Snell's Law Calculator
Calculate refraction angles, critical angles, and analyze light bending between media
Snell's Law of Refraction Calculator
Refractive index of incident medium
Refractive index of refracted medium
Angle between incident ray and normal
Refraction Results
Snell's Law
n₁ sin(θ₁) = n₂ sin(θ₂)
1.000 × sin(30.0°) = 1.330 × sin(0.4°)
0.5000 = 0.0089
Additional Properties
Relative Refractive Index: 1.3300
Speed Ratio (v₂/v₁): 0.7519
sin(θ₂): 0.3759
Light Behavior: Bends toward normal
Example Calculations
Air to Water Refraction
Given: Light ray travels from air (n₁ = 1.000) to water (n₂ = 1.333) at 30° incidence
Calculation:
sin(θ₂) = n₁ sin(θ₁) / n₂ = 1.000 × sin(30°) / 1.333
sin(θ₂) = 1.000 × 0.5 / 1.333 = 0.375
θ₂ = arcsin(0.375) = 22.1°
Result: Light bends toward the normal by 7.9°
Critical Angle Example
Scenario: Light traveling from glass (n₁ = 1.5) to air (n₂ = 1.0)
Critical angle: θc = arcsin(n₂/n₁) = arcsin(1.0/1.5) = 41.8°
Result: Angles > 41.8° cause total internal reflection
Refractive Indices
Applications
Optics & Lenses
Camera lenses, eyeglasses, microscopes, telescopes
Fiber Optics
Total internal reflection in optical fibers for communications
Prisms
Light dispersion, beam steering, and spectroscopy
Gemology
Diamond identification and quality assessment
Meteorology
Rainbow formation, mirages, atmospheric optics
Understanding Snell's Law
What is Snell's Law?
Snell's law, also known as the law of refraction, describes the relationship between the angles of incidence and refraction when light passes from one medium to another. It quantifies how much light bends at the interface.
The Formula
n₁ sin(θ₁) = n₂ sin(θ₂)
Key Variables
- •n₁, n₂: Refractive indices of medium 1 and 2
- •θ₁: Angle of incidence (measured from normal)
- •θ₂: Angle of refraction (measured from normal)
Physical Principles
- •Light travels at different speeds in different media
- •Higher refractive index = slower light speed
- •Light bends toward normal when entering denser medium
- •Light bends away from normal when entering less dense medium
Critical Angle
θc = arcsin(n₂/n₁)
When light travels from a denser to less dense medium, the critical angle is the minimum angle of incidence that results in total internal reflection.
Total Internal Reflection
Conditions
- • Light travels from denser to less dense medium
- • Angle of incidence > critical angle
- • sin(θ₂) would be > 1 (mathematically impossible)
Applications
- • Optical fiber communications
- • Periscopes and prisms
- • Diamond brilliance
Historical Context
Willebrord Snellius (1580-1626)
Dutch mathematician who formulated the mathematical law of refraction, though the physical principles were understood earlier by others including Ibn Sahl in 984 AD.
Modern Applications
Essential for lens design, optical instruments, laser technology, and understanding atmospheric phenomena like rainbows and mirages.