Snell's Law
Calculate refraction angle or refractive index with Snell's law. Useful for optics problems with step-by-step formula substitution.
Key formula
n1 sin(theta1) = n2 sin(theta2)
How do you use Snell's law?
Snell’s law is n₁ sinθ₁ = n₂ sinθ₂. Solve for an unknown angle with θ₂ = arcsin((n₁/n₂) sinθ₁), or for an index with n₂ = n₁ sinθ₁ / sinθ₂. Angles are from the normal. If (n₁/n₂) sinθ₁ > 1, total internal reflection can occur instead of refraction.
About this tool
Snell’s law describes how light bends when it crosses into a new medium: n₁ sinθ₁ = n₂ sinθ₂. This calculator keeps the formula, degree-from-normal angles, and the total-internal-reflection check visible so refraction homework stays consistent.
How to use this calculator
- Choose the variable you want to solve for and confirm which values are already known.
- Enter inputs in consistent units before calculating so the formula is applied correctly.
- Check whether the result is physically reasonable by comparing it with the size of the inputs.
- Use the step-by-step breakdown to see how the equation was rearranged and evaluated.
Worked examples
Example 1: air to glass
n₁ = 1.00, θ₁ = 30°, n₂ = 1.50. sinθ₂ = (1.00/1.50) sin30° = 0.333. θ₂ ≈ 19.5° toward the normal.
Example 2: find n₂
n₁ = 1.33 (water), θ₁ = 40°, θ₂ = 28°. n₂ = n₁ sinθ₁ / sinθ₂ = (1.33)(0.643)/0.469 ≈ 1.82.
Example 3: glass to air
n₁ = 1.50, θ₁ = 20°, n₂ = 1.00. sinθ₂ = 1.50 sin20° ≈ 0.513. θ₂ ≈ 30.9° — bends away from the normal.
Frequently asked questions
What is Snell's law formula?
n₁ sinθ₁ = n₂ sinθ₂, where n is refractive index and θ is the angle from the normal in each medium.
From where are the angles measured?
From the normal — the line perpendicular to the surface — not from the surface itself. Measuring from the surface is a common exam trap.
What is refractive index?
n = c/v for the medium (approx.), a number ≥ 1 for ordinary materials. Air ≈ 1.00, water ≈ 1.33, glass ≈ 1.5. Higher n means slower light in that medium.
What is total internal reflection?
When light tries to leave a denser medium and (n₁/n₂) sinθ₁ > 1, there is no real θ₂. The ray reflects inside instead. The smallest such θ₁ is the critical angle.
How does Snell's law relate to wave speed?
Because n ≈ c/v, a higher index means lower wave speed. Frequency stays the same across the boundary; wavelength and direction change.