.0	pY	bY	bOY	pB	G	R	bY	Y
42.5	pY	bY	bO	pB	bY	pR	O	G
45.0	pY	bY	R	pGB	bY	pG	RO	Y
47.5	pY	bY	P	pG	bY	G	O	Y
50.0	Y	brY	P	G	bO	bG	Y	bO
52.5	Y	brY	B	bY	R	bY	G	bO
55.0	Y	brY	B	bY	R	O	G	Y
57.5	Y	bO	B	brY	R	R	Y	Y
60.0	Y	bO	pG	bY	pP	R	O	Y
62.5	bY	R	G	bO	pG	O	bO	bY
65.0	bY	R	G	R	G	Y	O	bO
67.5	bY	P	bY	R	bG	G	Y	OY
70.0	bY	P	bY	R	bG	G	G	Y
72.5	bY	B	brY	pP	bY	Y	G	Y
75.0	bY	bB	bY	pGB	Y	Y	Y	Y
77.5	brY	B	bO	pG	O	O	bY	bY
80.0	brY	B	bO	G	R	bO	bO	bY
82.5	brY	pB	bO	bG	R	bO	O	bY
85.0	brY	pG	R	bG	R	Y	Y	Y
87.5	brY	pG	R	bG	O	Y	Y	Y
90.0	brY	G	R	bY	Y	Y	Y	bY
92.5	bO	bY	pR	O	G	Y	Y	bY
95.0	bO	bY	pB	R	G	Y	bY	bOY
97.5	bO	brY	pB	R	G	Y	bOY	bOY
100.0	R	brY	B	R	G	Y	bY	bY
102.5	R	brY	G	R	G	Y	Y	bY
105.0	bR	brY	G	O	Y	Y	Y	bY
107.5	bR	brY	pG	bY	OY	O	Y	bY
110.0	bP	bY	G	bY	R	O	bO	bO
112.5	bP	bY	Y	bG	R	O	bY	bY
115.0	bP	bO	bY	G	R	Y	Y	bY
117.5	bP	O	bY	G	bO	YG	G	Y
120.0	B	pR	bY	B	bY	G	G	bY
122.5	B	R	bY	pB	bY	G	bY	bO
125.0	bB	R	bY	pB	G	G	bO	bY
127.5	bB	P	bY	pR	pG	pR	O	Y
130.0	B	P	Y	O	B	R	Y	G
132.5	B	P	OY	bO	B	R	G	Y
135.0	B	bP	O	bY	pP	bY	G	O
137.5	B	P	pR	bY	pR	bY	pG	O
140.0	B	P	pR	bY	O	bG	R	Y
142.5	B	P	pP	bY	bY	pG	R	G
145.0	B	P	pP	Y	bY	B	bO	G
147.5	BG	pB	P	pY	bY	pV	bY	pR
150.0	pG	pB	P	pY	bY	R	bG	R
152.5	pG	pG	P	pB	Y	O	pG	bY
155.0	pG	pG	pP	pB	pG	brY	pB	bY
157.5	pG	G	pR	pBV	pB	brY	R	G
160.0	pG	G	Y	pG	pB	bY	brO	pB
162.5	pG	G	Y	pP	pB	G	brY	bR
165.0	pG	G	bY	pR	B	pG	bY	brO
167.5	pG	G	bY	OY	P	pB	Y	bY
170.0	pG	G	G	bY	R	B	G	bY
172.5	pG	G	G	bY	bO	bB	pG	Y
175.0	pG	G	G	bY	brY	bB	pG	bY
177.5	pG	G	G	bY	brY	bB	pB	bY
180	pG	G	G	bY	brY	B	pB	bY

