Calculator Inputs
Example Data Table
| Medium 1 | n₁ | Medium 2 | n₂ | Critical Angle | TIR Possible |
|---|---|---|---|---|---|
| Water | 1.33300 | Air | 1.00029 | 48.61° | Yes |
| Crown Glass | 1.52000 | Air | 1.00029 | 41.15° | Yes |
| Acrylic | 1.49000 | Water | 1.33300 | 63.45° | Yes |
| Diamond | 2.41700 | Air | 1.00029 | 24.43° | Yes |
| Air | 1.00029 | Water | 1.33300 | Not defined | No |
| Ice | 1.30900 | Ethanol | 1.36100 | Not defined | No |
Formula Used
1. Critical angle
θc = sin-1(n₂ / n₁)
This works only when n₁ is greater than n₂.
2. Snell's law
n₁ sin(θi) = n₂ sin(θt)
Used to find the refracted angle when a transmitted ray exists.
3. Total internal reflection condition
TIR occurs when n₁ > n₂ and θi > θc
At this point, no propagating refracted ray appears in medium 2.
4. Fresnel reflectance
Rs = ((n₁cosθi - n₂cosθt) / (n₁cosθi + n₂cosθt))²
Rp = ((n₁cosθt - n₂cosθi) / (n₁cosθt + n₂cosθi))²
Average reflectance is taken as (Rs + Rp) / 2.
5. Evanescent penetration depth
d = λ / (2πn₁√(sin²θi - (n₂/n₁)²))
This depth exists only under total internal reflection.
How to Use This Calculator
- Select preset materials or type custom refractive indices.
- Enter the incident angle in degrees.
- Enter the wavelength if you want penetration depth during TIR.
- Press Calculate to show the result card above the form.
- Review the graph, compare reflectance trends, and export the result as CSV or PDF.
FAQs
1. What is total internal reflection?
It is complete reflection at a boundary when light moves from a denser medium to a rarer medium and the incident angle exceeds the critical angle.
2. Why does the calculator need two refractive indices?
The two indices define the optical boundary. Their ratio determines whether a critical angle exists and how strongly the ray bends or reflects.
3. When is total internal reflection impossible?
It is impossible when light travels into an equal or higher refractive index medium. In that case, a critical angle is not defined.
4. What happens exactly at the critical angle?
The refracted ray travels along the boundary, which corresponds to a transmitted angle of 90 degrees. Any larger incident angle creates total internal reflection.
5. Why include wavelength in the calculator?
Wavelength helps estimate evanescent penetration depth during total internal reflection. That is useful in fiber optics, sensing, and near-surface field analysis.
6. Does the reflected angle always equal the incident angle?
Yes. Reflection follows the law of reflection, so the reflected angle equals the incident angle when both are measured from the normal.
7. What do s and p reflectance values mean?
They represent reflectance for two polarization directions. s is perpendicular to the plane of incidence, while p is parallel to it.
8. Where is this concept used in practice?
It is used in optical fibers, prisms, endoscopes, spectroscopy, waveguides, and sensors that depend on strong boundary reflection.