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The simplest way to obtain the power transmission coefficient (transmissivity, the ratio of transmitted power to incident power in the direction normal to the interface, i.e. the y direction) is to use R + T = 1 (conservation of energy). In this way we find
Mathematically, for the spectral power distribution of a radiant exitance or irradiance one may write: =where M(λ) is the spectral irradiance (or exitance) of the light (SI units: W/m 2 = kg·m −1 ·s −3); Φ is the radiant flux of the source (SI unit: watt, W); A is the area over which the radiant flux is integrated (SI unit: square meter, m 2); and λ is the wavelength (SI unit: meter, m).
A point source of light produces spherical wavefronts. The irradiance in this case varies inversely with the square of the distance from the source. = =, where r is the distance; P is the radiant flux; A is the surface area of a sphere of radius r.
For people with protanopia, the peak of the eye's response is shifted toward the short-wave part of the spectrum (approximately 540 nm), while for people with deuteranopia, there is a slight shift in the peak of the spectrum, to about 560 nm. [17] People with protanopia have essentially no sensitivity to light of wavelengths more than 670 nm.
The average annual solar radiation arriving at the top of the Earth's atmosphere is about 1361 W/m 2. This represents the power per unit area of solar irradiance across the spherical surface surrounding the Sun with a radius equal to the distance to the Earth (1 AU).
Luminous efficacy can be normalized by the maximum possible luminous efficacy to a dimensionless quantity called luminous efficiency.The distinction between efficacy and efficiency is not always carefully maintained in published sources, so it is not uncommon to see "efficiencies" expressed in lumens per watt, or "efficacies" expressed as a percentage.
Optical power meters usually display time-averaged power. So for pulse measurements, the signal duty cycle must be known to calculate the peak power value. However, the instantaneous peak power must be less than the maximum meter reading, or the detector may saturate, resulting in wrong average readings.
Ned Wright's cosmology calculator calculates a luminosity distance for a redshift of 1 to be 6701 Mpc = 2×10 26 m giving a radio luminosity of 10 −26 × 4 π (2×10 26) 2 / (1 + 1) (1 + 2) = 6×10 26 W Hz −1. To calculate the total radio power, this luminosity must be integrated over the bandwidth of the emission.