Fresnel reflection calculator

Index
Index
deg (°)

How it works?

The Fresnel reflection calculator computes the reflectivity and transmissivity at an optical interface. This behavior is governed by **Fresnel's Equations** and depends on Refractive Indices (\( n_1, n_2 \)), Angle of Incidence, and Polarization.

Fresnel Equations

S-Polarization (Perpendicular) $$ R_s = \left( \frac{n_1 \cos \theta_i - n_2 \cos \theta_t}{n_1 \cos \theta_i + n_2 \cos \theta_t} \right)^2 $$
P-Polarization (Parallel) $$ R_p = \left( \frac{n_1 \cos \theta_t - n_2 \cos \theta_i}{n_1 \cos \theta_t + n_2 \cos \theta_i} \right)^2 $$
Unpolarized (Average) & Transmissivity $$ R_{avg} = \frac{R_s + R_p}{2} \quad , \quad T = 1 - R $$

Variable Definitions:

\(R\) : Reflectivity
\(T\) : Transmissivity
\(\theta_i\) : Angle of Incidence
\(\theta_t\) : Refracted Angle (Snell's Law)

Why calculate Fresnel Reflection?

Impact on Systems
  • Power Loss: Up to 4% is lost at every single glass/air surface.
  • Ghost Images: Reflections cause flare and artifacts in imaging systems.
  • Safety: High-power back-reflections can damage laser sources.
  • AR Coatings: Calculation is essential for designing Anti-Reflective layers.

The "Optical Tax" at Interfaces

Whenever light travels from one medium to another (e.g., from air into a glass lens), a portion of that light bounces back. This phenomenon is known as Fresnel Reflection. While it is the reason we can see our reflection in a window, in optical engineering, it is often a significant problem.

For standard glass (\(n \approx 1.5\)) in air, the reflection loss is about 4% per surface at normal incidence. In a complex microscope or camera lens with 10 elements (20 surfaces), this could theoretically result in a loss of over 50% of the light if left untreated. Understanding and calculating these values allows engineers to maximize transmission efficiency.

Critical Engineering Applications

1. Anti-Reflective (AR) Coatings

The primary use of the Fresnel equations is in the design of thin-film coatings. By calculating the exact reflection based on refractive index, engineers can apply a dielectric layer with a precise thickness to create destructive interference.

This reduces the reflection from ~4% down to < 0.5%, significantly improving the throughput of laser systems and the contrast of imaging optics.

2. Fiber Optic Coupling

In telecom, the small gap between two fiber connectors acts as a Fresnel interface. This creates "Fresnel Loss" (typically -0.17 dB) and dangerous back-reflections (Return Loss).

To solve this, engineers use "Index Matching Gel" to eliminate the refractive index difference (\(\Delta n \approx 0\)), or use APC (Angled Physical Contact) connectors to deflect the reflection out of the core mode.

3. High-Power Laser Safety

In multi-kilowatt laser cutting systems, a 4% back-reflection from the workpiece or focus lens represents hundreds of watts of power traveling backward.

This "back-reflection" can burn out the laser diode or fiber delivery system. Accurate calculation helps engineers design optical isolators and tilt windows to safely manage this rejected energy.

4. Brewster Windows

By using this calculator, you will notice that at a specific angle (approx 56° for glass), the reflection for P-polarized light drops to exactly zero.

This is known as Brewster's Angle. It is widely used in gas lasers and polarized optical setups to allow light to exit the laser cavity with 100% transmission efficiency, effectively acting as a perfect window without needing coatings.

Total Internal Reflection (TIR)

When light travels from a high-index medium (like glass) to a low-index medium (like air), there is a critical angle where refraction stops completely.

Beyond this angle, the Fresnel equations break down, and 100% of the light is reflected back inside. This principle of Total Internal Reflection is exactly what traps light inside optical fibers, allowing the internet to function over global distances.