Angle of Refraction Calculator

Calculate angle of refraction using Snell's Law with comprehensive optics analysis

Refraction Calculator

Choose which angle you want to calculate

Refractive index: 1.000273

Refractive index: 1.520000

Known incidence angle

Refraction Results

27.73°
Angle of Refraction (θ₂)
5.3%
Light Reflected
56.65°
Brewster's Angle
3.35 mm
Lateral Displacement

Snell's Law: n₁ sin(θ₁) = n₂ sin(θ₂)

Refractive indices: n₁ = 1.000273, n₂ = 1.520000

Index ratio: n₁/n₂ = 0.658074

Transmission: 94.7% of light passes through

Light Behavior Analysis

✅ Light traveling from rarer to denser medium - bends toward normal

Example: Light Entering Glass

Problem Setup

Scenario: Light ray traveling from air into crown glass

Medium 1: Air (n₁ = 1.000273)

Medium 2: Crown Glass (n₂ = 1.52)

Angle of incidence: 45°

Solution Steps

1. Use Snell's Law: sin(θ₂) = (n₁/n₂) × sin(θ₁)

2. sin(θ₂) = (1.000273/1.52) × sin(45°)

3. sin(θ₂) = 0.6581 × 0.7071 = 0.4653

4. θ₂ = arcsin(0.4653) = 27.73°

The light bends toward the normal by 17.27°

Refractive Index Values

Vacuum1
Air (STP)1.000273
Water1.333
Ice1.31
Crown Glass1.52
Flint Glass1.62
Quartz1.544
Diamond2.42
Oil1.515
Ethanol1.361
Glycerol1.473
Plastic (PMMA)1.49
Sapphire1.77
Ruby1.76
Note: Higher refractive index = denser optical medium

Refraction Principles

Snell's Law

n₁sin(θ₁) = n₂sin(θ₂)

Bending Rules

Light bends toward normal in denser medium

Critical Angle

Maximum incident angle before total reflection

Brewster's Angle

Angle for complete polarization

Real-World Applications

👓

Eyeglasses & Lenses

Correcting vision by bending light rays

🔬

Optical Instruments

Microscopes, telescopes, cameras

🌈

Prisms & Rainbows

Separating white light into colors

🏥

Medical Imaging

Ultrasound and optical coherence tomography

Understanding Light Refraction

What is Refraction?

Refraction is the bending of light when it passes from one medium to another with a different optical density. This phenomenon occurs because light travels at different speeds in different materials, causing the light ray to change direction at the interface.

Why Does Light Bend?

  • Light speed changes between different materials
  • Denser materials slow down light more
  • Wavefront arrives at different times
  • Results in direction change to maintain energy conservation

Snell's Law Formula

n₁ sin(θ₁) = n₂ sin(θ₂)

sin(θ₂) = (n₁/n₂) × sin(θ₁)

  • n₁, n₂: Refractive indices of first and second media
  • θ₁: Angle of incidence (from normal)
  • θ₂: Angle of refraction (from normal)

Key Angles

Critical Angle: θc = sin⁻¹(n₂/n₁) [when n₁ > n₂]

Brewster's Angle: θB = tan⁻¹(n₂/n₁)

Grazing Incidence: θ₁ = 90° (parallel to surface)

Practical Applications

Vision Correction

Glasses and contact lenses use controlled refraction to focus light properly on the retina

Optical Devices

Cameras, microscopes, and telescopes rely on precise refraction calculations for optimal performance

Atmospheric Effects

Mirages, atmospheric distortion, and twinkling stars all result from atmospheric refraction

💡 Interesting Facts

  • • A spoon in water appears bent due to refraction at the air-water interface
  • • Diamond's high refractive index (2.42) creates its brilliant sparkle
  • • Optical fibers use total internal reflection to transmit data over long distances
  • • The apparent depth of swimming pools is less than actual depth due to refraction