Abstract

A general formula is derived that specifies the illumination (flux density) over an arbitrary receiver surface when light rays are reflected by or refracted through a curved surface. The direction of the deflected ray and its intersection with the receiving surface, used with the equation for the surfaces, lead to a transformation that maps an element of deflecting area onto the receiving area, by means of the jacobian determinant. A formula for the flux density along a ray path follows as a special case. An equation for the caustic surface is obtained from the latter. As an example radiation flux-density contours are calculated for a plane wave reflected from a sphere. Flux density and the caustic surface are calculated for a plane wave reflected onto a plane from a concave spherical lens and also for a plane wave refracted onto a plane through a hemisphere.

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  1. Max Herzberger, Modern Geometrical Optics (Wiley-Interscience, New York, 1958).
  2. E. R. G. Eckert and E. M. Sparrow, Int. J. Heat Mass Transfer 3.1, 42 (1961).
  3. S. H. Lin and E. M. Sparrow, J. Heat Transfer 87C, 299 (1965).
  4. J. A. Plamondon and T. E. Horton, Int. J. Heat Mass Transfer 10, 665 (1967).
  5. Joseph B. Keller and Herbert B. Keller, J. Opt. Soc. Am. 40, 48 (1950).
  6. Joseph B. Keller and William Streifer, J. Opt. Soc. Am. 61, 40 (1971).
  7. V. A. Fock, Electromagnetic Diffraction and Propagation Problems (Pergamon, New York, 1965).
  8. Hilbert Schenck, Jr., J. Opt. Soc. Am. 47, 653 (1957).
  9. Van Z. Barkowski, Optik 18, 22 (1961).
  10. Van Z. Barkowski, Optik 19, 226 (1962).
  11. M. M. Lipschutz, Differential Geometry (Schaum's Outline Series) (McGraw-Hill, New York, 1969).

Barkowski, Van Z.

Van Z. Barkowski, Optik 18, 22 (1961).

Van Z. Barkowski, Optik 19, 226 (1962).

Eckert, E. R. G.

E. R. G. Eckert and E. M. Sparrow, Int. J. Heat Mass Transfer 3.1, 42 (1961).

Fock, V. A.

V. A. Fock, Electromagnetic Diffraction and Propagation Problems (Pergamon, New York, 1965).

Herzberger, Max

Max Herzberger, Modern Geometrical Optics (Wiley-Interscience, New York, 1958).

Horton, T. E.

J. A. Plamondon and T. E. Horton, Int. J. Heat Mass Transfer 10, 665 (1967).

Keller, Herbert B.

Joseph B. Keller and Herbert B. Keller, J. Opt. Soc. Am. 40, 48 (1950).

Keller, Joseph B.

Joseph B. Keller and William Streifer, J. Opt. Soc. Am. 61, 40 (1971).

Joseph B. Keller and Herbert B. Keller, J. Opt. Soc. Am. 40, 48 (1950).

Lin, S. H.

S. H. Lin and E. M. Sparrow, J. Heat Transfer 87C, 299 (1965).

Lipschutz, M. M.

M. M. Lipschutz, Differential Geometry (Schaum's Outline Series) (McGraw-Hill, New York, 1969).

Plamondon, J. A.

J. A. Plamondon and T. E. Horton, Int. J. Heat Mass Transfer 10, 665 (1967).

Schenck, Jr., Hilbert

Hilbert Schenck, Jr., J. Opt. Soc. Am. 47, 653 (1957).

Sparrow, E. M.

S. H. Lin and E. M. Sparrow, J. Heat Transfer 87C, 299 (1965).

E. R. G. Eckert and E. M. Sparrow, Int. J. Heat Mass Transfer 3.1, 42 (1961).

Streifer, William

Joseph B. Keller and William Streifer, J. Opt. Soc. Am. 61, 40 (1971).

Other (11)

Max Herzberger, Modern Geometrical Optics (Wiley-Interscience, New York, 1958).

E. R. G. Eckert and E. M. Sparrow, Int. J. Heat Mass Transfer 3.1, 42 (1961).

S. H. Lin and E. M. Sparrow, J. Heat Transfer 87C, 299 (1965).

J. A. Plamondon and T. E. Horton, Int. J. Heat Mass Transfer 10, 665 (1967).

Joseph B. Keller and Herbert B. Keller, J. Opt. Soc. Am. 40, 48 (1950).

Joseph B. Keller and William Streifer, J. Opt. Soc. Am. 61, 40 (1971).

V. A. Fock, Electromagnetic Diffraction and Propagation Problems (Pergamon, New York, 1965).

Hilbert Schenck, Jr., J. Opt. Soc. Am. 47, 653 (1957).

Van Z. Barkowski, Optik 18, 22 (1961).

Van Z. Barkowski, Optik 19, 226 (1962).

M. M. Lipschutz, Differential Geometry (Schaum's Outline Series) (McGraw-Hill, New York, 1969).

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