# Radiant Flux and Luminous Flux

From any radiation source, the radiated energy per unit time is referred as the radiant flux. Suppose this radiated energy is denoted as Q joule then Where, Φ is the radiated energy per second and its unit is watt. That means radiant flux is nothing but radiated power.
Although it has already been considered that entire power or flux is radiated within optical range of wavelength but the radiant flux is not equal for all the wavelength. It varies with wavelength. Let us consider Φλ(λ) is radiant flux at wavelength λ.

Hence for entire optical range of wavelength the radiant flux will be Now if this radiation is within human visual sensation then this radiant flux is called luminous flux. Luminous flux has a unit i.e. Lumen (lm) instead of watt. The visible range of wavelengths is quite narrow compared to the optical range and sensitivity of human eyes varies considerably with the wavelength within this visible range. The sensitivity of human eyes to the different wavelengths of light can be represented by spectral sensitivity function or luminous efficacy function Vλ.

This is actually proportional to relative spectral sensitivity function V(λ). The sensitivity of human eyes in photopic vision is maximum at wavelength 555 nm. The relative spectral sensitivity at that wavelength is taken as 1. The luminous efficacy at the wavelength of 555 nm is 683 lumens/watt. Hence, luminous efficacy at any wavelength within visible range can be found from the equation Where, vλ is relative spectral sensitivity at wavelength λ that means it is the value of relative spectral sensitivity function V(λ) at wavelength λ.

Here, Vλ lumens is correlated to one-watt radiant flux at wavelength λ so at Φλ watts radiant flux, there will be ΦλVλ lumens. This quantity is defined as luminous flux at wavelength λ. For entire visible range of wavelength, the luminous flux will be This is the conversion equation that is used to quantify any photometric quantity from the radiometric quantity and we use the equation when we try to correlate the radiant flux and the luminous flux.
We can represent the spectral efficacy in the graph of the perceived optical stimulus vs. the incident radiant power as a function of wavelength. The human eye is almost 2.5 times as sensitive at the wavelength of maximum sensitivity when it is dark.  