Angle of observation	m = 1.46; 3200°K Source
	Radius (microns)
	a = 0.2	a = 0.3	a = 0.4	a = 0.5	a = 0.6	a = 0.8	a = 1.0	a = 1.2
0	pB	pG	Y	bY	bY	pB	G	OY
2.5	pB	pG	Y	bY	bY	pB	G	OY
5.0	pB	pG	Y	bY	bY	pB	G	O
7.5	pB	pG	Y	bY	bY	pB	bY	bO
10.0	pB	pG	Y	bY	bY	pB	bY	bO
12.5	pB	pY	Y	bY	brOY	pB	brY	bR
15.0	pB	pY	Y	bY	brO	B	bY	OY
17.5	pB	pY	Y	brY	brO	pG	R	G
20.0	pB	pY	bY	brY	bR	bG	P	bG
22.5	pB	Y	bY	brY	bR	brY	B	bY
25.0	pG	Y	bY	brO	P	bY	B	O
27.5	pY	Y	brY	bO	pB	bO	G	R
30.0	pY	Y	brY	R	pG	R	G	pO
32.5	pY	Y	brY	P	G	R	Y	G
35.0	pY	bY	brO	pB	bY	R	O	G
37.5	pY	bY	bO	pB	brY	Y	R	G
40.0	pY	bY	R	pG	brY	G	R	OY
42.5	pY	bY	R	G	pY	bG	O	O
45.0	Y	bY	P	bY	bO	bY	G	O
47.5	Y	brY	pP	bY	R	bY	G	Y
50.0	Y	bO	pB	brY	R	bO	Y	G
52.5	Y	bO	pGB	bY	pR	O	Y	Y
55.0	Y	bO	pG	bY	pG	O	bO	Y
57.5	Y	R	G	bO	pG	bO	bO	O
60.0	bY	pR	G	R	G	bY	OY	O
62.5	bY	pR	bG	R	bG	G	Y	0
65.0	bY	pB	brY	pR	bY	G	G	Y
67.5	brY	B	brY	pP	bY	Y	Y	Y
70.0	brY	B	brY	pG	bO	Y	Y	Y
72.5	brY	B	bY	G	O	bY	bO	Y
75.0	brY	B	bO	G	RO	bO	bO	O
77.5	brY	G	R	bY	O	bO	Y	O
80.0	brY	pG	bR	bY	O	bO	Y	Y
82.5	brY	pG	bR	bY	G	Y	Y	Y
85.0	bOY	G	bR	bY	G	Y	Y	Y
87.5	bO	G	R	Y	G	G	Y	Y
90.0	O	bY	pR	Y	G	G	Y	Y
92.5	R	bY	Y	Y	Y	bY	Y	Y
95.0	R	bY	G	Y	Y	bY	Y	Y
97.5	R	bO	bG	O	O	bO	bY	Y
100.0	P	brO	brG	R	O	bO	Y	Y
102.5	bP	brO	bG	R	O	bO	Y	bY
105.0	brP	brO	bG	R	bY	bY	Y	bY
107.5	bP	brO	G	O	bY	YG	bY	bY
110.0	bV	bO	pG	bY	bG	G	bY	Y
112.5	bB	bO	pO	bY	Y	G	bY	Y
115.0	bB	bO	R	bG	O	bY	bY	O
117.5	bB	O	bR	bG	R	bO	bO	bO
120.0	bB	O	bR	bG	O	bO	O	Y
122.5	bB	pR	bR	G	bY	bY	Y	Y
125.0	bB	pRP	bRO	pG	bY	bY	Y	O
127.5	B	pB	brO	G	brYG	bG	bY	O
130.0	B	pB	brOY	bG	bG	Y	bY	Y
132.5	pB	B	brY	bR	G	bO	O	Y
135.0	pG	B	bY	bR	pB	bO	pY	Y
137.5	pG	bB	Y	brO	P	brY	pY	bY
140.0	G	bB	G	brY	bP	brY	O	Y
142.5	G	bB	pG	brY	bO	bG	bO	pY
145.0	bG	bB	pB	bY	brOY	pG	bY	pR
147.5	bG	B	B	Y	brY	P	bY	O
150.0	bG	G	B	pG	bY	bR	Gj	bY
152.5	bG	bG	bB	pB	Y	brO	B	Y
155.0	bG	brY	bB	B	pG	brY	P	pG
157.5	bG	brY	B	B	pG	bY	bO	pV
160.0	bG	bY	Y	bB	B	Y	brY	O
162.5	bG	bY	brY	bB	B	pG	bY	bY
165.0	bG	bY	bY	R	bB	pB	Y	bY
167.5	bG	Y	bY	brY	R	B	pG	Y
170.0	bG	Y	Y	bY	brY	B	B	pG
172.5	bG	Y	Y	Y	bY	bO	pB	pB
175.0	bG	pY	Y	Y	Y	bY	bY	pR
177.5	bG	pY	pY	Y	Y	bY	bY	bY
180.0	bG	pY	pY	Y	Y	Y	bY	brY

