Physics and mechanics
Electromagnetic Wave Equilibrium Calculator
Solve the normal-incidence optical intensity that balances a declared opposing force using reflected, transmitted, and absorbed momentum transfer.
CURRENT MODEL
Define the target, optical fractions, and opposing force
Optomechanics students, photonics researchers, and preliminary instrument designers screening steady radiation-pressure force balance on a flat target.
Decision supportedFind the beam intensity and incident power that make radiation force equal a known opposite force, then compare the entered operating intensity with that balance point.
LIVE MOMENTUM BALANCE
Current force balance against the target
The live force diagram compares current radiation pressure with the declared opposing force and shows how reflection, transmission, and absorption shape momentum transfer.
| Quantity | Equation | Current value | Unit |
|---|
How to use
Declare a mechanical balance before solving intensity
- Enter the steady opposing force in the direction opposite beam propagation.
- Enter the uniformly illuminated projected area normal to the beam.
- Provide measured or specified reflectance and transmittance at the operating wavelength and angle.
- Check that their sum does not exceed 100%; the remainder is treated as absorptance.
- Enter the current beam intensity to compare operation against the solved equality.
- Read the net-force sign and power partition, then verify that optical powers reconcile to incident power.
Force-balance fundamentals
Six facts behind radiation-pressure equilibrium
- Mechanical equilibrium
- The page solves equality of two collinear forces, not a thermal or field equilibrium.
- Momentum flux
- Intensity divided by c sets the incident electromagnetic momentum delivered per area and time.
- Absorption
- Absorbed light removes forward momentum once and also creates a thermal load outside this force-only model.
- Reflection
- Backward reflection reverses optical momentum and doubles that portion's ideal normal force contribution.
- Transmission
- Forward transmitted light retains momentum, reducing transfer to the target compared with absorption.
- Equality versus stability
- A zero net force at one position does not show that a displacement produces a restoring force.
Calculation method
Power fractions become a momentum coefficient
The model converts area to square metres and force to newtons. Since absorptance is 1 - R - T, the combined normal momentum coefficient A + 2R becomes 1 + R - T. The required intensity follows by rearranging the force equality.
The separate current-intensity branch computes present incident, reflected, transmitted, and absorbed powers. It then compares current radiation force with the opposing force, so the equilibrium target and operating state remain distinct.
Beam-profile integration
Intensity times area is valid for a uniform spot. Gaussian or clipped beams require integrating local irradiance over the target and accounting for local angle.
Angular incidence
Oblique beams alter projected area, momentum components, polarization fractions, and torque. This model is deliberately normal-incidence and one-dimensional.
Thermal recoil
Absorbed power can drive temperature gradients, outgassing, or thermal-radiation recoil. Those mechanisms are separate from immediate optical momentum transfer.
Control margin
A force ratio near one can still be unusable if intensity noise, suspension stiffness, damping, or actuator range is inadequate.
Detailed calculation process
Symbols, current substitution, intermediate quantities, and reconciliation
F_rad = (1 + R - T) I A / c; I_eq = F_ext c / [(1 + R - T) A]Power fractions remain unrounded in the momentum coefficient. Force, intensity, and power are rounded only for display after the one-second power and force checks.
| Symbol | Meaning | Default | Unit |
|---|---|---|---|
| F_ext | Opposing mechanical force | 1 | microN |
| A | Uniform illuminated area | 1 | cm^2 |
| R | Power reflectance | 80 | % |
| T | Power transmittance | 5 | % |
| I | Current beam intensity | 1,800,000 | W/m^2 |
| c | Speed of light | 299,792,458 | m/s |
| C_m | Momentum coefficient 1+R-T | calculated | dimensionless |
Waiting for valid inputs.
Interpretation
Read target intensity and operating net force separately
The required intensity is the equality point for the declared force and target. Current net force is positive when radiation dominates and negative when the opposing force dominates. The ratio describes magnitude only; it does not certify positional or angular stability.
