Photometry
`text(Photometry :)`
In optics, photometry is the measurement of light's brightness, or luminous intensity. Photometry frequently focuses on the perceived brightness to the human eye. As such, it takes into account the eye's sensitivity to varying degrees of light and focuses primarily on the visible light spectrum.
`text(Solid Angle :)`
In geometry, a solid angle (symbol `Omega`) is the two-dimensional angle in three-dimensional space that an object subtends at a point. It is a measure of how large the object appears to an observer looking from that point. In the International System of Units (SI), a solid angle is expressed in a dimensionless unit called a steradian.
`dOmega=(dA)/r^2`
`text(Radiant Flux :)`
Radiant flux or radiant power is the radiant energy emitted, reflected, transmitted or received, per unit time, and spectral flux or spectral power is the radiant flux per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength.
`text(Luminous Flux :)`
Luminous flux is the quantity of the energy of the light emitted per second in all directions. The unit of luminous flux is lumen (lm). One lumen is the luminous flux of the uniform point light source that has luminous intensity of 1 candela and is contained in one unit of spatial angle (or 1 steradian). It is denoted by `F`.
`text(Luminous Intensity :)`
Luminous intensity is a measure of the wavelength-weighted power emitted by a light source in a particular direction per unit solid angle, based on the luminosity function, a standardized model of the sensitivity of the human eye. The SI unit of luminous intensity is the candela (cd), an SI base unit.
`I=(DeltaF)/(DeltaOmega)`
`text(Relation between Luminous Flux and Luminous Intensity :)`
`I=text(Luminous Flux)/text(Solid Angle)=F/(4pi)`
`F=4piI`
`text(Illuminance or Intensity of Illumination of a Surface :)`
`E=(DeltaF)/(DeltaA)`
Unit `=>text(lumen)/(meter)^2 = text(lux)`
`1 text(phot)=1text(lumen)/(meter)^2`
`text(Luminous Efficiency of Electric Bulbs :)`
`text(Luminous efficiency)=text[luminous flux (in lumen)]/text[power (in watt)]`
`text(Inverse Square Law for Illuminance :)`
As one of the fields which obey the general inverse square law, the light from a point source can be put in the form
`E=I/r^2`
`Eprop1/r^2`
`text(Lambert's Cosine Law for Illuminance :)`
Suppose `S` is a light source with luminous intensity `I`. A surface `DeltaA` is at a distance `r` from `S`.
`DeltaA^'=DeltaAcostheta` (from fig.)
`DeltaF=IxxDeltaOmega`
`DeltaOmega=(DeltaA^')/r^2=(DeltaAcostheta)/r^2`
`:.` `DeltaF=Ixx(DeltaAcostheta)/r^2`
`(DeltaF)/(DeltaA)=(Icostheta)/r^2`
But we know, `(DeltaF)/(DeltaA)=E`
`:.` `E=(Icostheta)/r^2`
`text(Principle of Photometry :)`
If two light sources of luminous intensities `I_1` and `I_2` are at distance `r_1` and `r_2` respectively from a screen and light falls on screen normally, then illuminance will be same at screen due to both light sources.
`E_1=E_2`
`(I_1)/(r_1^2)=(I_2)/(r_2^2)`
`(I_1)/(I_2)=(r_1^2)/(r_2^2)`
In optics, photometry is the measurement of light's brightness, or luminous intensity. Photometry frequently focuses on the perceived brightness to the human eye. As such, it takes into account the eye's sensitivity to varying degrees of light and focuses primarily on the visible light spectrum.
`text(Solid Angle :)`
In geometry, a solid angle (symbol `Omega`) is the two-dimensional angle in three-dimensional space that an object subtends at a point. It is a measure of how large the object appears to an observer looking from that point. In the International System of Units (SI), a solid angle is expressed in a dimensionless unit called a steradian.
`dOmega=(dA)/r^2`
`text(Radiant Flux :)`
Radiant flux or radiant power is the radiant energy emitted, reflected, transmitted or received, per unit time, and spectral flux or spectral power is the radiant flux per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength.
`text(Luminous Flux :)`
Luminous flux is the quantity of the energy of the light emitted per second in all directions. The unit of luminous flux is lumen (lm). One lumen is the luminous flux of the uniform point light source that has luminous intensity of 1 candela and is contained in one unit of spatial angle (or 1 steradian). It is denoted by `F`.
`text(Luminous Intensity :)`
Luminous intensity is a measure of the wavelength-weighted power emitted by a light source in a particular direction per unit solid angle, based on the luminosity function, a standardized model of the sensitivity of the human eye. The SI unit of luminous intensity is the candela (cd), an SI base unit.
`I=(DeltaF)/(DeltaOmega)`
`text(Relation between Luminous Flux and Luminous Intensity :)`
`I=text(Luminous Flux)/text(Solid Angle)=F/(4pi)`
`F=4piI`
`text(Illuminance or Intensity of Illumination of a Surface :)`
`E=(DeltaF)/(DeltaA)`
Unit `=>text(lumen)/(meter)^2 = text(lux)`
`1 text(phot)=1text(lumen)/(meter)^2`
`text(Luminous Efficiency of Electric Bulbs :)`
`text(Luminous efficiency)=text[luminous flux (in lumen)]/text[power (in watt)]`
`text(Inverse Square Law for Illuminance :)`
As one of the fields which obey the general inverse square law, the light from a point source can be put in the form
`E=I/r^2`
`Eprop1/r^2`
`text(Lambert's Cosine Law for Illuminance :)`
Suppose `S` is a light source with luminous intensity `I`. A surface `DeltaA` is at a distance `r` from `S`.
`DeltaA^'=DeltaAcostheta` (from fig.)
`DeltaF=IxxDeltaOmega`
`DeltaOmega=(DeltaA^')/r^2=(DeltaAcostheta)/r^2`
`:.` `DeltaF=Ixx(DeltaAcostheta)/r^2`
`(DeltaF)/(DeltaA)=(Icostheta)/r^2`
But we know, `(DeltaF)/(DeltaA)=E`
`:.` `E=(Icostheta)/r^2`
`text(Principle of Photometry :)`
If two light sources of luminous intensities `I_1` and `I_2` are at distance `r_1` and `r_2` respectively from a screen and light falls on screen normally, then illuminance will be same at screen due to both light sources.
`E_1=E_2`
`(I_1)/(r_1^2)=(I_2)/(r_2^2)`
`(I_1)/(I_2)=(r_1^2)/(r_2^2)`