Snell's Law Calculator
Calculate refraction angles and refractive indices using Snell's law
How to Use This Calculator
Select What to Calculate
Choose whether you want to calculate the angle of refraction, angle of incidence, or refractive index of the second medium.
Enter Known Values
Input the refractive indices of both media and the known angle(s). Common values: air = 1.0, water = 1.33, glass = 1.5, diamond = 2.42.
Calculate
Click the "Calculate" button to get the unknown value. The calculator will alert you if total internal reflection occurs.
Formula
n₁sin(θ₁) = n₂sin(θ₂)
Where:
- n₁ = Refractive index of first medium
- n₂ = Refractive index of second medium
- θ₁ = Angle of incidence (in degrees)
- θ₂ = Angle of refraction (in degrees)
Solving for different variables:
θ₂ = arcsin((n₁sin(θ₁))/n₂)
θ₁ = arcsin((n₂sin(θ₂))/n₁)
n₂ = (n₁sin(θ₁))/sin(θ₂)
Example Calculation:
Light entering glass from air at 30°:
n₁ = 1.0, n₂ = 1.5, θ₁ = 30°
sin(θ₂) = (1.0 × sin(30°)) / 1.5 = 0.5 / 1.5 = 0.333
θ₂ = arcsin(0.333) = 19.47°
About Snell's Law Calculator
Snell's law (also called the law of refraction) describes how light bends when it passes from one medium to another with a different refractive index. It's one of the fundamental laws of optics and is essential for understanding lenses, prisms, optical fibers, and many optical phenomena. This calculator helps you solve for any variable in Snell's law when you know the others.
When to Use This Calculator
- Optics Problems: Solve physics homework problems involving refraction
- Optical Design: Calculate refraction angles in lens and prism design
- Educational Purposes: Understand how light bends at interfaces
- Research: Analyze optical systems and refraction phenomena
- Material Analysis: Determine refractive indices from measured angles
Why Use Our Calculator?
- ✅ Three Calculations: Calculate angle of refraction, angle of incidence, or refractive index
- ✅ Instant Results: Get accurate calculations immediately
- ✅ Total Internal Reflection Detection: Alerts when refraction is impossible
- ✅ Educational: Includes formula explanations and worked examples
- ✅ 100% Free: No registration required
Common Applications
Lens Design: Lens designers use Snell's law to calculate how light rays bend through lenses, determining focal lengths and image formation. This is fundamental to designing cameras, telescopes, and eyeglasses.
Optical Fibers: Fiber optic cables use total internal reflection (which occurs when Snell's law cannot be satisfied) to guide light. Understanding Snell's law is essential for designing fiber optic systems.
Prisms: Prisms use refraction to separate light into colors (dispersion). Snell's law helps calculate the angles at which different wavelengths are refracted.
Tips for Best Results
- Angles are measured from the normal (perpendicular to the surface)
- When light enters a denser medium (higher n), it bends toward the normal
- When light enters a less dense medium (lower n), it bends away from the normal
- Total internal reflection occurs when the calculated sin(θ₂) > 1
- For light entering from air, n₁ ≈ 1.0 is a good approximation
- Remember that refractive index depends on wavelength (dispersion)
Frequently Asked Questions
What is Snell's law?
Snell's law (also called the law of refraction) states that n₁sin(θ₁) = n₂sin(θ₂), where n₁ and n₂ are the refractive indices of the two media, and θ₁ and θ₂ are the angles of incidence and refraction. It describes how light bends when crossing an interface between two media.
What happens when total internal reflection occurs?
Total internal reflection occurs when light tries to pass from a denser to a less dense medium at an angle where refraction is impossible. This happens when the calculated sin(θ₂) exceeds 1, which is mathematically impossible. Instead, all light is reflected back into the denser medium.
Why does light bend when entering a different medium?
Light bends because it travels at different speeds in different media. The speed change causes the wavefront to change direction, resulting in refraction. The amount of bending depends on the ratio of the speeds (which equals the ratio of refractive indices).
Can Snell's law be used for non-visible light?
Yes, Snell's law applies to all electromagnetic waves, including ultraviolet, infrared, X-rays, and radio waves. However, the refractive indices are different for different wavelengths, which is why prisms separate white light into colors.
What's the critical angle?
The critical angle is the angle of incidence at which total internal reflection first occurs. It's given by θ_c = arcsin(n₂/n₁), where light travels from medium 1 to medium 2, and n₁ > n₂. At angles greater than the critical angle, total internal reflection occurs.