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 edit

Definitions, Quantities edit


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 edit

Law of Reflection  
Snell's Law of Refraction,

Angles of Refraction



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  


Thin Lens, Focal Length  


Newton's Formula  




Minimum Deviation Angle

A = Prism Angle

D = Deviation Angle



Radiometry edit

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 edit

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]
Luminance 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 edit

Luminal EM Waves edit

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 edit

Diffraction edit

Path Length Difference  
Diffraction Grating Equation  






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 edit

External Links edit

Poynting Vector

EM Waves




References edit

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