An amber LED's spectral flux is not flat across its band

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Geometrical optics and imaging · Geometrical optics and imaging

Optics and Photonics, Ch Radiometry and photometry

Problem

An amber LED's spectral flux is not flat across its band. Measured at 20 nm steps it reads as in the table, and it is negligible below 550 nm and above 650 nm. The standard luminous efficiency function at the same five wavelengths is listed alongside. Data at λ=560,580,600,620,640 nm\lambda=560, 580, 600, 620, 640\ \mathrm{nm}: the spectral flux Φλ\Phi_\lambda in mW nm−1\mathrm{mW\,nm^{-1}} is 0.05,0.20,0.50,0.40,0.150.05, 0.20, 0.50, 0.40, 0.15, and V(λ)V(\lambda) is 0.995,0.870,0.631,0.381,0.1750.995, 0.870, 0.631, 0.381, 0.175. Treat Φλ\Phi_\lambda as varying linearly between the tabulated points and as zero at 540 nm and 660 nm, so that each integral over wavelength is a sum of trapezia of width 20 nm. ((a)) Find the LED's total radiant flux Φ\Phi. ((b)) Find its luminous flux Φv\Phi_v, integrating V(λ)ΦλV(\lambda)\Phi_\lambda the same way. ((c)) A designer replaces the LED by one emitting the same radiant flux at the single wavelength of the peak, 600 nm. By what factor does the luminous flux change, and why is the answer not 11? ((d)) How many lumens does the real LED deliver per radiant watt, and how far below the ceiling of 683683 lm W−1^{-1} does that sit?

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