Physics / Optics
Snell's Law Calculator: Refraction and Critical Angle
Work out how much light bends between two materials from their refractive indices and the angle of incidence, find the critical angle for total internal reflection, and pick common materials such as water, glass, and diamond from a list.
Snell's Law Calculator: Refraction and Critical Angle: n₁ sin θ₁ = n₂ sin θ₂ gives the refraction angle. Light entering water from air at 30° bends to 22.04°, towards the normal. Going the other way, from water to air, angles beyond the critical angle of 48.63° cannot leave the water at all and reflect back, which is total internal reflection. Runs 100% locally in your browser with zero server file uploads.
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Light changes direction where it crosses into a material with a different refractive index: n₁ sin θ₁ = n₂ sin θ₂, with angles measured from the normal, the line at right angles to the surface. Going into a denser medium it bends towards the normal. Going into a less dense one it bends away, and beyond the critical angle it cannot leave at all, which is how optical fibres and the sparkle of diamonds work. The indices are for yellow light; they vary slightly with colour.
Optical fibres
A glass fibre's core has a slightly higher index than its cladding, so light hitting the boundary beyond the critical angle reflects totally and travels kilometres along the fibre with little loss.
The presets
Water 1.333, crown glass 1.52, acrylic 1.49, and diamond 2.417 are standard values for sodium yellow light; real samples vary slightly with temperature and composition. For focusing rather than bending, the lens equation calculator finds where an image forms.
How to use it
- Pick or type the refractive indices of the two materials.
- Enter or drag the angle of incidence, measured from the normal.
- Read the refraction angle and the critical angle, and see the diagram.
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Frequently asked questions
What is the normal?
A line at right angles to the surface where the light hits; all angles are measured from it, not from the surface.
Why does diamond sparkle?
Its refractive index, 2.42, gives a critical angle of only 24.4°, so light that enters bounces around inside many times before it escapes.
Why do the indices change with colour?
Most materials bend blue light more than red, which is why a prism splits white light into a spectrum; the presets are for yellow light at 589 nm.
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