Snell refraction critical angle and Brewster angle calculator

What this calculation answers

Refraction changes a ray’s direction at an interface because its propagation speed changes. Snell’s law connects angles measured from the surface normal. The same two refractive indices also define critical and Brewster angles under specific conditions.

This page reports those three quantities together while keeping their meanings separate. A critical angle describes the onset of total internal reflection; a Brewster angle describes vanishing ideal p-polarized reflection.

The Normal incidence Fresnel interface power balance calculator accounts for power at normal incidence. A refracted ray angle alone does not determine transmitted power.

Use the right input conventions

Enter the incident medium first and the transmitted medium second. Swapping them changes the physical direction of travel and whether a critical angle exists. All angles are measured from the normal, not from the interface plane.

The refractive indices are real positive inputs for transparent isotropic nonmagnetic media. The page does not look up material indices or account for their variation with wavelength, temperature or pressure.

Interpret the result

Total internal reflection is possible only when light travels from higher to lower refractive index. Above the critical angle, the page reports that condition rather than attempting an inverse sine beyond its real domain.

Brewster’s relation is polarization-specific. It does not mean all reflected light disappears for unpolarized illumination, and it is not a direct substitute for a full Fresnel reflectance calculation at arbitrary angles.

Work through the example

For light from index one into index 1.5 at thirty degrees, the transmitted sine is one third. The refracted angle is about 19.4712 degrees, bending toward the normal.

The Brewster angle for that direction is about 56.3099 degrees and no critical angle exists. Reversing the indices gives a critical angle about 41.8103 degrees; a fifty-degree incident ray then undergoes total internal reflection.

Where the model stops

Only an ideal flat interface with real refractive indices is represented. Absorbing metals, anisotropic crystals and surface coatings require more complete optical models.

The page does not compute evanescent-field depth, interface roughness or transmission losses. A transmitted-ray angle is a geometric result, not an estimate of how much optical power reaches a detector.