Library / Foundations: Physics / FPH-33
Foundations: Physics
Refraction (Snell’s law)
Angle of the refracted ray when light crosses a boundary.
- Ref
- FPH-33
- Rev
- v1
- Field
- Foundations: Physics
- Result
- θ₂ [°]
Angles are measured from the normal. n₁ and n₂ are the refractive indices of the two media.
Light bends towards the normal when it enters a denser (higher-index) medium.
Calculator
- Deviation θ₁ − θ₂14.63 °
- Speed in medium 21.999 10⁸ m/s
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- Going into a denser medium bends light towards the normal; leaving it bends light away.
- Beyond the critical angle there is no refracted ray at all.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (°) | Local step | Change in result |
|---|---|---|---|---|---|---|
| θ₁ Incident angle | 5 to 80 ° | 3.331 | 41.04 | 37.71 | +10% | +2.21 ° |
| n₁ Index of medium 1 | 1 to 2 | 25.37 | 58.99 | 33.61 | +undefined% | — |
| n₂ Index of medium 2 | 1 to 2.5 | 14.9 | 40 | 25.1 | +undefined% | — |
Sweep of Incident angle
| Incident angle (°) | Refracted angle (°) |
|---|---|
| 5 | 3.331 |
| 14.38 | 9.527 |
| 23.75 | 15.57 |
| 33.13 | 21.37 |
| 42.5 | 26.77 |
| 51.88 | 31.63 |
| 61.25 | 35.77 |
| 70.63 | 38.97 |
| 80 | 41.04 |
Sweep one variable
Variables and how each one contributes
Refracted angle
What the equation gives you. Everything else feeds it.
Index of medium 1
Refractive index where the ray starts. A higher n₁ bends the ray further from the normal.
Index of medium 2
Refractive index where the ray goes. A higher n₂ bends the ray towards the normal.
Incident angle
Angle to the normal in medium 1. Raises the refracted angle.
Worked example with the values above
- sin θ₂ = n₁ sin θ₁ / n₂ = 1 × 0.6428 / 1.5 = 0.4285.
- Take the inverse sine.
- θ₂ = 25.37 °.
Assumptions and limits
- Smooth boundary between uniform media.
- Angles measured from the normal.
Common mistakes
- Measuring angles from the surface instead of the normal.
- Swapping n₁ and n₂.
Statistics and uncertainty
Refractive indices vary with wavelength by about 1% across the visible range, which causes colour dispersion.
Where it is used
- Lens and window design.
- Optical fibres and sensors.
Maths you need
- Sine: angle ratio
- Normal line: perpendicular to the boundary