Understanding Snell's Law

Snell's Law describes how light bends when passing between different media. This is crucial for lens design, fiber optics, and understanding natural phenomena like mirages. Common pitfalls include confusing incident/refracted angles and incorrect refractive indices.

Calculation Steps

Identify known values: n₁, θ₁, and n₂
Ensure angles are measured from normal (perpendicular)
Apply formula: n₁ × sin(θ₁) = n₂ × sin(θ₂)
Solve for unknown angle using inverse sine
Check for total internal reflection (when θ₂ ≥ 90°)

Examples

Air (n=1.00) to Water (n=1.33) at 45°: θ₂ ≈ 32.12°
Water to Glass (n=1.52) at 30°: θ₂ ≈ 25.46°
Glass to Air at 41°: θ₂ ≈ 90° (critical angle)

Reference Table

Material	Refractive Index
Vacuum	1.000
Air	1.0003
Water	1.333
Glass	1.52
Diamond	2.42

Warning: Measurements should be precise as small angle errors compound. Total internal reflection occurs when light cannot exit a medium (n₁ > n₂ and θ₁ ≥ critical angle).

Frequently Asked Questions

Q: What is the precision of this calculator?

A: Results use JavaScript's Math library with double-precision floating points. Final displayed values are rounded to selected decimal places.

Q: Why does light bend when changing media?

A: Light changes speed in different media, causing refraction. The bending direction depends on whether light enters a denser (slower) or rarer (faster) medium.

Q: When should I consult a professional?

A: For optical system design, lens manufacturing, or medical applications, always consult qualified optical engineers or physicists.

Formulas & Assumptions

n₁ × sin(θ₁) = n₂ × sin(θ₂) θ₂ = arcsin((n₁ × sin(θ₁)) / n₂) Critical Angle = arcsin(n₂ / n₁) [when n₁ > n₂]

Angles are converted between degrees and radians using standard conversion factors. Calculations use IEEE 754 floating-point standards. Results are rounded to specified decimal places using half-up rounding.

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