Evidence and measurement
Preserve what made the force coefficient credible
Record beam power calibration, spatial profile, target area and alignment, wavelength, polarization, coating lot, measured R and T, force-sensor calibration and drift, vacuum or gas conditions, and whether scattered light was counted. Retain uncertainty and sign convention with the exported case.
Scope and limitations
What this equality does not certify
- Angular incidence, torque, off-axis beam shape, or polarization coupling
- Position stability, damping, feedback bandwidth, or disturbance rejection
- Thermal deformation, recoil, outgassing, or coating degradation
- Near-field, resonant-cavity, gradient-force, or optical-trapping behavior
- Relativistic target motion or time-varying pulse momentum
- Laser exposure limits or laboratory safety procedure
Equilibrium means one-dimensional mechanical force balance at normal incidence on a flat target. The beam uniformly covers the declared area; reflectance and transmittance are power fractions; thermal, electrostatic, gravity-gradient, and dynamic control effects are outside scope.
Key terminology
Radiation-force glossary
- Irradiance
- Incident optical power divided by illuminated area, expressed here in W/m^2.
- Radiation pressure
- Mechanical pressure produced by electromagnetic momentum transfer.
- Reflectance
- Fraction of incident optical power reflected from the target.
- Transmittance
- Fraction continuing forward through the target.
- Absorptance
- Fraction removed from the optical field as absorption, calculated as 1-R-T.
- Momentum coefficient
- Normal-incidence multiplier 1+R-T connecting IA/c to force.
- Net force
- Signed radiation force minus the declared opposing force.
- Stable equilibrium
- An equality that also responds to displacement with restoring dynamics, not established here.
Practical cases
Two balances that demand different follow-up
Micro-force calibration target
A lab compares a 1 microN reference force with a coated foil. Required watts establish an optical calibration target, but beam-profile and force-sensor uncertainties determine the usable accuracy.
Reflective sail screening
A concept team compares coating options at fixed area and external load. Higher reflectance raises momentum coefficient, yet structural dynamics and off-axis torque remain separate analyses.
Important note
Force equality is not an operating-safety determination
The output is a normal-incidence screening balance. Keep the unrounded power and force evidence, and obtain qualified optical, mechanical, thermal, and safety review before exposing real hardware.
Frequently asked questions
What does equilibrium mean on this page?
It means steady one-axis mechanical force balance: radiation force equals the entered opposing force. It is not thermal equilibrium, electromagnetic field equilibrium, or a stable feedback-control proof.
Why does reflection contribute more momentum than absorption?
Absorbed light transfers its forward momentum once. Ideal backward reflection reverses photon momentum and approaches twice the incident momentum transfer.
Why is the coefficient 1 + R - T?
For normal incidence, absorbed power contributes one unit, reflected power contributes two, and transmitted forward power contributes none of the removed forward momentum: A + 2R = 1 + R - T.
Can I use irradiance that varies across the target?
Only after replacing intensity times area with a spatial integral of intensity weighted by local momentum transfer. The current model assumes uniform irradiance and uniform optical fractions.
Does a zero opposing force require zero light?
The solved equilibrium intensity is zero. Any positive entered intensity then produces a positive radiation-dominant net force under this one-axis model.
Does the balance point guarantee positional stability?
No. Stability requires how force changes with displacement, angle, beam profile, suspension stiffness, damping, and controls. A single force equality can be unstable.
Authority and follow-on work
Reliable sources and related calculators
- NASA NIAC — Radiation pressure forceGives radiation-pressure force in the form F = (IA/c)Q and notes Q = 2 for an ideal normal reflector.
- NIST — SI defining constantsSupports the exact speed of light used in the momentum balance.
- OpenStax University Physics — Momentum and Radiation PressureExplains electromagnetic momentum flux and radiation pressure for absorption and reflection.
Related calculators
Continue with a distinct optics question without silently changing the model boundary.