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
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
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
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