Abstract

A new class of rainbows is created when a droplet is illuminated from the inside by a point light source. The position of the rainbow depends on both the index of refraction of the droplet and the position of the light source, and the rainbow vanishes when the point source is too close to the center of the droplet. Here we experimentally measure the position of the transmission and one-internal-reflection total-internal-reflection rainbows, and the standard (primary) rainbow, as a function of light-source position.

© 2003 Optical Society of America

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References

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  1. R. L. Lee, “What are ‘all the colors of the rainbow’?” Appl. Opt. 30, 3401–3407 (1991).
    [CrossRef] [PubMed]
  2. J. A. Lock, “Semi-classical scattering of an electric dipole source inside a spherical particle,” J. Opt. Soc. Am. A 18, 3085–3097 (2001).
    [CrossRef]
  3. H. M. Nussenzveig, “Complex angular momentum theory of the rainbow and the glory,” J. Opt. Soc. Am. 69, 1068–1079 (1979).
    [CrossRef]
  4. D. S. Langley, M. J. Morrell, “Rainbow-enhanced forward and backward glory scattering,” Appl. Opt. 30, 3459–3467 (1991).
    [CrossRef] [PubMed]
  5. J. A. Lock, J. M. Jamison, C.-Y. Lin, “Rainbow scattering by a coated sphere,” Appl. Opt. 33, 4677–4690 (1994).
    [CrossRef] [PubMed]
  6. C. L. Adler, J. A. Lock, J. K. Nash, K. W. Saunders, “Experimental observation of rainbow scattering by a coated cylinder: twin primary rainbows and thin-film interference,” Appl. Opt. 40, 1548–1558 (2001).
    [CrossRef]
  7. C. L. Adler, J. A. Lock, B. R. Stone, “Rainbow scattering by a cylinder with a nearly elliptical cross section,” Appl. Opt. 37, 1540–1550 (1998).
    [CrossRef]
  8. M. Kerker, S. D. Druger, “Raman and fluorescent scattering by molecules embedded in spheres with radii up to several multiples of the wavelength,” Appl. Opt. 18, 1172–1179 (1979).
    [CrossRef] [PubMed]
  9. M. D. Barnes, K. C. Ng, W. B. Whitten, J. M. Ramsey, “Detection of single Rhodamine 6G molecules in levitated microdroplets,” Anal. Chem. 65, 2360 (1993).
    [CrossRef]
  10. M. D. Barnes, N. Lermer, C.-Y. Kung, W. B. Whitten, J. M. Ramsey, S. C. Hill, “Real-time observation of single-molecule fluorescence in microdroplet streams,” Opt. Lett. 22, 1265–1267 (1997).
    [CrossRef] [PubMed]
  11. S. C. Hill, V. Boutou, J. Yu, S. Ramstein, J. P. Wolf, W. L. Pan, S. Holler, R. K. Chang, “Enhanced backward-directed multiphoton-excited fluorescence from dielectric microcavities,” Phys. Rev. Lett. 85, 54–57 (2000).
    [CrossRef] [PubMed]
  12. A. Young, “Green flashes,” presented at the 7th Topical Meeting on Meteorological Optics, Boulder, Colo., 6–8 June 2001.

2001

2000

S. C. Hill, V. Boutou, J. Yu, S. Ramstein, J. P. Wolf, W. L. Pan, S. Holler, R. K. Chang, “Enhanced backward-directed multiphoton-excited fluorescence from dielectric microcavities,” Phys. Rev. Lett. 85, 54–57 (2000).
[CrossRef] [PubMed]

1998

1997

1994

1993

M. D. Barnes, K. C. Ng, W. B. Whitten, J. M. Ramsey, “Detection of single Rhodamine 6G molecules in levitated microdroplets,” Anal. Chem. 65, 2360 (1993).
[CrossRef]

1991

1979

Adler, C. L.

Barnes, M. D.

M. D. Barnes, N. Lermer, C.-Y. Kung, W. B. Whitten, J. M. Ramsey, S. C. Hill, “Real-time observation of single-molecule fluorescence in microdroplet streams,” Opt. Lett. 22, 1265–1267 (1997).
[CrossRef] [PubMed]

M. D. Barnes, K. C. Ng, W. B. Whitten, J. M. Ramsey, “Detection of single Rhodamine 6G molecules in levitated microdroplets,” Anal. Chem. 65, 2360 (1993).
[CrossRef]

Boutou, V.

