Snell’s Law & Refraction Calculator
Understand perfectly how light rays bend when transitioning between different physical materials using our interactive Snell’s Law Calculator. Also known widely as the law of refraction, it allows you to instantly calculate the exact angle of refraction, or determine if Total Internal Reflection (TIR) occurs.
Snell’s Law Calculator
Adjust the refractive indices or incidence angle below to see how light refracts dynamically.
The angle of incidence is greater than the critical angle, so no light is transmitted.
What is Snell’s Law?
Snell’s Law is a primary optics principle that dictates that the ratio of the sines of the angles of incidence and refraction is strictly equivalent to the ratio of phase velocities (or the reciprocal of the refractive indices) in the two intersecting media:
n₁ × sin(θ₁) = n₂ × sin(θ₂)
Light actually slows down when it penetrates a medium with a higher refractive index (like passing from loose air into dense water). This slowing down forces the light ray to fundamentally bend towards the normal line mathematically. Conversely, if it escapes into a medium with a lower refractive index, it speeds up completely and bends away from the normal.
Total Internal Reflection and the Critical Angle
When an electromagnetic light wave attempts to travel from a phenomenally denser medium (higher refractive index n) directly to a less dense medium, it has to bend violently away from the normal. Because of this, there exists a rigid mathematical Critical Angle.
If the targeted angle of incidence exceeds this exact critical angle, the light wave cannot physically pass through the designated boundary at all. Instead, it gets fully reflected back into the original medium—an extraordinary optic phenomenon completely utilized by modern fiber optic internet cables to relay data instantly across oceans, and also what gives brilliant cut diamonds their inner sparkling brightness!