Snell's Law Calculator (n₁ sin θ₁ = n₂ sin θ₂)
Snell's Law Calculator (n₁ sin θ₁ = n₂ sin θ₂)
Snell's law describes how light bends when it crosses the boundary between two materials with different refractive indices - the basis for how lenses, prisms, and even the apparent bending of a straw in a glass of water work. Choose the variable you need, enter the other three known values (two refractive indices and one angle), and this calculator solves for the fourth.
- n₁ sin θ₁ = n₂ sin θ₂, so light hitting a water surface (n₂=1.33) from air (n₁=1.0) at a 30° angle of incidence refracts to sin θ₂ = sin(30°)/1.33 = 0.376, giving θ₂ ≈ 22.1°.
- Light bends toward the normal when entering a denser medium (higher refractive index) and away from the normal when exiting into a less dense one - which is why the refraction angle above (22.1°) is smaller than the incidence angle (30°).
- Total internal reflection occurs when going from a denser to a less dense medium at too steep an angle - if the required sine value exceeds 1, there is no refraction angle and the calculator reports total internal reflection instead.
How do I calculate the angle of refraction?
Use θ₂ = asin(n₁ sin θ₁ / n₂). For light going from air (n₁=1.0) into water (n₂=1.33) at 30°: θ₂ = asin(1.0 × sin(30°) / 1.33) ≈ 22.1°.
What is total internal reflection?
It happens when light traveling in a denser medium hits the boundary with a less dense one at an angle steep enough that no refraction angle exists (the calculated sine value would exceed 1) - all the light reflects back instead of refracting through.
Snell's Law Calculator (n₁ sin θ₁ = n₂ sin θ₂)
Snell's law describes how light bends when it crosses the boundary between two materials with different refractive indices - the basis for how lenses, prisms, and even the apparent bending of a straw in a glass of water work. Choose the variable you need, enter the other three known values (two refractive indices and one angle), and this calculator solves for the fourth.
- n₁ sin θ₁ = n₂ sin θ₂, so light hitting a water surface (n₂=1.33) from air (n₁=1.0) at a 30° angle of incidence refracts to sin θ₂ = sin(30°)/1.33 = 0.376, giving θ₂ ≈ 22.1°.
- Light bends toward the normal when entering a denser medium (higher refractive index) and away from the normal when exiting into a less dense one - which is why the refraction angle above (22.1°) is smaller than the incidence angle (30°).
- Total internal reflection occurs when going from a denser to a less dense medium at too steep an angle - if the required sine value exceeds 1, there is no refraction angle and the calculator reports total internal reflection instead.
How do I calculate the angle of refraction?
Use θ₂ = asin(n₁ sin θ₁ / n₂). For light going from air (n₁=1.0) into water (n₂=1.33) at 30°: θ₂ = asin(1.0 × sin(30°) / 1.33) ≈ 22.1°.
What is total internal reflection?
It happens when light traveling in a denser medium hits the boundary with a less dense one at an angle steep enough that no refraction angle exists (the calculated sine value would exceed 1) - all the light reflects back instead of refracting through.