Advanced Optical Reflectivity Calculator

Incident Medium

Real Refractive Index ($n_1$)

Example: 1.000 (Air)

Extinction Coefficient ($k_1$)

Example: 0.000 (Transparent medium)

Quick Presets

Substrate Medium

Real Refractive Index ($n_2$)

Example: 1.500 (Standard Glass)

Extinction Coefficient ($k_2$)

Example: 0.000 or metal absorption value

Quick Presets

Wave & Geometry

Angle of Incidence (Degrees)

0° for normal incidence

Polarization State

Wavelength ($\lambda$ in nm)

Reference wavelength (e.g. 589.3 nm)

Formula Used

This calculator implements the generalized Fresnel Equations for electromagnetic wave reflection at a planar interface between two media with complex refractive indices $\tilde{n}_1 = n_1 + i k_1$ and $\tilde{n}_2 = n_2 + i k_2$.

For s-polarized light (electric field perpendicular to the plane of incidence):

$$r_s = \frac{\tilde{n}_1 \cos(\theta_1) - \tilde{n}_2 \cos(\theta_2)}{\tilde{n}_1 \cos(\theta_1) + \tilde{n}_2 \cos(\theta_2)}, \quad R_s = |r_s|^2$$

For p-polarized light (electric field parallel to the plane of incidence):

$$r_p = \frac{\tilde{n}_2 \cos(\theta_1) - \tilde{n}_1 \cos(\theta_2)}{\tilde{n}_2 \cos(\theta_1) + \tilde{n}_1 \cos(\theta_2)}, \quad R_p = |r_p|^2$$

The transmission angle $\theta_2$ is determined via complex Snell's Law, and unpolarized reflectance is evaluated as the arithmetic mean of $R_s$ and $R_p$.

How to Use This Calculator

Enter the real refractive index ($n_1$) and extinction coefficient ($k_1$) of your incident medium (default is air at 1.00).
Input the parameters for the substrate or transmission medium ($n_2$ and $k_2$). You can also choose quick preset materials.
Specify your angle of incidence in degrees, desired polarization state, and operational wavelength.
Click the Calculate Reflectivity button to instantly view rigorous reflectivity percentages, phase shifts, and transmission estimates.

Understanding Optical Reflectivity and Refractive Index

Optical reflectivity is a fundamental property in photonics, optics, and material science. It defines the fraction of incident electromagnetic radiation reflected from a boundary between different optical media. Understanding this phenomenon is essential for designing anti-reflective coatings, laser cavities, optical sensors, and precision lenses.

The Role of Complex Refractive Indices

While transparent materials like glass or water are easily modeled using purely real refractive indices, absorbing materials such as metals and semiconductors require complex indices. The imaginary component, known as the extinction coefficient ($k$), accounts for internal attenuation and absorption, directly modifying boundary reflection amplitudes.

Frequently Asked Questions

Normal incidence occurs when light strikes the interface perpendicularly ($\theta = 0^\circ$). At this angle, s-polarization and p-polarization yield identical reflection values.

At non-zero angles, s-polarized light reflects more strongly than p-polarized light. At Brewster's angle, p-polarization reflectivity drops to zero for transparent dielectrics.