About Snell's Law
Snell's Law (the law of refraction) describes how a light ray bends when it crosses the boundary between two transparent media with different optical densities. It states n₁ sin θ₁ = n₂ sin θ₂, where n₁ and n₂ are the refractive indices of the first and second media, θ₁ is the angle of incidence measured from the normal (the line perpendicular to the surface), and θ₂ is the angle of refraction. The relationship follows from Fermat's principle of least time and was formalized by Willebrord Snell in 1621.
Solving for the refraction angle
Rearranging Snell's Law gives θ₂ = arcsin[(n₁ / n₂) × sin θ₁]. Enter the refractive index of the medium the light starts in (n₁), the angle of incidence measured from the normal, and the refractive index of the medium it enters (n₂). The calculator computes sin θ₂ first, then converts it to the refraction angle in degrees. A higher refractive index means a denser optical medium, where light travels more slowly and bends more sharply toward the normal.
Total internal reflection and the critical angle
If (n₁ / n₂) × sin θ₁ works out to more than 1, no real angle θ₂ satisfies the equation — the light cannot refract into the second medium and instead reflects entirely back into the first. This can only happen when light travels from a denser medium into a less dense one (n₁ > n₂), and only beyond a threshold called the critical angle, θc = arcsin(n₂ / n₁). Total internal reflection is the principle behind fiber-optic cables, which guide light down a glass or plastic core by keeping every bounce beyond θc.
Common mistakes to avoid
- Measuring from the surface instead of the normal: both θ₁ and θ₂ are always measured from the line perpendicular to the interface, not from the surface itself.
- Swapping n₁ and n₂: n₁ belongs to the medium the light is leaving, and n₂ to the medium it is entering — reversing them inverts the direction of bending.
- Forgetting total internal reflection: when n₁ > n₂, always check the incidence angle against the critical angle before assuming a refracted ray exists.
Frequently Asked Questions
What is Snell's Law?
How do I find the critical angle for total internal reflection?
What does it mean if sin θ₂ comes out greater than 1?
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Common Measurement Conversions for Everyday Use
| Quantity | US / Imperial | Metric Equivalent |
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| 1 cup | 8 fl oz | 237 mL |
| 1 pint | 16 fl oz | 473 mL |
| 1 quart | 32 fl oz | 946 mL |
| 1 gallon | 128 fl oz | 3.785 L |
| 1 lb | 16 oz | 453.6 g |
| 1 ft | 12 in | 30.48 cm |