Snell's Law Calculator

Calculate angle of refraction

Snell's Law

n₁ × sin(θ₁) = n₂ × sin(θ₂)

Formula
n₁ × sin(θ₁) = n₂ × sin(θ₂)

What Is Snell's Law?

Snell's Law (also called the Law of Refraction) describes how light bends when it crosses the boundary between two media with different indices of refraction. When light moves from one medium to another, it changes speed and direction — this bending is refraction.

Formulated by Dutch mathematician Willebrord Snellius in 1621, the law relates the angle of incidence to the angle of refraction through the refractive indices of the two media. It is essential in optics, lens design, fiber optics, and corrective eyewear prescription calculations.

How to Use Snell's Law Calculator

  1. Enter the refractive index of the first medium (n₁). Air ≈ 1.0003, glass ≈ 1.5, water ≈ 1.33.
  2. Enter the angle of incidence (θ₁) in degrees — the angle between the incoming ray and the surface normal.
  3. Enter the refractive index of the second medium (n₂).
  4. Click Calculate to get the angle of refraction (θ₂) in degrees.

Formula & Explanation

n₁ × sin(θ₁) = n₂ × sin(θ₂) θ₂ = arcsin(n₁ × sin(θ₁) / n₂) n₁ = refractive index of medium 1 n₂ = refractive index of medium 2 θ₁ = angle of incidence (degrees) θ₂ = angle of refraction (degrees)

Total internal reflection occurs when n₁ > n₂ and θ₁ exceeds the critical angle θ_c = arcsin(n₂/n₁). This is the principle behind optical fibers.

Worked Examples

Air to Glass

Light hits glass (n₂ = 1.5) from air (n₁ = 1.0) at 45°. sin(θ₂) = 1.0 × sin(45°) / 1.5 = 0.7071 / 1.5 = 0.4714. θ₂ = arcsin(0.4714) ≈ 28.1°. The ray bends toward the normal as it enters the denser medium.

Water to Air

Light travels from water (n₁ = 1.33) to air (n₂ = 1.0) at 30°. sin(θ₂) = 1.33 × sin(30°) / 1.0 = 1.33 × 0.5 = 0.665. θ₂ = arcsin(0.665) ≈ 41.7°. The ray bends away from the normal entering the less dense medium.

Total Internal Reflection in Fiber Optics

Glass fiber (n₁ = 1.5) in air (n₂ = 1.0). Critical angle = arcsin(1.0/1.5) = arcsin(0.667) ≈ 41.8°. Any light hitting the fiber wall at > 41.8° is totally internally reflected — this is how data travels in fiber optic cables.

Frequently Asked Questions

What is the refractive index?▾
The refractive index (n) is the ratio of the speed of light in vacuum (c) to its speed in the medium: n = c/v. Vacuum = 1.0, air ≈ 1.0003, water ≈ 1.33, glass ≈ 1.5, diamond = 2.42. Higher n means slower light and more bending.
What is total internal reflection?▾
When light moves from a denser medium (higher n) to a less dense one and the angle of incidence exceeds the critical angle, all light is reflected back — none passes through. This is total internal reflection, the basis of fiber optic communications.
Why does a straw look bent in water?▾
Light from the submerged part of the straw refracts as it exits the water, bending away from the normal. Your brain projects the light rays back in straight lines, making the straw appear at a different position — displaced toward the surface.
How is Snell's Law used in lens design?▾
Lens makers use Snell's Law to trace rays through glass surfaces and predict focal length, aberrations, and image quality. Prescription eyeglasses are calculated using Snell's Law to determine the exact curvature needed to correct refractive errors.
What is the difference between reflection and refraction?▾
Reflection is when light bounces off a surface (angle of incidence = angle of reflection). Refraction is when light passes through a surface and bends due to change in speed. Both can occur simultaneously — a glass window both reflects and transmits light.