Fresnel’s equations describe the reflection and transmission of light at the boundary between two transparent media by calculating how much of the light is reflected back and how much is transmitted (refracted) into the second medium. These equations take into account the angle of incidence, the refractive indices of both media, and the polarization of the incoming light.
Here’s how they work:
- Reflection Coefficients:
Fresnel’s equations give separate reflection coefficients for:- s-polarized light (electric field perpendicular to the plane of incidence)
- p-polarized light (electric field parallel to the plane of incidence)
- Transmission Coefficients:
Similarly, transmission coefficients describe how much of the light’s electric field passes into the second medium. These also vary based on polarization and angle of incidence. - Angle Dependence:
The equations show that reflection and transmission change with the angle of incidence. At normal incidence, reflection is usually small if the refractive index difference is not large. As the angle increases:- Reflection increases for both polarizations.
- For p-polarized light, reflection becomes zero at the Brewster angle.
- At angles beyond the critical angle (when going from denser to rarer medium), transmission drops to zero, and total internal reflection occurs.
- Energy Conservation:
The reflected and transmitted intensities together always add up to the incident intensity (assuming no absorption), consistent with the conservation of energy.
Through this framework, Fresnel’s equations explain how light splits into reflected and transmitted parts and how the behavior depends on material properties and wave polarization.