Physics Formulae/Equations of Light

Lead Article: Tables of Physics Formulae


This article is a summary of the laws, principles, defining quantities, and useful formulae in the analysis of photonics.


Geometric Optics

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Definitions, Quantities

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Definitions


For conveinece in the table below, "r-surface" refers to reflecting/refracting surface. This is not a standard abbreviation.

Quantity (Common Name/s) (Common) Symbol/s Defining Equation SI Units Dimension
Refractive Index of substance n  

 

dimensionless dimensionless
Object Distance s m [L]
Image Distance s' m [L]
Focal Length f m [L]
Optcal Power P   D (Dipotres) = m-1 [L]-1
Radius of Curvature

of r-surface

f m [L]
Lateral Magnification m  

m and h negative when upside down

dimensionless dimensionless
Angular Magnification m   dimensionless dimensionless
Dispersive Power ω  


The refractive indicies are determined

by the frequencies of the Fraunhöfer lines.

dimensionless dimensionless


Sign Conventions and Implications

There are different sign conventions which can be used, perhaps the the simplist to understand and recall is the one below[1].


The general pattern is the following:


Distances for real rays of light actually traversed are positve

Distances for apparent (i.e. virtual) rays of light not actually traversed are negative.

Distances are measured to the the apex of the r-surface on the optic axis.


Quantity + -
s Object in front of r-surface Object behind r-surface
s' Real image Virtual image
f, P Converging r-surface Diverging r-surface
r r-surface centre of curvature

on same side as object

r-surface centre of curvature

on opposite side as object

Laws of Geomtric Optics

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Law of Reflection  
Snell's Law of Refraction,

Angles of Refraction

 


Mirrors


Image distance in a Plane Mirror  
Image distance in a Spherical Mirror  
Spherical Mirror Focal Length  
Spherical Mirror  


General Media


Critical Angle of Total Internal Reflection  


Lenses


Thin Lens, Focal Length  

 

Newton's Formula  


 

 


Prisms


Minimum Deviation Angle


A = Prism Angle

D = Deviation Angle

 

 

Radiometry

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Quantity (Common Name/s) (Common) Symbol/s Defining Equation SI Unit Dimension
Radiant Power Q J = [M] [L]2 [T]-2
Radiant Flux, Radiant Power Φ W
Radiant Intensity I W sr-1 [M] [L]2 [T]-3
Radiance, Radiant Intensity L W sr-1 m-2
Irradiance, Incident Intensity,

Intensity incident on a surface

E, I W sr-1 m-2
Radiant Exitance, Radiant Emittance M W m-2
Radiosity (heat transfer), Radiosity, emitted plus

reflected Intensity leaving a surface

J, Jλ W m-2
Spectral Radiance Lλ, Lν W sr-1 m-3 = W sr-1 Hz-2
Spectral Irradiance Eλ, Eν W m-3 = W m-2 Hz-1

Photometry

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Quantity (Common Name/s) (Common) Symbol/s Defining Equation SI Units Dimension
Luminous energy Qv J = lm s [M] [L]2 [T]-2
Luminous flux, luminous power F, Φv cd sr = lm = J s-1 [Φ]
Luminous intensity Iv cd = lm sr-1 [Φ]
Lunannce Lv cd m-2 [Φ] [L]-2
Illuminance (light incident on a surface) Ev lx = lm m-2 [Φ] [L]-2
Luminous Emittance (light emitted from a surface Mv lx = lm m2 [Φ] [L]-2
Luminous efficacy   lm W-1 [Φ] [T]2 [M]-1 [L]-2


Physical Optics

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Luminal EM Waves

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Electric Field Component  
Magnetic Field Component  
Luminal Speed in Meduim  
Poynting Vector   = Admittance of Free Space


  = Impedance of Free Space


 

 


 


 


 

Poynting Vector Magnitude  
Root Mean Square Electric Field of Light  
Irradiance, Light Intensity  
Irradiance, Light Intensity

due to a Point Source

  = solid angle

  = position from source

 
Radiation Momentum, Total Absorption (Inelastic)  
Radiation Momentum, Total Reflection (Elastic)  
Radiation Pressure, Total Absorption (Inelastic)  
Radiation Pressure, Total Reflection (Elastic)  
Intensity Unpolarized Light  
Malus' Law, Plane Polarized Light  
Brewster's Law of Total

Reflective Polarisation,

Brewster's Angle

 

Diffraction/Interferance

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Diffraction

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Path Length Difference  
Diffraction Grating Equation  

Minima

 


Maxima

 


 

Diffraction Grating Half-Width  
Diffraction Grating Dispersion  
Diffraction Grating resolving power  
X-Ray Molecular Lattice

Diffraction, Bragg's law,

Lattice Distance

 
Double-Slit Interference Intensity  
Thin-Film Optics Air Minima

 

Air Maxima

 

Single-Slit Intensity  
Double Slit Intensity  

 

Multiple-Slit Intensity  
Circular Aperture First Minimum  
Rayleigh's Criterion  

Other Aperatures

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Poynting Vector

EM Waves

Photometry

Radiometry

Interferometry


References

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  1. Essential Principles of Physics, M.J. Hodgson and P.M. Whelan, John Murray 2nd Edition, 1978, ISBN 0-7195-3382-1