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incident wave in physics
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Short definition
- An incident wave (or incoming wave) is the wave that arrives at — and interacts with — some target or boundary. It is the wave before any reflection, transmission, scattering, or absorption by that target.
Where you see it
- Optics / electromagnetism: light or EM wave arriving at an interface (air → glass), producing reflected and transmitted waves.
- Acoustics: sound wave arriving at a change in acoustic impedance.
- Quantum scattering: an incident wavefunction (often a plane wave) that scatters off a potential and produces outgoing scattered waves.
Typical mathematical form
- A common model is a plane incident wave: psi_inc = A · exp[i(k · r − ωt)], where A is amplitude (and polarization for EM), k is the wavevector giving propagation direction, r position, and ω angular frequency.
- For spherical waves: psi_inc = (A/r) · exp[i(kr − ωt)] for a point source.
Key concepts
- Angle of incidence (θi): angle between the incident wavevector and the normal to the surface. It determines reflection and refraction directions (Snell’s law).
- Incident intensity or flux: the power per unit area carried by the incident wave (for EM, proportional to |E_inc|^2; for QM, the probability current of the incident wave).
- Conservation of energy: incident power = reflected + transmitted + absorbed (if absorption present).
- Boundary conditions at interfaces determine reflected and transmitted amplitudes (e.g., Fresnel equations in optics, impedance matching in acoustics).
Simple results/examples
- Normal incidence (light on a dielectric): reflection coefficient (power) R = ((n1 − n2)/(n1 + n2))^2 and transmission T = 1 − R (for lossless media), where n1,n2 are refractive indices.
- Scattering in quantum mechanics: total wavefunction = incident plane wave + outgoing scattered wave. The differential cross section relates scattered intensity to incident flux.
If you want
- I can show derivations for Fresnel coefficients, calculate reflection/transmission for oblique incidence, write out the electromagnetic boundary conditions, or go through the QM scattering decomposition. Which application are you interested in?
- An incident wave (or incoming wave) is the wave that arrives at — and interacts with — some target or boundary. It is the wave before any reflection, transmission, scattering, or absorption by that target.
Where you see it
- Optics / electromagnetism: light or EM wave arriving at an interface (air → glass), producing reflected and transmitted waves.
- Acoustics: sound wave arriving at a change in acoustic impedance.
- Quantum scattering: an incident wavefunction (often a plane wave) that scatters off a potential and produces outgoing scattered waves.
Typical mathematical form
- A common model is a plane incident wave: psi_inc = A · exp[i(k · r − ωt)], where A is amplitude (and polarization for EM), k is the wavevector giving propagation direction, r position, and ω angular frequency.
- For spherical waves: psi_inc = (A/r) · exp[i(kr − ωt)] for a point source.
Key concepts
- Angle of incidence (θi): angle between the incident wavevector and the normal to the surface. It determines reflection and refraction directions (Snell’s law).
- Incident intensity or flux: the power per unit area carried by the incident wave (for EM, proportional to |E_inc|^2; for QM, the probability current of the incident wave).
- Conservation of energy: incident power = reflected + transmitted + absorbed (if absorption present).
- Boundary conditions at interfaces determine reflected and transmitted amplitudes (e.g., Fresnel equations in optics, impedance matching in acoustics).
Simple results/examples
- Normal incidence (light on a dielectric): reflection coefficient (power) R = ((n1 − n2)/(n1 + n2))^2 and transmission T = 1 − R (for lossless media), where n1,n2 are refractive indices.
- Scattering in quantum mechanics: total wavefunction = incident plane wave + outgoing scattered wave. The differential cross section relates scattered intensity to incident flux.
If you want
- I can show derivations for Fresnel coefficients, calculate reflection/transmission for oblique incidence, write out the electromagnetic boundary conditions, or go through the QM scattering decomposition. Which application are you interested in?
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