Calculator Form
Example Data Table
| Case | Angle (deg) | n1 | n2 | Rs | Rp | Average | Note |
|---|---|---|---|---|---|---|---|
| Air to glass | 30 | 1.000 | 1.500 | 0.058 | 0.025 | 0.041 | Ordinary partial reflection |
| Air to glass | 56.31 | 1.000 | 1.500 | 0.148 | 0.000 | 0.074 | Near Brewster angle |
| Glass to air | 50 | 1.500 | 1.000 | 1.000 | 1.000 | 1.000 | Total internal reflection |
Formula Used
Law of reflection: θr = θi
Snell's law: n1 sin(θi) = n2 sin(θt)
s-polarized reflectance: Rs = [ (n1 cos θi − n2 cos θt) / (n1 cos θi + n2 cos θt) ]²
p-polarized reflectance: Rp = [ (n1 cos θt − n2 cos θi) / (n1 cos θt + n2 cos θi) ]²
Unpolarized reflectance: R = (Rs + Rp) / 2
Brewster angle: θB = arctan(n2 / n1)
Critical angle: θc = arcsin(n2 / n1), only when n1 > n2
If sin(θt) exceeds 1, total internal reflection occurs.
How to Use This Calculator
- Enter the angle of incidence in degrees.
- Enter the refractive index for the first medium.
- Enter the refractive index for the second medium.
- Choose s, p, or unpolarized output mode.
- Select the number of decimal places.
- Choose whether the selected reflectance should show percentage.
- Click the calculate button.
- Read the result panel shown above the form.
- Use the export buttons to save CSV or PDF output.
Optical Reflection Basics and Practical Meaning
What this calculator measures
Optical reflection happens when light reaches a boundary. A portion returns to the first medium. Another portion may pass through the surface. This calculator estimates both the reflection geometry and the Fresnel reflectance values. It also checks for total internal reflection.
Why angle and refractive index matter
The angle of incidence controls how strongly light interacts with the surface. Refractive indices describe how light travels inside each material. A small index difference often causes modest reflection. A larger difference usually increases reflected power. These inputs shape Rs, Rp, Brewster angle, and critical angle.
How polarization changes the answer
Optical reflection depends on polarization. s-polarized light reflects differently from p-polarized light. At Brewster angle, p-polarized reflectance ideally reaches zero for transparent dielectric surfaces. That makes polarization important in lens design, glare control, coatings, sensors, and optical testing.
Why total internal reflection is important
Total internal reflection occurs when light moves from a denser medium to a less dense medium beyond the critical angle. In that case, all incident power reflects. This effect supports fiber optics, prisms, waveguides, and many precision instruments. It also changes the transmitted angle result.
Where this tool is useful
This optical reflection calculator is useful for physics study, lab preparation, lens analysis, coating checks, photonics planning, and engineering estimation. It gives a quick view of reflection angle, transmission angle, and reflectance behavior. The export features also help document repeated test cases and share results with others.
Frequently Asked Questions
1. What does this calculator mainly compute?
It computes reflection angle, transmission angle, s and p reflectance, average reflectance, Brewster angle, critical angle, and total internal reflection status.
2. Why is the reflection angle equal to incidence angle?
That comes from the law of reflection. For a flat boundary, the reflected ray leaves at the same angle it arrived, measured from the normal.
3. What is the difference between s and p polarization?
s polarization is perpendicular to the plane of incidence. p polarization is parallel to that plane. Their reflectance values differ at most nonzero angles.
4. When does total internal reflection happen?
It happens when light travels from higher refractive index to lower refractive index and the incidence angle exceeds the critical angle.
5. What is Brewster angle used for?
Brewster angle helps identify where p-polarized reflected light becomes minimal. It is useful in anti-glare systems, optical alignment, and polarization control.
6. Can I use this for metals?
This version is best for transparent, non-absorbing dielectric interfaces. Metals require complex refractive indices and a different treatment of absorption.
7. Why might the transmission angle show not available?
That appears during total internal reflection. No real transmitted propagation angle exists because the wave does not pass as an ordinary refracted ray.
8. What units should I enter?
Enter angles in degrees. Refractive index is unitless. Reflectance outputs are also unitless, with an optional percentage display for convenience.