Physics Formulae/Equations of Light - Wikiversity (2024)

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.

Contents

  • 1 Geometric Optics
    • 1.1 Definitions, Quantities
    • 1.2 Laws of Geomtric Optics
  • 2 Radiometry
  • 3 Photometry
  • 4 Physical Optics
    • 4.1 Luminal EM Waves
  • 5 Diffraction/Interferance
    • 5.1 Diffraction
    • 5.2 Other Aperatures
  • 6 External Links
  • 7 References

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/sDefining EquationSI UnitsDimension
Refractive Index of substancenPhysics Formulae/Equations of Light - Wikiversity (1)

Physics Formulae/Equations of Light - Wikiversity (2)

dimensionlessdimensionless
Object Distancesm[L]
Image Distance s' m[L]
Focal Lengthfm[L]
Optcal PowerPPhysics Formulae/Equations of Light - Wikiversity (3)D (Dipotres) = m-1[L]-1
Radius of Curvature

of r-surface

fm[L]
Lateral MagnificationmPhysics Formulae/Equations of Light - Wikiversity (4)

m and h negative when upside down

dimensionlessdimensionless
Angular MagnificationmPhysics Formulae/Equations of Light - Wikiversity (5)dimensionlessdimensionless
Dispersive PowerωPhysics Formulae/Equations of Light - Wikiversity (6)


The refractive indicies are determined

by the frequencies of the Fraunhöfer lines.

dimensionlessdimensionless


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+-
sObject in front of r-surfaceObject behind r-surface
s' Real imageVirtual image
f, PConverging r-surfaceDiverging r-surface
rr-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 ReflectionPhysics Formulae/Equations of Light - Wikiversity (7)
Snell's Law of Refraction,

Angles of Refraction

Physics Formulae/Equations of Light - Wikiversity (8)


Mirrors

Image distance in a Plane MirrorPhysics Formulae/Equations of Light - Wikiversity (9)
Image distance in a Spherical MirrorPhysics Formulae/Equations of Light - Wikiversity (10)
Spherical Mirror Focal LengthPhysics Formulae/Equations of Light - Wikiversity (11)
Spherical MirrorPhysics Formulae/Equations of Light - Wikiversity (12)


General Media

Critical Angle of Total Internal ReflectionPhysics Formulae/Equations of Light - Wikiversity (13)


Lenses

Thin Lens, Focal LengthPhysics Formulae/Equations of Light - Wikiversity (14)

Physics Formulae/Equations of Light - Wikiversity (15)

Newton's FormulaPhysics Formulae/Equations of Light - Wikiversity (16)


Physics Formulae/Equations of Light - Wikiversity (17)

Physics Formulae/Equations of Light - Wikiversity (18)


Prisms

Minimum Deviation Angle


A = Prism Angle

D = Deviation Angle

Physics Formulae/Equations of Light - Wikiversity (19)

Physics Formulae/Equations of Light - Wikiversity (20)

Quantity (Common Name/s)(Common) Symbol/sDefining EquationSI UnitDimension
Radiant PowerQJ =[M] [L]2 [T]-2
Radiant Flux, Radiant PowerΦW
Radiant IntensityIW sr-1[M] [L]2 [T]-3
Radiance, Radiant IntensityLW sr-1 m-2
Irradiance, Incident Intensity,

Intensity incident on a surface

E, IW sr-1 m-2
Radiant Exitance, Radiant EmittanceMW m-2
Radiosity (heat transfer), Radiosity, emitted plus

reflected Intensity leaving a surface

J, JλW m-2
Spectral RadianceLλ, LνW sr-1 m-3 = W sr-1 Hz-2
Spectral IrradianceEλ, EνW m-3 = W m-2 Hz-1

Photometry

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Quantity (Common Name/s)(Common) Symbol/sDefining EquationSI UnitsDimension
Luminous energyQvJ = lm s[M] [L]2 [T]-2
Luminous flux, luminous powerF, Φvcd sr = lm = J s-1[Φ]
Luminous intensityIvcd = lm sr-1[Φ]
LunannceLvcd m-2[Φ] [L]-2
Illuminance (light incident on a surface)Evlx = lm m-2[Φ] [L]-2
Luminous Emittance (light emitted from a surfaceMvlx = lm m2[Φ] [L]-2
Luminous efficacyPhysics Formulae/Equations of Light - Wikiversity (21)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 ComponentPhysics Formulae/Equations of Light - Wikiversity (22)
Magnetic Field ComponentPhysics Formulae/Equations of Light - Wikiversity (23)
Luminal Speed in MeduimPhysics Formulae/Equations of Light - Wikiversity (24)
Poynting VectorPhysics Formulae/Equations of Light - Wikiversity (25) = Admittance of Free Space


