Snells law formulas and interpretation
Snell’s law relates ray angles and refractive indices at an interface between optical media.
The calculator preserves all four unknown-variable modes and total-internal-reflection detection.
How to use the Snells law calculator
- Choose a model: Select the relationship matching the problem.
- Choose the unknown: Select the quantity to calculate.
- Enter values: Enter all known values with matching units and signs.
- Calculate: Review the result, formula, units, and direction.
Formula and variables
The product of refractive index and angle sine is equal on both sides of the interface.
n₁ sin θ₁ = n₂ sin θ₂- n₁,n₂ — Refractive indices
- Optical indices of both media (dimensionless)
- θ₁ — Incidence angle
- Angle from interface normal (degrees)
- θ₂ — Refraction angle
- Transmitted angle from normal (degrees)
Air-to-glass example
Light enters glass of index 1.5 from air at 30 degrees.
- n₁
- 1.0
- θ₁
- 30°
- n₂
- 1.5
- sin θ₂ = 1 × sin 30° / 1.5
- θ₂ ≈ 19.47°
Result: Refraction angle is about 19.47 degrees.
The ray bends toward the normal in the higher-index material.
Understanding your results
Interpreting the result
Angles are measured from the surface normal, and indices can depend on wavelength.
Assumptions
- The selected equation represents the physical system.
- Inputs use a consistent reference direction.
- Values are converted through coherent SI units.
Limitations
- Vector components must be resolved along a common axis.
- External forces or energy losses are not added automatically.
- Results depend on the accuracy of entered measurements.
Common mistakes
- Mixing incompatible units.
- Dropping negative signs that represent direction.
- Using weight where mass is required.
- Entering a zero divisor.
Practical use cases
Physics problems
Check classroom, laboratory, and mechanics calculations.
Practical estimates
Estimate motion, forces, and energy for real systems.
Frequently asked questions
Can a result be negative?
Yes. For directional quantities, the sign indicates direction relative to the chosen positive axis.
Should I use SI units?
The interface can convert supported units, while the formulas are evaluated through coherent SI units.
Sources and review
- SI Brochure, 9th edition — BIPM. Accessed 2026-07-11.
- Special Publication 811 — NIST. Accessed 2026-07-11.
Reviewed 2026-07-11.