= Photopic luminous efficiency function
{title2=$V(\lambda)$}
The <photopic luminous efficiency function> $V(\lambda)$ is dimensionless and describes standardized relative sensitivity for <photopic vision>. It is normalized to $V(555\,\mathrm{nm})=1$ and tabulated over $360$–$830\,\mathrm{nm}$. The <wavelength> coordinate is in standard air, rather than <vacuum>; changing coordinates requires converting the <spectral radiant flux> density as well. The official prescription uses linear <interpolation> between the specified 1 nm entries.<The International System of Units (SI), ninth edition, SI Brochure/Mise en pratique for the definition of the candela and associated derived units for photometric and radiometric quantities in the SI>[§3.1, printed pp. 2–3: wavelength convention, normalized functions and interpolation]{ref}
Write $\lambda_a$ for the standard-air <wavelength> at $540\,\mathrm{THz}$. With <spectral radiant flux> $\Phi_{e,\lambda}$ in $\mathrm{W\,nm^{-1}}$ and $d\lambda$ in nanometres, the <luminous flux> is
$$
\Phi_v=K_m\int_{360\,\mathrm{nm}}^{830\,\mathrm{nm}}V(\lambda)\Phi_{e,\lambda}(\lambda)\,d\lambda,
\qquad K_m=\frac{K_{\mathrm{cd}}}{V(\lambda_a)},\qquad K_{\mathrm{cd}}=683\,\mathrm{lm\,W^{-1}}.
$$
The <integral> has units of <watts>, and $K_m$ converts them to \x[lumens]{magic}. For radiation at a single <wavelength> $\lambda_0$ with total <radiant flux> $P$, this reduces to $\Phi_v=K_mV(\lambda_0)P$. For a sufficiently narrow finite band, this is an approximation requiring nearly constant $V$ across the band.<The International System of Units (SI), ninth edition, SI Brochure/Mise en pratique for the definition of the candela and associated derived units for photometric and radiometric quantities in the SI>[§3.1, equation (2), printed p. 3: spectral weighting normalized at the defining frequency]{ref}
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