Lei de Snell

The Snell's Law Calculator solves the equation n₁ sin θ₁ = n₂ sin θ₂ for any of the four variables: refractive index of medium 1 (n₁), angle of incidence (θ₁), refractive index of medium 2 (n₂), or angle of refraction (θ₂). It is aimed at students, teachers, and professionals in optics, physics, and engineering who need to quickly determine how light bends when passing between different media. The tool also provides the critical angle for total internal reflection, when applicable. The calculation is based on the fundamental law of refraction, which relates the change in light direction to the ratio of the refractive indices. Simply enter three known values to automatically obtain the fourth.

Snell's law, also known as Snell-Descartes law, describes the behavior of light when crossing the boundary between two transparent materials. The formula n₁ sin θ₁ = n₂ sin θ₂ shows that the product of the refractive index and the sine of the angle is constant. When light passes from a less refractive medium (lower n) to a more refractive one (higher n), it bends toward the normal (the perpendicular line to the surface). Otherwise, it bends away. If the calculated refraction angle exceeds 90°, total internal reflection occurs, and the calculator indicates this phenomenon. Additionally, the tool calculates the critical angle, which is the angle of incidence beyond which all light is internally reflected.

Use this calculator in practical situations such as designing lenses, optical fibers, prisms, or lighting systems. For example, when sizing an optical fiber, it is essential to know the critical angle to ensure efficient light transmission. In ophthalmology, Snell's law explains vision correction with glasses. In meteorology, it helps understand rainbows and mirages. The calculator is also useful for solving lab problems, such as measuring the refractive index of an unknown material from measured angles. Remember that Snell's law assumes isotropic and homogeneous media; in crystals or anisotropic media, the behavior may be more complex.

Cautions: verify that angles are in degrees or radians and use the correct unit. The calculator assumes light travels from medium 1 to medium 2. If you reverse the media, the angles of incidence and refraction swap roles. For angles very close to 90°, small measurement errors can cause large variations in the result. Note that Snell's law does not apply to opaque or absorbing materials. In problems with multiple layers, apply the law sequentially. The calculator does not consider polarization or wavelength effects; for chromatic dispersion, use the specific refractive index for each color.