Fresnel reflection calculator

Refractive Index 1 ($n_1$)

Index

Refractive Index 2 ($n_2$)

Index

Angle of Incidence ($\theta_i$)

deg (°)

Polarization	Reflectance (R)	Transmittance (T)
S-Pol (Perpendicular)	---%	---%
P-Pol (Parallel)	---%	---%
Average (Unpolarized)	---%	---%

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 ≈ 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.

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). Engineers use Index Matching Gel to eliminate the index difference (Δn ≈ 0).

3. High-Power Laser Safety

In multi-kilowatt laser cutting systems, a 4% back-reflection represents hundreds of watts traveling backward. This "back-reflection" can burn out the laser diode. Accurate calculation helps engineers design optical isolators to manage this 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 Brewster's Angle, used in gas lasers for 100% transmission efficiency.

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, 100% of the light is reflected back inside. This principle of Total Internal Reflection is exactly what traps light inside optical fibers.

Deep Dive Article Fresnel Reflection: The Physics of Light at Interfaces Understand the derivations, the S-Pol vs P-Pol distinction, and how to minimize losses in your optical system.

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Related Engineering Tools

Snell's Law Calculator

Calculate the angle of refraction used in the Fresnel equations.

Brewster's Angle

Find the exact angle where P-polarization reflection drops to zero.

dB ↔ Percentage

Convert the Fresnel reflection percentage (e.g., 4%) into Decibel loss.