Snell's Law Calculator — Refraction, Critical Angle, Total Internal Reflection

Real-world use cases

• Check a physics refraction homework answer

  Your problem says light hits a water surface at 40 degrees from the normal — find the refraction angle. Set n1 = 1 for air, n2 = 1.33 for water, θ1 = 40, leave θ2 blank, and read θ2 ≈ 28.9 degrees. The tool also notes the ray bends toward the normal, so you can sanity-check that your hand calculation has the geometry right before you turn in the worksheet.

• Find when an optical fiber traps light

  A step-index fiber has a glass core (n1 = 1.5) against a thinner cladding. Put the cladding index in n2 and read the critical angle: a 1.5 core against air gives 41.8 degrees, against a 1.46 cladding only about 76.7 degrees. Any ray hitting the wall steeper than that totally internally reflects and stays in the core — exactly the condition that lets a fiber carry a signal for kilometers.

• Identify a liquid with a refractometer reading

  A bench refractometer gives you the incidence and refraction angles across a known prism. Leave n2 blank, fill n1, θ1 and θ2, and the tool back-solves the unknown index from n2 = n1·sin θ1 / sin θ2. Compare that number against a reference table to tell sugar syrup from saline, or to flag an adulterated sample whose index drifts off the expected value.

• Explain why a diamond sparkles more than glass

  Set n1 = 2.42 for diamond and n2 = 1 for air and read the critical angle of about 24.4 degrees, then do the same for glass (1.5 → air) and get 41.8 degrees. The much smaller diamond angle means light entering a cut stone hits most facets past critical and bounces internally many times before escaping, which is the optics behind the fire jewelers talk about.

• Prep a worked example for a physics class

  Teaching refraction, you want the same numbers on the board and on the handout. Build the air-to-glass case, copy the result, and share the URL so students open the identical setup at home. Then nudge θ1 up to the critical angle live in class and let them watch the refracted ray vanish into total internal reflection on the diagram.

Common pitfalls

• Measuring the angle from the surface instead of from the normal. Snell's law uses the angle between the ray and the perpendicular (normal) to the boundary. A ray grazing 10 degrees above the surface is θ1 = 80 degrees in the formula, not 10. Get this backward and every refraction angle comes out wrong.

• Expecting a critical angle when going from a thinner to a denser medium. Total internal reflection only happens dense to rare (n1 > n2). Entering n1 = 1 (air) and n2 = 1.5 (glass) has no critical angle at all — the tool returns none because light always refracts into the denser medium, no matter the incidence angle.

• Swapping n1 and n2. The first index belongs to the medium the light starts in (the incident side), the second to the medium it enters. Flipping them turns a bend toward the normal into a bend away from it and can invent or erase a critical angle. Always enter the indices in the direction the light actually travels.

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