Tip: Use refractive indices like air ≈ 1.0003, water ≈ 1.33, glass ≈ 1.50.
Angles are measured from the normal to the surface.
Example data
| # | Medium 1 (n₁) | Medium 2 (n₂) | Incident θ₁ | Expected θ₂ | Notes |
|---|---|---|---|---|---|
| 1 | 1.0003 | 1.33 | 45° | ≈ 32.13° | Air to water, bends toward normal. |
| 2 | 1.50 | 1.0003 | 30° | ≈ 48.58° | Glass to air, bends away from normal. |
| 3 | 1.33 | 1.0003 | 60° | Not real | Total internal reflection possible. |
Examples are approximate and depend on rounding.
Formula used
Snell’s law relates angles and refractive indices at a boundary:
n₁ sin(θ₁) = n₂ sin(θ₂)
- θ₂ = asin((n₁/n₂)·sin(θ₁))
- θ₁ = asin((n₂/n₁)·sin(θ₂))
- n₂ = n₁·sin(θ₁)/sin(θ₂)
- θc = asin(n₂/n₁) when n₁ > n₂
How to use this calculator
- Select a mode, such as computing θ₂.
- Enter the known angles and refractive indices.
- Choose degrees or radians for your output.
- Click Calculate to see results above the form.
- Use the download buttons to save CSV or PDF.
If the tool reports TIR, refraction does not occur.
FAQs
1) What is the refraction angle?
The refraction angle θ₂ is the angle the transmitted ray makes with the normal after crossing a boundary between two media.
2) What causes total internal reflection?
Total internal reflection happens when light goes from higher index to lower index, and the incident angle exceeds the critical angle. Then no real θ₂ exists.
3) Do angles use the surface or the normal?
Snell’s law uses angles measured from the normal, not from the surface. Measuring from the surface will give incorrect results.
4) Can refractive index be less than one?
In many common materials, n is near or above 1. In special situations it can be below 1, but this tool assumes positive values and standard optics.
5) Why is θ₂ sometimes larger than θ₁?
When light enters a lower refractive index medium, it bends away from the normal, increasing θ₂ relative to θ₁. The opposite happens when entering a higher index.
6) What does “critical angle” mean?
The critical angle θc is the incident angle in the higher-index medium that yields θ₂ = 90° in the lower-index medium. Larger θ₁ leads to TIR.
7) How accurate are the results?
Accuracy depends on input values and rounding. Use more decimals for intermediate work, and confirm with measured indices at your wavelength if needed.
8) Why offer CSV and PDF downloads?
CSV is great for spreadsheets and lab logs. PDF is helpful for sharing a fixed report. Both exports use your current inputs and computed outputs.