Order	m = 1.31
	Radius (microns)
	a = 0.2	a = 0.3	a = 0.4	a = 0.5	a = 0.6	a = 0.8	a = 1.0	a = 1.2
R-1
G-1	30	15	7.5
R-2	105	62.5	45	35	27.5	20	7.5
G-2	147.5	75	62.5	50	40	27.5	17.5	12.5
R-3		122.5	85	65	52.5	37.5	30	20
G-3		157.5	102.5	80	65	47.5	37.5	27.5
R-4			135(O)	95	80	57.5	45	35(O)
G-4			170	115	92.5	67.5	52.5	42.5
R-5				130(O)	110	YO	YO	YO
G-5				160	125	120	117.5	YO
R-6				165	140	130	125(0)	YO
G-6					155	140	132.5	130
R-7					170	150	140	135
G-7						162.5	150	142.5
R-8							157.5	150
G-8							170	157.5
R-9								162.5

Angle of observation	Radius (microns)
Angle of observation	a = 0.1	a = 0.2	a = 0.4
0°	B	Y	pB
2.5	“	“	“
5.0	“	“	“
7.5	“	“	“
10.0	“	“	“
12.5	“	“	“
15.0	“	“	pG
17.5	“	“	“
20.0	“	“	“
22.5	“	“	G
25.0	“	bY	G
27.5	“	“	bG
30.0	“	“	bY
32.5	“	“	bY
35.0	“	“	brY
37.5	“	“	bY
40.0	“	“	bO
42.5	“	“	bO
45.0	“	“	R
47.5	“	“	“
50.0	“	“	“
52.5	“	“	“
55.0	“	“	O
57.5	“	“	Y
60.0	“	“	G
62.5	“	O	“
65.0	B	RO	G
67.5	“	R	“
70.0	“	R	“
72.5	pB	P	“
75.0	“	bP	YG
77.5	“	“	Y
80.0	“	“	Y
82.5	“	R	bY
85.0	“	“	“
87.5	“	“	“
90.0	“	O	“
92.5	pB	Y	Y
95.0	“	bY	O
97.5	“	“	O
100.0	“	“	R
102.5	“	“	“
105.0	“	“	“
107.5	“	brY	“
110.0	“	brYG	O
112.5	“	brG	bY
115.0	“	brG	“
117.5	“	bG	“
120.0	“	“	“
122.5	pP	“	“
125.0	“	“	“
127.5	“	“	“
130.0	pP	bG	Y
132.5	“	“	“
135.0	“	“	“
137.5	“	“	bO
140.0	“	“	“
142.5	“	“	“
145.0	“	“	“
147.5	“	“	brO
150.0	“	“	“
152.5	P	“	“
155.0	“	“	“
157.5	“	“	“
160.0	“	brG	“
162.5	“	“	“
165.0	“	“	“
167.5	“	“	“
170.0	“	“	“
172.5	“	“	“
175.0	“	“	“
177.5	“	“	“
180.0	“	“	“

Abstract

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Figures (6)

Tables (7)

Equations (7)

Journal of the Optical Society of America