What Is Fresnel Reflection?

Fresnel reflection is the partial reflection of electromagnetic waves that occurs at an interface between two media with different refractive indices. Named after French physicist Augustin-Jean Fresnel, who derived the governing equations in the early nineteenth century, the phenomenon arises from the boundary conditions that the electric and magnetic fields must satisfy when crossing from one medium to another. The Fresnel equations quantify both the fraction of incident energy that reflects and the fraction that transmits, and they are foundational to optics, photonics, and electromagnetic wave theory.

The behavior at an interface depends on two properties: the ratio of the refractive indices of the two media and the polarization state of the incident wave. Because these two variables interact, Fresnel reflection cannot be reduced to a single coefficient but requires treating two orthogonal polarization components separately.

S- and P-Polarization

The incident wave is decomposed into two polarization components defined relative to the plane of incidence, the plane containing the incident ray and the surface normal. The s-polarization component (from the German senkrecht, meaning perpendicular) has its electric field oriented perpendicular to the plane of incidence; the p-polarization component has its electric field lying within that plane. The Fresnel equations give a distinct reflection coefficient for each component, and the two coefficients diverge significantly as the angle of incidence increases. For a glass-air interface near normal incidence, each polarization component reflects roughly 4% of the incident power, but that figure changes substantially with angle.

Brewster's Angle and Polarization Effects

At a specific angle of incidence known as Brewster's angle, the reflection coefficient for p-polarized light falls to zero. The angle satisfies the relation tan(θ_B) = n₂/n₁, where n₁ and n₂ are the refractive indices of the incident and transmitted media, respectively. At Brewster's angle, the reflected and refracted rays are perpendicular to each other, and only the s-polarized component reflects. Unpolarized light incident at Brewster's angle therefore produces a reflected beam that is completely s-polarized. This polarization selectivity is exploited in optical systems that require polarized output without the insertion loss of a traditional polarizer.

Total Internal Reflection

When light travels from a medium of higher refractive index into one of lower refractive index, a critical angle θ_c exists, defined by sin(θ_c) = n₂/n₁. For angles of incidence exceeding the critical angle, the refracted wave becomes evanescent: it decays exponentially in the direction normal to the interface and transports energy parallel to the surface rather than into the second medium. Under this condition, called total internal reflection, the reflectance reaches unity. The evanescent field does extend a short distance into the second medium, a property exploited in fiber optic waveguides and in prism-coupling and frustrated-total-internal-reflection devices.

Applications

Fresnel reflection has applications in a range of fields, including:

• Optical fiber design, where total internal reflection confines guided light within the core
• Anti-reflection coatings for lenses, camera optics, and solar cells, which use thin-film interference to cancel the reflected component
• Ellipsometry and optical metrology for measuring thin-film thickness and refractive index
• Laser cavity design, where Brewster-angle windows eliminate polarization-dependent reflection losses
• Remote sensing and radar, where Fresnel coefficients model reflection from terrain, sea surfaces, and atmospheric layers
• Optical coherence tomography and interferometric sensors, which rely on precise control of partial reflectance at interfaces