What is the critical angle?
θ_c = arcsin(n₂/n₁) for n₁ > n₂. At this angle, θ₂ = 90°. Beyond it, total internal reflection occurs.
Snell's Law Calculator
n₁ sin θ₁ = n₂ sin θ₂
Snell's Law calculator — find refraction angle from incident angle and refractive indices. n₁sinθ₁ = n₂sinθ₂.
Calculate
Enter values above to calculate
How it calculates
1
Compute sin θ₂ = (n₁/n₂) sin θ₁
2
Check: if |sin θ₂| > 1, total internal reflection occurs
3
θ₂ = arcsin(sin θ₂) in degrees
Formula
n₁ sin θ₁ = n₂ sin θ₂
Variable Table
| Symbol | Quantity | SI Unit |
|---|---|---|
| n₁ | Refractive index medium 1 | dimensionless |
| θ₁ | Angle of incidence | degrees |
| n₂ | Refractive index medium 2 | dimensionless |
| θ₂ | Angle of refraction | degrees |
How to Use This Calculator
This snell's law calculator is built for quick physics checks and worked-problem review. Enter values in the units shown beside each input, then compare the result with the formula and variable table before using it in a longer solution. The calculator does the arithmetic, but the physics still depends on choosing a model that matches the situation.
Start by identifying the system, the known quantities, and the quantity you want to find. If a value is given in a non-SI unit, convert it before substitution. A correct numerical answer with mixed units can still be physically wrong, especially when squared units, inverse seconds, charges, temperatures, or distances are involved.
Assumptions and Limits
The formula n₁ sin θ₁ = n₂ sin θ₂ is a model, not a universal description of every possible case. It assumes the quantities in the variable table are the relevant quantities for the problem and that hidden effects are either negligible or already included in the inputs. If friction, drag, relativistic speeds, changing fields, non-constant temperature, or geometry-specific effects matter, check whether a more complete model is needed.
Use the result as a magnitude and units check. Ask whether the answer has the right sign, whether it grows or shrinks when an input changes, and whether the limiting cases make sense. Setting an input to zero, doubling a quantity, or using a very large value is often enough to catch a formula choice or unit mistake before it reaches a final answer.
Worked Example
Light passes from air (n=1.00) at 45° into glass (n=1.50). Find θ₂.
Step 1: sin θ₂ = (1.00/1.50) sin 45° = 0.6667 × 0.7071 = 0.4714
Step 2: θ₂ = arcsin(0.4714)
Answer: θ₂ ≈ 28.1°
Common Mistakes
- Angles are measured from the normal to the surface, not from the surface itself
- Total internal reflection occurs when going from high-n to low-n medium at steep angles
- n = c/v, so higher n means slower light
Related
Waves and OpticsOptical FibresBrewster's Angle
Frequently Asked Questions
Why does a straw look bent in water?
Snell's Law — light from the underwater part of the straw bends at the surface, making it appear displaced.