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Synthesis of Parabolic Light Reflector

Problem Description

The purpose of the task is to calculate the profile of the reflector and ensure coincidence with the parabola. The light distribution is given in the analytical form of the corresponding distributions obtained from the parabolic light reflector.

Specify luminous intensity distribution (LID) of the light source in the form:

I(γ) = (1 - cos(γ)) / 2(cardioid)

and profile as parabola with focus F = 0.5 m
γs = 180o, γf = 90o

Height of the light center:
h = 1 m

Illuminance distribution on the working plane from paraboloid:

Rotational symmetryE = (1+x2)-3

Cylindrical symmetry E = (1+x2)-2

Criteria for calculating the parabolic mirror:

  • when γ = 90o the value of the coordinates of the reflector R = 1 m
  • reflected rays should be strictly vertical α = 0o

Solution for Rotational Symmetry

Optical SchemeLuminous Intensity Distribution of the Light SourceIlluminance Distribution on the Working PlaneCalculated Reflector

Solution for Cylindrical Symmetry with Point Light Source

Cylindrical Symmetry with Point Light SourceLuminous Intensity Distribution of the Light SourceIlluminance Distribution on the Working PlaneCalculated Reflector

Solution for Cylindrical Symmetry with Line Light Source

Cylindrical Symmetry with Line Light SourceLuminous Intensity Distribution of the Light SourceIlluminance Distribution on the Working PlaneCalculated Reflector