Bill C.

asked • 11/20/14

looking for someone to help me calculate a formula for light reflection with parabolic mirrors

Ok I see formulas regarding direct light hitting parabolic mirrors in which you derive to the focal point.  Im trying to do the opposite that in which my focal point is the light source feeding outward.  Is their a simple formula for this?  The light source is LEDs at 12,000 lumens located 20" from the bottom of the center farthest distance from the
parabolic.

1 Expert Answer

By:

Ben B. answered • 11/21/14

Tutor
5 (8)

Experience Aerospace Engineer with Master's Degree in Physics

Bill C.

Hi Ben,  Thank you for the answer to this but I was looking for more of the formula in which you have the x and y axis using the law of reflection.  I see these formulas for rays hitting outer surface directing inward to a focal point but I do not see the formula in which the opposite occurs.  Any ideas?
 
Bill
 
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11/21/14

Ben B.

Bill,
 
For a parabolic reflector, the rays converge to a point only if the incident rays are parallel to the axis of the reflector. Similarly, for a source at the focus that is not on the axis (off-axis), the outgoing rays will not be parallel. I am not aware of any simple formula. This phenomenon, is known as "coma" for reflecting telescopes of short focal length. That is - the rays do not focus to a point, resulting in images that are clear only for objects (stars) that are near the center of view. For stars that are off axis, the image does not appear as a point, but as a V-shaped object that looks somewhat like a comet. The coma effect is worse for object farther from the center line.
 
- Ben
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11/21/14

Bill C.

Hi Ben,
 
Great, thank for the information for I am striving to create a homogeneous light pattern with LEDs by using a spherical concave reflection and this will help.
 
Kind Regards,
 
Bill Cliff
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11/22/14

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