Prove that a linear compound parabolic concentrator realizes the maximum possible concentration for a given acceptance angle θ. Suggestion: following the notation of Figure 24.11, work in a coordinate system where parabola 2 is described by the equation y = x²/4F. Identify B and Q as the points on parabola 2 where the slopes are tan α and tan 2α, with 2α + θ = π/2. Then show that Q̅A̅/B̅A̅ = (1 + sin θ)/2 sin² θ, which proves the desired result.