colour.phenomena.polarised_light_magnitude_elements#

colour.phenomena.polarised_light_magnitude_elements(n_1: ArrayLike, n_2: ArrayLike, theta_i: ArrayLike, theta_t: ArrayLike) → Tuple[NDArrayComplex, NDArrayComplex, NDArrayComplex, NDArrayComplex][source]#

Compute common magnitude elements for Fresnel equations.

This function computes the common terms used in the Fresnel equations for both s-polarisation (perpendicular) and p-polarisation (parallel) components of light at a dielectric interface.

Parameters:

  • n_1 (ArrayLike) – Refractive index of the incident medium \(n_1\).

  • n_2 (ArrayLike) – Refractive index of the transmitted medium \(n_2\).

  • theta_i (ArrayLike) – Incident angle \(\theta_i\) in degrees.

  • theta_t (ArrayLike) – Transmitted angle \(\theta_t\) in degrees.

Returns:

Tuple of precomputed magnitude elements: \((n_1 \cos \theta_i, n_1 \cos \theta_t, n_2 \cos \theta_i, n_2 \cos \theta_t)\)

Return type:

tuple

Notes

These magnitude elements are fundamental components in the Fresnel equations:

  • \(n_1 \cos \theta_i\): Incident medium magnitude

  • \(n_1 \cos \theta_t\): Incident medium magnitude (transmitted angle)

  • \(n_2 \cos \theta_i\): Transmitted medium magnitude (incident angle)

  • \(n_2 \cos \theta_t\): Transmitted medium magnitude

These terms appear in all Fresnel amplitude and power coefficients for both reflection and transmission at dielectric interfaces.

Examples

>>> polarised_light_magnitude_elements(1.0, 1.5, 0.0, 0.0)
((1+0j), (1+0j), (1.5+0j), (1.5+0j))