Reflection and Refraction Calculator
Find reflected and refracted ray directions from incidence angle and two refractive indices. Detect total internal reflection and show the critical angle.
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Result
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Calculation steps
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How to calculate
Reflection preserves the angle to the normal. Snell’s law relates the two refractive indices and sine angles. When light travels toward a lower refractive index, incidence above the critical angle gives total internal reflection.
θreflected=θincident; n1 sinθ1=n2 sinθ2; θcritical=asin(n2/n1) when n1>n2
Worked example
Fromn1=1 ton2=1.5 at30° incidence, refraction is about19.4712°. Fromn1=1.5 ton2=1, the critical angle is about41.8103°;50° incidence gives total internal reflection.
Assumptions and input details
Indices must be real values1–10 for ordinary transparent media; incidence0–89.999999°. Angles are measured from the normal, not the surface. The ray layout shows direction, not wavelength, energy or reflected intensity. Absorption, dispersion, polarization and surface roughness are omitted. Quantitative Snell calculations extend the introductory middle-school light model.
References: OpenStax refraction and total internal reflection
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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