Physics Formulae/Equations of Light - Wikiversity (26) = Impedance of Free Space


Physics Formulae/Equations of Light - Wikiversity (27)

Physics Formulae/Equations of Light - Wikiversity (28)


Physics Formulae/Equations of Light - Wikiversity (29)


Physics Formulae/Equations of Light - Wikiversity (30)


Physics Formulae/Equations of Light - Wikiversity (31)

Poynting Vector MagnitudePhysics Formulae/Equations of Light - Wikiversity (32)
Root Mean Square Electric Field of LightPhysics Formulae/Equations of Light - Wikiversity (33)
Irradiance, Light IntensityPhysics Formulae/Equations of Light - Wikiversity (34)
Irradiance, Light Intensity

due to a Point Source

Physics Formulae/Equations of Light - Wikiversity (35) = solid angle

Physics Formulae/Equations of Light - Wikiversity (36) = position from source

Physics Formulae/Equations of Light - Wikiversity (37)
Radiation Momentum, Total Absorption (Inelastic)Physics Formulae/Equations of Light - Wikiversity (38)
Radiation Momentum, Total Reflection (Elastic)Physics Formulae/Equations of Light - Wikiversity (39)
Radiation Pressure, Total Absorption (Inelastic)Physics Formulae/Equations of Light - Wikiversity (40)
Radiation Pressure, Total Reflection (Elastic)Physics Formulae/Equations of Light - Wikiversity (41)
Intensity Unpolarized LightPhysics Formulae/Equations of Light - Wikiversity (42)
Malus' Law, Plane Polarized LightPhysics Formulae/Equations of Light - Wikiversity (43)
Brewster's Law of Total

Reflective Polarisation,

Brewster's Angle

Physics Formulae/Equations of Light - Wikiversity (44)

Diffraction/Interferance

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Diffraction

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Path Length DifferencePhysics Formulae/Equations of Light - Wikiversity (45)
Diffraction Grating EquationPhysics Formulae/Equations of Light - Wikiversity (46)

Minima

Physics Formulae/Equations of Light - Wikiversity (47)


Maxima

Physics Formulae/Equations of Light - Wikiversity (48)


Physics Formulae/Equations of Light - Wikiversity (49)

Diffraction Grating Half-WidthPhysics Formulae/Equations of Light - Wikiversity (50)
Diffraction Grating DispersionPhysics Formulae/Equations of Light - Wikiversity (51)
Diffraction Grating resolving powerPhysics Formulae/Equations of Light - Wikiversity (52)
X-Ray Molecular Lattice

Diffraction, Bragg's law,

Lattice Distance

Physics Formulae/Equations of Light - Wikiversity (53)
Double-Slit Interference IntensityPhysics Formulae/Equations of Light - Wikiversity (54)
Thin-Film OpticsAir Minima

Physics Formulae/Equations of Light - Wikiversity (55)

Air Maxima

Physics Formulae/Equations of Light - Wikiversity (56)

Single-Slit IntensityPhysics Formulae/Equations of Light - Wikiversity (57)
Double Slit IntensityPhysics Formulae/Equations of Light - Wikiversity (58)

Physics Formulae/Equations of Light - Wikiversity (59)

Multiple-Slit IntensityPhysics Formulae/Equations of Light - Wikiversity (60)
Circular Aperture First MinimumPhysics Formulae/Equations of Light - Wikiversity (61)
Rayleigh's CriterionPhysics Formulae/Equations of Light - Wikiversity (62)

Other Aperatures

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External Links

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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, ISBN0-7195-3382-1

Retrieved from ""

Physics Formulae/Equations of Light - Wikiversity (2024)

FAQs

What is the formula for calculating light in physics? ›

The formula for light is the square root of E (Energy) over m (mass) hence E=mc^2. C being the speed of light. Using simple algebra you can isolate c and make it equal into 2 (possibly known) values. Energy and Mass can never be negative, therefore, square rooting it is always possible.

