How to Use This Calculator
- Enter the refractive indices (n₁ and n₂) of the two media. These values can typically be found in material reference tables.
- Input the angle of incidence (θᵢ) in degrees. This is the angle between the incident ray and the normal to the interface.
- Click the "Calculate" button to compute the inner reflection coefficient and other results.
- Use the "Reset" button to clear all inputs and start over.
Understanding the Results
- Inner Reflection Coefficient (γ): This value represents the fraction of light reflected at the interface. A value of 1 means all light is reflected, while 0 means none is reflected.
- Angle of Reflection (θᵣ): For reflection at an interface, the angle of reflection equals the angle of incidence.
- Total Internal Reflection (TIR) Condition: When light travels from a medium with higher refractive index to one with lower refractive index, TIR occurs if the angle of incidence exceeds the critical angle. The calculator indicates if TIR occurs for your input values.
Principle Behind the Calculation
The inner reflection coefficient is calculated using the Fresnel equation, which depends on the refractive indices of the two media and the angle of incidence. For simplicity, this calculator uses a formula based on Snell's Law and the Fresnel equations for normal incidence:
γ = (n₁cosθᵢ - n₂cosθᵣ)/(n₁cosθᵢ + n₂cosθᵣ)
Where θᵣ (angle of reflection) is calculated using Snell's Law: n₁sin(θᵢ) = n₂sin(θᵣ).
Applications
This calculator is useful in various fields including:
- Optical engineering for designing optical systems and coatings
- Physics for studying light-matter interactions
- Material science for analyzing material properties
- Telecommunications for fiber optic design