Refraction Calculator

Apply Snell's Law to calculate refraction angles, critical angles, and total internal reflection. Includes a live ray diagram and step-by-step solution.

Apply Snell's Law: n₁ sin θ₁ = nβ‚‚ sin ΞΈβ‚‚ to find the refracted angle.

Air
Β°
Measured from the normal
Water

The critical angle exists when light travels from a denser medium to a less dense one (n₁ > nβ‚‚). Beyond this angle, total internal reflection occurs.

Must be greater than nβ‚‚

Find the unknown refractive index given the other index and both angles.

Β°
Β°

Calculate the speed of light in a medium from its refractive index. Speed = c Γ· n.

n = 1 for vacuum, 1.0003 for air, 1.333 for water, ~1.5 for glass

How to use

  • 🌊 Snell's Law
    Enter two refractive indices and the angle of incidence to find the angle of refraction. Use presets to auto-fill common materials.
  • πŸ”Ί Critical Angle
    Find the critical angle for total internal reflection when light passes from a denser medium (higher n) to a less dense one.
  • πŸ” Find Refractive Index
    Enter one known refractive index and both angles to solve for the unknown refractive index nβ‚‚.
  • πŸ’¨ Light Speed in Medium
    Calculate the speed of light in any medium from its refractive index using v = c Γ· n.

Key Formulas

Snell's Law: n₁ sin θ₁ = nβ‚‚ sin ΞΈβ‚‚
ΞΈβ‚‚ = arcsin(n₁ sin θ₁ Γ· nβ‚‚)
Critical: ΞΈ_c = arcsin(nβ‚‚ Γ· n₁)
Speed: v = c Γ· n
n = c Γ· v (c = 3Γ—10⁸ m/s)

Common Refractive Indices

Materialn
Vacuum1.0000
Air (20Β°C)1.0003
Water1.333
Ethanol1.362
Crown glass1.52
Flint glass1.62
Diamond2.417

What is Refraction?

Refraction is the bending of light (or any wave) as it passes from one medium to another with a different refractive index. When light moves from air into water, it slows down and bends toward the normal (the perpendicular to the surface). When it moves from water to air, it speeds up and bends away from the normal. This is why a straw in a glass of water appears bent.

Snell's Law

Snell's Law describes the relationship between angles of incidence and refraction: n₁ sin θ₁ = nβ‚‚ sin ΞΈβ‚‚. Here n₁ and nβ‚‚ are the refractive indices of the two media, and θ₁ and ΞΈβ‚‚ are the angles measured from the normal to the boundary surface. When nβ‚‚ > n₁ (denser medium), the light bends toward the normal and ΞΈβ‚‚ < θ₁.

Total Internal Reflection

When light travels from a denser medium to a less dense one (e.g., glass to air), there is a critical angle beyond which all light is reflected back β€” none is transmitted. This is total internal reflection. The critical angle is given by ΞΈ_c = arcsin(nβ‚‚ Γ· n₁). Optical fibers use total internal reflection to transmit light signals over long distances with minimal loss.

Frequently Asked Questions

Why does light bend when it changes medium?

Light bends because its speed changes as it enters a new medium. The refractive index n = c/v, where c is the speed of light in vacuum and v is the speed in the medium. When light slows down entering a denser medium, the wavefront changes direction to maintain continuity β€” this bending is refraction.

What is the refractive index?

The refractive index (n) of a medium is the ratio of the speed of light in vacuum to the speed of light in that medium: n = c Γ· v. It has no units and is always β‰₯ 1. A higher refractive index means light travels more slowly in that medium. Diamond's high refractive index (2.417) is responsible for its exceptional brilliance.

What is total internal reflection used for?

Total internal reflection is used in optical fibers (telecommunications and internet cables), endoscopes for medical imaging, binoculars and periscopes (using prisms), retroreflectors, and diamond cutting (maximizing brilliance). It occurs when light hits a boundary at an angle greater than the critical angle while traveling in the denser medium.

Does refraction change the frequency of light?

No β€” only the speed and wavelength change when light enters a new medium. The frequency stays constant. Since color is determined by frequency, light doesn't change color when refracted. However, different frequencies refract by slightly different amounts (dispersion), which is why a prism splits white light into a rainbow spectrum.

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