S. C. Hill, V. Boutou, J. Yu, S. Ramstein, J. P. Wolf, W. L. Pan, S. Holler, R. K. Chang, “Enhanced backward-directed multiphoton-excited fluorescence from dielectric microcavities,” Phys. Rev. Lett. 85, 54–57 (2000).
[CrossRef] [PubMed]

Chang, R. K.

S. C. Hill, V. Boutou, J. Yu, S. Ramstein, J. P. Wolf, W. L. Pan, S. Holler, R. K. Chang, “Enhanced backward-directed multiphoton-excited fluorescence from dielectric microcavities,” Phys. Rev. Lett. 85, 54–57 (2000).
[CrossRef] [PubMed]

Druger, S. D.

Hill, S. C.

S. C. Hill, V. Boutou, J. Yu, S. Ramstein, J. P. Wolf, W. L. Pan, S. Holler, R. K. Chang, “Enhanced backward-directed multiphoton-excited fluorescence from dielectric microcavities,” Phys. Rev. Lett. 85, 54–57 (2000).
[CrossRef] [PubMed]

M. D. Barnes, N. Lermer, C.-Y. Kung, W. B. Whitten, J. M. Ramsey, S. C. Hill, “Real-time observation of single-molecule fluorescence in microdroplet streams,” Opt. Lett. 22, 1265–1267 (1997).
[CrossRef] [PubMed]

Holler, S.

S. C. Hill, V. Boutou, J. Yu, S. Ramstein, J. P. Wolf, W. L. Pan, S. Holler, R. K. Chang, “Enhanced backward-directed multiphoton-excited fluorescence from dielectric microcavities,” Phys. Rev. Lett. 85, 54–57 (2000).
[CrossRef] [PubMed]

Jamison, J. M.

Kerker, M.

Kung, C.-Y.

Langley, D. S.

Lee, R. L.

Lermer, N.

Lin, C.-Y.

Lock, J. A.

Morrell, M. J.

Nash, J. K.

Ng, K. C.

M. D. Barnes, K. C. Ng, W. B. Whitten, J. M. Ramsey, “Detection of single Rhodamine 6G molecules in levitated microdroplets,” Anal. Chem. 65, 2360 (1993).
[CrossRef]

Nussenzveig, H. M.

Pan, W. L.

S. C. Hill, V. Boutou, J. Yu, S. Ramstein, J. P. Wolf, W. L. Pan, S. Holler, R. K. Chang, “Enhanced backward-directed multiphoton-excited fluorescence from dielectric microcavities,” Phys. Rev. Lett. 85, 54–57 (2000).
[CrossRef] [PubMed]

Ramsey, J. M.

M. D. Barnes, N. Lermer, C.-Y. Kung, W. B. Whitten, J. M. Ramsey, S. C. Hill, “Real-time observation of single-molecule fluorescence in microdroplet streams,” Opt. Lett. 22, 1265–1267 (1997).
[CrossRef] [PubMed]

M. D. Barnes, K. C. Ng, W. B. Whitten, J. M. Ramsey, “Detection of single Rhodamine 6G molecules in levitated microdroplets,” Anal. Chem. 65, 2360 (1993).
[CrossRef]

Ramstein, S.

S. C. Hill, V. Boutou, J. Yu, S. Ramstein, J. P. Wolf, W. L. Pan, S. Holler, R. K. Chang, “Enhanced backward-directed multiphoton-excited fluorescence from dielectric microcavities,” Phys. Rev. Lett. 85, 54–57 (2000).
[CrossRef] [PubMed]

Saunders, K. W.

Stone, B. R.

Whitten, W. B.

M. D. Barnes, N. Lermer, C.-Y. Kung, W. B. Whitten, J. M. Ramsey, S. C. Hill, “Real-time observation of single-molecule fluorescence in microdroplet streams,” Opt. Lett. 22, 1265–1267 (1997).
[CrossRef] [PubMed]

M. D. Barnes, K. C. Ng, W. B. Whitten, J. M. Ramsey, “Detection of single Rhodamine 6G molecules in levitated microdroplets,” Anal. Chem. 65, 2360 (1993).
[CrossRef]

Wolf, J. P.

