Physics Formulae/Equations of Light

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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]

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[edit]

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[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

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[edit]

External Links[edit]

Poynting Vector

EM Waves

Photometry

Radiometry

Interferometry


References[edit]

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