Snell's Law Calculator

Snell’s Law (also called the Law of Refraction) describes how light bends when it passes from one medium into another. It was formulated by Willebrord Snellius in 1621 in the Netherlands.

The formula:

n₁ × sin(θ₁) = n₂ × sin(θ₂)

Where:

• n₁ = refractive index of the first medium (where light comes from)
• θ₁ = angle of incidence (measured from the surface normal)
• n₂ = refractive index of the second medium (where light enters)
• θ₂ = angle of refraction (what we solve for)

Solving for the refraction angle:

θ₂ = arcsin((n₁ / n₂) × sin(θ₁))

Common refractive indices:

• Vacuum: 1.0000
• Air: 1.0003 (essentially 1.0)
• Water: 1.333
• Glass (crown): 1.52
• Glass (flint): 1.62
• Diamond: 2.417
• Ice: 1.31

Total Internal Reflection: When light travels from a denser medium (higher n) to a less dense medium (lower n), there exists a critical angle beyond which all light is reflected back instead of passing through. The critical angle is calculated as: θc = arcsin(n₂ / n₁). This phenomenon is the principle behind fiber optic cables, which transmit data as light pulses over long distances with minimal loss.

Practical applications: Snell’s Law is used in designing eyeglasses and contact lenses, camera lenses, microscopes, telescopes, and optical instruments of all kinds. It explains why a straw in a glass of water appears bent, why pools look shallower than they are, and how rainbows form when sunlight refracts through water droplets.

Tips:

• Angles are measured from the normal (perpendicular to the surface), not from the surface itself.
• If the calculated sin(θ₂) exceeds 1, total internal reflection occurs and no refracted ray exists.
• This calculator also shows the critical angle when applicable.