Secondary reflectors for solar collectors and methods of making the same

A device comprising:

• a reflecting surface for a concentrating solar system using a tracking system, the reflector surface having a length aligned along a first axis (z), wherein:
• a cross-section of the reflecting surface in a plane perpendicular to the first axis (z) forms a curve comprising a concave section positioned between a first endpoint and a second endpoint,
• at least a portion of the concave section is accurately approximated by a polynomial equation,
• the concave section is configured to focus a plurality of beams of light onto a focal point,
• the plane contains a second axis (x) that is perpendicular to the first axis (z) and a third axis (y) that is perpendicular to the second axis (x),
• the third axis (y) intersects the second axis (x) to form a dimensionless xy-coordinate system having an origin of (0, 0) at the intersection,
• the concave section is positioned in the dimensionless xy-coordinate system,
• the concave section comprises a first portion that starts at the first endpoint positioned at (1, 0) and terminates at an intermediate point at (0, D),
• D is a dimensionless number between 0.55 and 0.93, inclusively,
• the polynomial equation is a third-order polynomial equation defined as
• y=a′x3+b′x2+c′x+D
• a′ is between −0.15 and −0.09, inclusively,
• b′ is between −0.45 and −0.07, inclusively,
• c′ is between 0.10 and 0.24, inclusively, and
• a′, b′, and c′ are all dimensionless numbers.