Abstract

A theoretical discussion of certain hypotheses to explain diffuse reflection. That diffuse reflection of light from a matt surface can be explained by the hypothesis of countless small mirrors, (Bouguer’s hypothesis) was denied by L. Grabowski. His objections to the hypothesis are not entirely valid. Three ideal surfaces are assumed and the laws of diffuse reflection from these are calculated and compared with experimental results. The agreement is only fair but perhaps as good as can be expected under the circumstances. The ideal surfaces are defined, statistically, and as the surface of ideal foam respectively.

© 1923 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Bouguer, Histoire de l’Académie Royale des sciences, Paris, 1757 (1762); and Traite d’optique sur la gradation de la lumière (Ouvrage posthume de M. Bouguer, et publié par M. l’Abbe de Lacaille), Paris, 1760.
  2. L. Grabowski, On the Theoretical Photometry of Diffuse Reflection, Astrophysical Journal,  39, pp. 299–306; 1914.
    [Crossref]
  3. Rayleigh, On the intensity of light reflected from certain surfaces at nearly perpendicular incidence, Proc. Roy. Soc. 41, pp. 275–294, 1886; Scientific Papers, 2, pp. 522–542.
    [Crossref]
  4. T. K. Chinmayanandam, On the spectular Reflection from Rough Surfaces, Phys. Rev. Ser. 2,  13, pp. 96–101; Feb., 1919.
    [Crossref]

1919 (1)

T. K. Chinmayanandam, On the spectular Reflection from Rough Surfaces, Phys. Rev. Ser. 2,  13, pp. 96–101; Feb., 1919.
[Crossref]

1914 (1)

L. Grabowski, On the Theoretical Photometry of Diffuse Reflection, Astrophysical Journal,  39, pp. 299–306; 1914.
[Crossref]

1886 (1)

Rayleigh, On the intensity of light reflected from certain surfaces at nearly perpendicular incidence, Proc. Roy. Soc. 41, pp. 275–294, 1886; Scientific Papers, 2, pp. 522–542.
[Crossref]

Bouguer,

Bouguer, Histoire de l’Académie Royale des sciences, Paris, 1757 (1762); and Traite d’optique sur la gradation de la lumière (Ouvrage posthume de M. Bouguer, et publié par M. l’Abbe de Lacaille), Paris, 1760.

Chinmayanandam, T. K.

T. K. Chinmayanandam, On the spectular Reflection from Rough Surfaces, Phys. Rev. Ser. 2,  13, pp. 96–101; Feb., 1919.
[Crossref]

Grabowski, L.

L. Grabowski, On the Theoretical Photometry of Diffuse Reflection, Astrophysical Journal,  39, pp. 299–306; 1914.
[Crossref]

Rayleigh,

Rayleigh, On the intensity of light reflected from certain surfaces at nearly perpendicular incidence, Proc. Roy. Soc. 41, pp. 275–294, 1886; Scientific Papers, 2, pp. 522–542.
[Crossref]

Astrophysical Journal (1)

L. Grabowski, On the Theoretical Photometry of Diffuse Reflection, Astrophysical Journal,  39, pp. 299–306; 1914.
[Crossref]

Phys. Rev. Ser. 2 (1)

T. K. Chinmayanandam, On the spectular Reflection from Rough Surfaces, Phys. Rev. Ser. 2,  13, pp. 96–101; Feb., 1919.
[Crossref]

Proc. Roy. Soc. (1)

Rayleigh, On the intensity of light reflected from certain surfaces at nearly perpendicular incidence, Proc. Roy. Soc. 41, pp. 275–294, 1886; Scientific Papers, 2, pp. 522–542.
[Crossref]

Other (1)

Bouguer, Histoire de l’Académie Royale des sciences, Paris, 1757 (1762); and Traite d’optique sur la gradation de la lumière (Ouvrage posthume de M. Bouguer, et publié par M. l’Abbe de Lacaille), Paris, 1760.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

A comparison between Fresnel’s reflection formula and a law of reflection which Grabowski finds must be satisfied by the small mirrors of a perfect malt surface. The full line is Fresnel’s law for glass, the index of refraction being taken as 1.5.

Fig. 2
Fig. 2

A comparison between Lambert’s cosine law and the theoretical law for diffuse reflection from an ideal surface whose slopes are distributed according to the Gaussian probability law. The dotted curves are for Lambert’s cosine law.

Fig. 3
Fig. 3

A comparison between Lambert’s cosine law and the theoretical law for diffuse reflection from an ideal surface whose slopes are distributed according to a law which is somewhat similar to the Gaussian probability law. The dotted curves are for Lambert’s cosine law.

Fig. 4
Fig. 4

Surface of ideal foam.

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

f ( θ ) = f ( 0 ) sec 2 n θ .
Sec 2 n θ =             for θ = π 2 .
d A = K e - a 2 p 2 d p
ψ = 1 2 ( θ - θ ) , θ 1 = θ 1 = 1 2 ( θ + θ )
d ω = π ( d θ 1 ) 2 4
d ω = π cos θ 1 ( d θ 1 ) 2 = 4 cos θ 1 d ω
R 2 d ω = 4 R 2 cos θ 1 d ω             I = K 1 cos θ 1 d A 4 R 2 cos θ 1 d ω = K 1 d A 4 R 2 d ω
I = K K 1 e - a 2 p 2 d p 4 R 2 d ω
But p = tan ψ = tan 1 2 ( θ - θ ) and d p = - 1 2 sec 2 1 2 ( θ - θ ) d θ
I = - K K 1 d θ 8 R 2 d ω sec 2 1 2 ( θ - θ ) · e - a 2 tan 2 1 2 ( θ - θ )
C = C 0 sec 2 1 2 ( θ - θ ) · e - a 2 tan 2 1 2 ( θ - θ )
d A = K d p a 2 + p 2 ,
C = C 0 a 2 sec 2 1 2 ( θ - θ ) a 2 + tan 2 1 2 ( θ - θ ) .
d A = K d p 1 + p 2 = - 1 2 K d θ ,
C = C 0 d s cos θ cos θ .