S. C. Hill, V. Boutou, J. Yu, S. Ramstein, J. P. Wolf, W. L. Pan, S. Holler, R. K. Chang, “Enhanced backward-directed multiphoton-excited fluorescence from dielectric microcavities,” Phys. Rev. Lett. 85, 54–57 (2000).
[CrossRef] [PubMed]

Young, A.

A. Young, “Green flashes,” presented at the 7th Topical Meeting on Meteorological Optics, Boulder, Colo., 6–8 June 2001.

Yu, J.

S. C. Hill, V. Boutou, J. Yu, S. Ramstein, J. P. Wolf, W. L. Pan, S. Holler, R. K. Chang, “Enhanced backward-directed multiphoton-excited fluorescence from dielectric microcavities,” Phys. Rev. Lett. 85, 54–57 (2000).
[CrossRef] [PubMed]

Anal. Chem.

M. D. Barnes, K. C. Ng, W. B. Whitten, J. M. Ramsey, “Detection of single Rhodamine 6G molecules in levitated microdroplets,” Anal. Chem. 65, 2360 (1993).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Lett.

Phys. Rev. Lett.

S. C. Hill, V. Boutou, J. Yu, S. Ramstein, J. P. Wolf, W. L. Pan, S. Holler, R. K. Chang, “Enhanced backward-directed multiphoton-excited fluorescence from dielectric microcavities,” Phys. Rev. Lett. 85, 54–57 (2000).
[CrossRef] [PubMed]

Other

A. Young, “Green flashes,” presented at the 7th Topical Meeting on Meteorological Optics, Boulder, Colo., 6–8 June 2001.

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Figures (9)

Fig. 1
Fig. 1

Ray diagram for light scattered by a point light source inside a spherical droplet.

Fig. 2
Fig. 2

Scattering angle (θ) as a function of the internal impact parameter (τ) for zero internal reflections (p = 1). For this diagram, r/ a = 0.8 and n = 1.33.

Fig. 3
Fig. 3

Scattering angle (θ) as a function of internal impact parameter (τ) for one internal reflection (p = 2). For this diagram, r/ a = 0.8 and n = 1.33.

Fig. 4
Fig. 4

Experimental setup. In our experiment, L = 67.5 cm and a = 8 cm.

Fig. 5
Fig. 5

Photograph of droplet and assembly used to move the light source. The cross arm holding the light bulb was built on a linear translation stage, which was moved in 0.5-mm increments to change the position of the bulb.

Fig. 6
Fig. 6

Photographs of the light scattered by the droplet projected onto a screen. (a) r/ a = 0.96. 1. p = 1 TIRR rainbow, 2. p = 2 standard rainbow. (b) r/ a = 0.8. 1. p = 1 TIRR rainbow, 2. p = 2 TIRR rainbow, 3. p = 2 “standard” rainbow. (c) r/ a = 0.75. At this light source position, the p = 1 TIRR vanishes, leaving only the p = 2 TIRR and the standard rainbows. 1. p = 2 TIRR rainbow, 2. p = 2 standard rainbow. (d) r/ a = 0.6. At this light source position, the p = 2 standard rainbows converge at a scattering angle of θ = 180°. For smaller values of r/ a, they cease to exist.

Fig. 7
Fig. 7

Ray diagram showing the origin of the α and β rainbows.

Fig. 8
Fig. 8

Position of the p = 1 and p = 2 TIRRs and the p = 2 standard α and β rainbows as a function of light source position. Points, experiment; solid curve, theoretical fit.

Fig. 9
Fig. 9

Glare-spot sequence. r/ a = 0.9. (a) One-ray region. Light source clearly visible; one image of it seen. (b) Zero-ray region. Light source invisible because of total internal reflection. (c) Two-ray region. Two images of light source visible. The light source is in about the right position for the viewer to see the p = 1 TIRR.

Equations (5)

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r/asin τ=sin α,
n sin α=sin γ,
θ=τ+p-1π-2p-1α+γ.
dθdτ=1-2p-1ξ cos τcos α+nξ cos τcos γ.
1+nξx1-n2ξ21-x21/2-2p-1×ξx1-ξ21-x21/2=0,

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