What is the hardest physics equation? ›

Answer to the question (What is the hardest physics equation?): * The hardest general equation to arrive at is perhaps the relativistic mass-energy equation E = {m_0} c^2/ \sqrt{1 - {v^2}/{c^2}} . * The hardest specific equations to solve are perhaps the nonlinear Schrodinger equations or nonlinear solito…

What are the 20 formulas in physics? ›

List of All Physics Formulas
Physics FormulasFormulas
Shear Modulus Formula(shear stress)/(shear strain) = (F/A)/(x/y)
Water Pressure FormulaWater pressure= ρ g h
Refractive Index Formulan = c/v
Centroid FormulaC = [(x1 + x2 + x3)/ 3, (y1 + y2 + y3)/ 3]
35 more rows

How to learn physics formulas easily? ›

Here we have listed the best ways to learn them easily:
  1. Practice Makes a Difference. ...
  2. Writing Formulas and Understanding Their Purpose. ...
  3. Distraction: A Key to Failure. ...
  4. Make a Visual Note of Formulas. ...
  5. Be a Teacher. ...
  6. Use Memory Palaces. ...
  7. Spatial Memory. ...
  8. Organize a Bit.
May 7, 2024

What is the mathematical equation for light? ›

c = 1/(e0m0)1/2 = 2.998 X 108m/s. Light is an electromagnetic wave: this was realized by Maxwell circa 1864, as soon as the equation c = 1/(e0m0)1/2 = 2.998 X 108m/s was discovered, since the speed of light had been accurately measured by then, and its agreement with c was not likely to be a coincidence.

What is the formula for calculating lighting? ›

If your room is 10 feet in length and 10 feet in width, your surface area will be 100 Square Feet. Now: Generally, experts recommend multiplying the square footage by 1.5 to get the number of watts need to comfortably and adequately illuminate a room.

What is the number 1 rule of physics? ›

Newton's first law: An object at rest remains at rest, or if in motion, remains in motion at a constant velocity unless acted on by a net external force. Note the repeated use of the verb remains. We can think of this law as preserving the status quo of motion.

What is the most elegant physics equation? ›

The formula most commonly rated as beautiful in the study, in both the initial survey and the brain scan, was Euler's equation, eiπ+ 1 = 0.

What is the single most important equation in all of physics? ›

The equation E = Mc2 is perhaps the most famous equation of twentieth- century physics. It is a statement that mass and energy are two forms of the same thing, and that one can be converted into the other (ibid., p.

What is the tricky physics formula? ›

Answer to the question (What is the hardest physics equation?): The hardest general equation to arrive at is perhaps the relativistic mass-energy equation E=m0c2/√1−v2/c2 E = m 0 c 2 / 1 − v 2 / c 2 .

What does r stand for in physics? ›

Physics Symbols in Electricity & Magnetism:
Physical QuantitySymbol(s)SI Unit
ResistanceROhms (Ω)
InductanceLHenry (H)
CapacitanceCFarad (F)
Electric Potential DifferenceVVolt (V)
4 more rows

Should you memorize physics formulas? ›

Formulas form an important aspect of the Physics subject, and they need to be memorized and easily picked out from the back of your head during exams. If you don't remember them, it may cause you to lose a few marks in the exam. Here are some handy methods to effectively memorize your Physics formulas.

How to solve physics quickly? ›

  1. Focus on the Problem. Establish a clear mental image of the problem. A. ...
  2. Describe the Physics. Refine and quantify your mental image of the problem. A. ...
  3. Plan a Solution. Turn the concepts into math. A. ...
  4. Execute the Plan. This is the easiest step – it's just the algebra/calculus/etc. A. ...
  5. Evaluate the Answer. Be skeptical.

What are the formulas for light? ›

Photometry
Quantity (Common Name/s)(Common) Symbol/sSI Units
Luminous flux, luminous powerF, Φvcd sr = lm = J s-1
Luminous intensityIvcd = lm sr-1
LunannceLvcd m-2
Illuminance (light incident on a surface)Evlx = lm m-2
3 more rows
Jun 19, 2024

What is the formula for the amount of light? ›

Calculating Lumens and Candela

The formula will look like this, 1lm = 1cd * 1. 1 lumen = 1 candela; a light source with 1 candela intensity produces 1 lumen of luminous flux in a sphere with 1 square meter surface area.

How do you calculate light value? ›

Light Value represents the amount of light the camera sees from a scene and it is derived from other EXIF Camera data. It is given by: LV=log2(N**2/t)-log2(ISO/100) where N is the f-stop, t is the shutter speed in seconds and ISO is the sensor ISO value.

References

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