How to use (3 steps)
- Select the mode: refraction (Snell's law) or critical angle / total internal reflection.
- Enter the refractive indices and angles. Pick which quantity is unknown—the field turns off automatically.
- Tap Compute to see the solved value, the critical-angle check, and the step-by-step log. Copy URL shares the exact setup.
A common air → glass example is preloaded and computed on page load so you can see the results immediately.
Inputs
Angles are measured from the normal (0–90°). Values stay on this device.
Results
Ray diagram
Angles are measured from the normal; illustration not to scale.
How it's calculated
Using refraction and critical-angle mode
This page solves the missing quantity in n₁ sin θ₁ = n₂ sin θ₂. Angles are measured from the normal, so a grazing ray has an angle close to 90°, not 0°.
Suggested workflow
- Pick two refractive indices that match your media, or start from an air-water-glass preset.
- Enter either the incidence angle or the refraction angle, then compute to solve the missing value.
- If the tool reports total internal reflection, use the critical-angle line to explain why no refracted ray exists.
What the calculator assumes
It models a sharp interface between isotropic media and ignores wavelength-dependent dispersion, absorption, and surface roughness. That makes it appropriate for teaching examples and first-pass checks, not optical-system design.
Common mistakes to avoid
- Measuring the angle from the surface instead of from the normal.
- Trying to trigger total internal reflection when light goes from a lower index into a higher index medium.
- Comparing with a geometry diagram that uses rounded angles while the calculator keeps more precision internally.
See also
FAQ
What is Snell's law?
It states n₁ sin θ₁ = n₂ sin θ₂, linking indices and angles measured from the normal. Enter any three of n₁, n₂, θ₁, θ₂ and the tool solves the last one.
When does total internal reflection happen?
When light goes from a higher to a lower refractive index and the incidence angle exceeds the critical angle. The calculator shows the critical angle and whether your chosen incidence angle triggers total internal reflection.
How accurate are the presets?
Air, water, and glass presets use typical values and ignore small dispersion or temperature effects. They are intended for quick learning examples rather than optical design.
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