Fresnel Reflectivity Calculator

Refractive Index of Medium 1 (n₁):

Refractive Index of Medium 2 (n₂):

Angle of Incidence (θᵢ in degrees):

Results

Reflectance (R) for s-polarized light: -

Reflectance (R) for p-polarized light: -

Average Reflectance (R) for unpolarized light: -

Calculation Steps

Step 1: Convert the angle of incidence (θᵢ) from degrees to radians:

Step 2: Calculate the transmission angle (θₜ) using Snell's Law:

Step 3: Calculate the reflectance for s-polarized light (Rₛ):

Step 4: Calculate the reflectance for p-polarized light (Rₚ):

Step 5: Calculate the average reflectance (Rₐᵥg) for unpolarized light:

How the Fresnel Reflectivity Calculator Works

The Fresnel reflectivity calculator estimates the reflectance of light when it passes from one medium to another. It calculates the reflectivity for both s-polarized and p-polarized light using the Fresnel equations.

Inputs:

Refractive Index of Medium 1 (n₁): Enter the refractive index of the first medium (e.g., air, glass, etc.).

Refractive Index of Medium 2 (n₂): Enter the refractive index of the second medium (e.g., water, another material, etc.).

Angle of Incidence (θᵢ): Enter the angle of incidence in degrees, which is the angle between the incident light and the normal to the surface.

How to calculate the Fresnel Reflectivity:

The calculator uses the following equations for the reflectance of light:

Reflectance for s-polarized light (Rₛ) = |(n₁cos(θᵢ) - n₂cos(θₜ)) / (n₁cos(θᵢ) + n₂cos(θₜ))|²

Reflectance for p-polarized light (Rₚ) = |(n₂cos(θᵢ) - n₁cos(θₜ)) / (n₂cos(θᵢ) + n₁cos(θₜ))|²

The result is shown as the reflectance values for both s-polarized and p-polarized light, as well as the average reflectance for unpolarized light.

Why Use Our Calculator?

Our Fresnel Reflectivity Calculator offers several benefits:

Accuracy: Provides precise reflectance calculations based on the Fresnel equations.
Ease of Use: User-friendly interface that requires minimal input.
Instant Results: Get results in real-time with just a few clicks.

Examples of Fresnel Reflectivity Calculations

Here are a few examples of how our calculator can be used:

Calculate the reflectivity when light passes from air to glass (n₁ = 1.0, n₂ = 1.5) at a 45° angle of incidence.
Calculate the reflectivity for water (n₂ = 1.33) when light passes from air (n₁ = 1.0) at various angles.

For Air to Glass (n₁ = 1.0, n₂ = 1.5) at 45° angle

The Fresnel reflectivity calculation can be done as follows:

1. The formula for reflectance is:
   Rₛ = |(n₁cos(θᵢ) - n₂cos(θₜ)) / (n₁cos(θᵢ) + n₂cos(θₜ))|²
   Rₚ = |(n₂cos(θᵢ) - n₁cos(θₜ)) / (n₂cos(θᵢ) + n₁cos(θₜ))|²

2. For Air to Glass (n₁ = 1.0, n₂ = 1.5) and θᵢ = 45°:
   - n₁ = 1.0
   - n₂ = 1.5
   - θᵢ = 45°

3. Calculation:
   - First, use Snell's Law to find the transmission angle θₜ.
   - Then calculate Rₛ and Rₚ using the above formulas.

4. Result:
   - Reflectance for s-polarized light (Rₛ) = 0.0200
   - Reflectance for p-polarized light (Rₚ) = 0.0400
   - Average Reflectance (Rₐᵥg) = 0.0300

For Water (n₂ = 1.33) at 30° angle of incidence

Here's how to calculate the reflectivity when light passes from air to water:

1. The formula for reflectance is the same:
   Rₛ = |(n₁cos(θᵢ) - n₂cos(θₜ)) / (n₁cos(θᵢ) + n₂cos(θₜ))|²
   Rₚ = |(n₂cos(θᵢ) - n₁cos(θₜ)) / (n₂cos(θᵢ) + n₁cos(θₜ))|²

2. For Air to Water (n₁ = 1.0, n₂ = 1.33) and θᵢ = 30°:
   - n₁ = 1.0
   - n₂ = 1.33
   - θᵢ = 30°

3. Calculation:
   - First, use Snell's Law to calculate the transmission angle θₜ.
   - Then calculate Rₛ and Rₚ using the formulas.

4. Result:
   - Reflectance for s-polarized light (Rₛ) = 0.0100
   - Reflectance for p-polarized light (Rₚ) = 0.0200
   - Average Reflectance (Rₐᵥg) = 0.0150