There is a set of equations exactly describing what you are asking for: they are called the Fresnel equations.

Scattering is, however, not covered as it would depend on the roughness of the surface. So there can't be a generic formula for the scattering without quantifying the roughness (it also would be very dependent on the wavelength). The Fresnel equations assume a smooth surface (i.e. roughness much smaller than wavelength).

Absorption doesn't matter, as it doesn't happen at the surface but requires a non-zero length of medium to be passed.

The Fresnel equations give coefficients of reflectance (i.e. ratio of reflected power to incident power) for EM radiation that is either polarized in the plane of incidence (p-polarized) or polarized perpendicular to the plane of incidence (s-polarized).

\$R_s = \lvert\frac{Z_2\cos\theta_i - Z_1\cos\theta_i}{Z_2\cos\theta_i + Z_1\cos\theta_i}\rvert^2\$

\$R_p = \lvert\frac{Z_2\cos\theta_t - Z_1\cos\theta_i}{Z_2\cos\theta_t + Z_1\cos\theta_i}\rvert^2\$

where
\$\theta_i =\$angle of incidence
\$\theta_t =\$angle of transmission

\$Z_k=\frac{\mu_k}{\epsilon_k}\$ and \$k\$ is an index 1 or 2 for the medium.

There are other versions of the formulars. E.g. under the assumption that \$\mu_1= \mu_2 = \mu_0\$ (permeability of vacuum) they can be rewritten as expressions of indices of refraction of both media.

(Note: since there are no non-linear effects involved you can compose any polarization into a linear combination of p- and s- polarized components).

There is a set of equations exactly describing what you are asking for: they are called the Fresnel equations.

Reflection and transmission are covered by the Fresnel equations.

Scattering is, however, not covered as it would depend on the roughness of the surface. So there can't be a generic formula for the scattering without quantifying the roughness (it also would be very dependent on the wavelength). The Fresnel equations assume a smooth surface (i.e. roughness much smaller than wavelength).

Absorption doesn't matter, as it doesn't happen at the surface but requires a non-zero length of medium to be passed.

The Fresnel equations give coefficients of reflectance \$R\$ (i.e. ratio of reflected power to incident power) for EM radiation that is either polarized in the plane of incidence (p-polarized) or polarized perpendicular to the plane of incidence (s-polarized).

\$R_s = \lvert\frac{Z_2\cos\theta_i - Z_1\cos\theta_i}{Z_2\cos\theta_i + Z_1\cos\theta_i}\rvert^2\$

\$R_p = \lvert\frac{Z_2\cos\theta_t - Z_1\cos\theta_i}{Z_2\cos\theta_t + Z_1\cos\theta_i}\rvert^2\$

where
\$\theta_i =\$angle of incidence
\$\theta_t =\$angle of transmission

\$Z_k=\frac{\mu_k}{\epsilon_k}\$ and \$k\$ is an index 1 or 2 for the medium.

There are other versions of the formulars. E.g. under the assumption that \$\mu_1= \mu_2 = \mu_0\$ (permeability of vacuum) they can be rewritten as expressions of indices of refraction of both media.

(Note: since there are no non-linear effects involved you can compose any polarization into a linear combination of p- and s- polarized components).

There is a set of equations exactly describing what you are asking for: they are called the Fresnel equations.

Scattering is, however, not covered as it would depend on the roughness of the surface. So there can't be a generic formula for the scattering without quantifying the roughness (it also would be very dependent on the wavelength). The Fresnel equations assume a smooth surface (i.e. roughness much smaller than wavelength).

Absorption doesn't matter, as it doesn't happen at the surface but requires a non-zero length of medium to be passed.

The Fresnel equations give coefficients of reflectance (i.e. ratio of reflected power to incident power) for EM radiation that is either polarized in the plane of incidence (p-polarized) or polarized perpendicular to the plane of incidence (s-polarized).

\$R_s = \lvert\frac{Z_2\cos\theta_i - Z_1\cos\theta_i}{Z_2\cos\theta_i + Z_1\cos\theta_i}\rvert^2\$

\$R_p = \lvert\frac{Z_2\cos\theta_t - Z_1\cos\theta_i}{Z_2\cos\theta_t + Z_1\cos\theta_i}\rvert^2\$

where
\$\theta_i =\$angle of incidence
\$\theta_t =\$angle of transmission

\$Z_k=\frac{\mu_k}{\epsilon_k}\$ and \$k\$ is an index 1 or 2 for the medium.

There are other versions of the formulars. E.g. under the assumption that \$\mu_1= \mu_2 = \mu_0\$ (permeability of vacuum) they can be rewritten as expressions of indices of refraction of both media.

(Note: since there are no non-linear effect involved you can compose any polarization into a linear combination of p- and s- polarized components).

There is a set of equations exactly describing what you are asking for: they are called the Fresnel equations.

Scattering is, however, not covered as it would depend on the roughness of the surface. So there can't be a generic formula for the scattering without quantifying the roughness (it also would be very dependent on the wavelength). The Fresnel equations assume a smooth surface (i.e. roughness much smaller than wavelength).

Absorption doesn't matter, as it doesn't happen at the surface but requires a non-zero length of medium to be passed.

The Fresnel equations give coefficients of reflectance (i.e. ratio of reflected power to incident power) for EM radiation that is either polarized in the plane of incidence (p-polarized) or polarized perpendicular to the plane of incidence (s-polarized).

\$R_s = \lvert\frac{Z_2\cos\theta_i - Z_1\cos\theta_i}{Z_2\cos\theta_i + Z_1\cos\theta_i}\rvert^2\$

\$R_p = \lvert\frac{Z_2\cos\theta_t - Z_1\cos\theta_i}{Z_2\cos\theta_t + Z_1\cos\theta_i}\rvert^2\$

where
\$\theta_i =\$angle of incidence
\$\theta_t =\$angle of transmission

\$Z_k=\frac{\mu_k}{\epsilon_k}\$ and \$k\$ is an index 1 or 2 for the medium.

There are other versions of the formulars. E.g. under the assumption that \$\mu_1= \mu_2 = \mu_0\$ (permeability of vacuum) they can be rewritten as expressions of indices of refraction of both media.

(Note: since there are no non-linear effects involved you can compose any polarization into a linear combination of p- and s- polarized components).