Free · Optics
Snell Refraction Angle and Index Calculator
Solve a transmitted ray angle or custom refractive index using Snell’s law, with critical-angle explanations and static material presets.
- Formula & worked example
- Private in your browser
- No signup
Calculator inputs
Loading calculator…
How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
For vacuum index 1, diamond index 2.419 and incidence 30°, the transmitted angle is about 11.9289°.
n₁ sin θ₁ = n₂ sin θ₂; θc = asin(nlower / nhigher). Both angles are measured from the surface normal.
Worked example
Enter these known values and leave the other values blank.
- Medium 1
- Vacuum
- Medium 2
- Diamond 💎
- Angle of incidence (θ₁)
- 30 deg
- Refractive index 1 (n₁)
- 1
- Refractive index 2 (n₂)
- 2.419
- Angle of refraction (θ₂)
- 11.92886 deg
Assumptions and limitations
- This is a planar interface between uniform, isotropic, transparent media described by positive real phase indices at the same vacuum wavelength. It does not model absorption, anisotropy, dispersion, coatings or Fresnel intensities.
- Preset values are static illustrative references, rather than a temperature or wavelength model. Air uses 1.000293 at 0 °C and 1 atm; fresh water uses 1.333 and diamond 2.419 at about 20 °C and 589 nm. Ethanol 1.36 and ice 1.31 preserve the captured rounding of published values 1.361 and 1.309. The ice reference is at 0 °C.
- Acrylic 1.49 represents a manufacturer PMMA grade at 589 nm and 23 °C. Window glass 1.52 rounds a float-glass sodium-D value of 1.523; temperature is not specified for that index row. Material grades and wavelength change actual indices. Use custom measured values for the conditions that apply to your calculation.
- Select custom for an index you want to enter or solve. Preset indices are read-only. Clear a known value before using an inverse; zero-angle data alone cannot determine an unknown index.
- A critical-angle equality is a grazing 90° boundary solution. Total internal reflection applies above the critical incidence angle from higher to lower index, rather than at equality.
- A phase index below one is not a claim of information travelling faster than light. The retained positive custom-index input is mathematical; verify that this simplified ray model applies to the actual medium.
- The interface illustration is a fixed schematic showing bending toward the normal when the second index exceeds the first; it does not plot your calculated ray. Refractive-index measurements and static presets have limited precision. Results extremely close to a critical boundary are sensitive to that precision.
Common questions
How do I find refractive index instead of angle?
Choose custom in the corresponding medium selector, clear that index, and enter the other index plus a compatible nonzero angle pair. Locks retain known observations.
Why is the transmitted angle blank?
A high-to-low-index incident angle above its critical value has no real transmitted ray. The calculator explains that state. An unknown index cannot be determined from two zero angles; enter additional information.
Does the critical angle itself produce total internal reflection?
The boundary solution refracts at90° along the interface. Total internal reflection occurs above that incident angle for propagation from higher to lower index.
Are the material presets exact for every wavelength?
No. They are static illustrative values with stated reference conditions. Choose custom values for the actual material and wavelength.
References
- OpenStax: Snell’s law and refractive-index inverse
- OpenStax: critical-angle boundary and total internal reflection
- OpenStax: reference indices and conditions
- OpenStax: explicit ice at 0 °C reference
- Röhm: representative acrylic grade at 589 nm and 23 °C
- Pilkington ATS129: float-glass wavelength dependence
- NASA/JPL: phase-index and group-delay distinction
- Calculation definition and unit reference
Both conventional ray angles must lie between zero and ninety degrees inclusive. At a critical boundary the grazing solution is valid; total internal reflection requires strict exceedance toward the lower-index medium. Zero-angle data cannot identify an unknown index; phase index below one does not imply superluminal information propagation.