Snell's Law Calculator
Calculate the angle of refraction or refractive index using Snell’s law.
e.g. 1.0 (air)
e.g. 1.33 (water)
Angle of Refraction θ₂
Note
Calculation Details
Understanding Snell's Law
Snell's law describes how light bends, or refracts, when it travels from one transparent medium into another. The amount of bending depends on the refractive indices of the two media and the angle at which the light strikes the boundary. The relationship is expressed as n₁ sinθ₁ = n₂ sinθ₂, where n₁ and n₂ are the refractive indices of the first and second media, and θ₁ and θ₂ are the angles of incidence and refraction measured from the normal to the surface.
Key Concepts
- Refractive index (n): A measure of how much a medium slows down light compared to a vacuum. A vacuum has n = 1, air ≈ 1.0003, water ≈ 1.33, and glass ≈ 1.5.
- Bending toward the normal: When light enters a denser medium (higher n), it bends toward the normal, so θ₂ < θ₁.
- Bending away from the normal: When light enters a less dense medium (lower n), it bends away from the normal, so θ₂ > θ₁.
- Total internal reflection: When light travels into a less dense medium at a steep enough angle, no refraction occurs and all the light is reflected back.
Key Formula
- n₁ sinθ₁ = n₂ sinθ₂ — Snell's law
- sinθ₂ = (n₁ sinθ₁) / n₂ — Solving for the refraction angle
- θ₂ = arcsin[(n₁ sinθ₁) / n₂] — Refraction angle in degrees
Common Refractive Indices
Gases and Liquids
- • Vacuum: n = 1 (exactly)
- • Air: n ≈ 1.0003
- • Water (20°C): n ≈ 1.333
- • Ethanol: n ≈ 1.361
Solids
- • Ice: n ≈ 1.31
- • Crown glass: n ≈ 1.52
- • Sapphire: n ≈ 1.77
- • Diamond: n ≈ 2.42
Real-World Examples
Snell's law is fundamental to optics and underpins many everyday phenomena and technologies:
- Light passing from air (n = 1.0) into water (n = 1.33) at 30° refracts to about 22.1°, which is why objects underwater appear shifted.
- Eyeglass and camera lenses use refraction to focus light onto the retina or sensor.
- Optical fibers rely on total internal reflection to carry light signals over long distances with minimal loss.
- A straw in a glass of water appears bent at the surface because of refraction.
References
The formulas and refractive index values used in this calculator are based on established physics principles and verified sources:
Related Calculators
Note: This calculator assumes monochromatic light, smooth planar boundaries, and homogeneous isotropic media. Real-world refraction can vary with wavelength (dispersion), temperature, and material impurities. Angles are measured from the normal to the surface.