Snell's Law, also known as the law of refraction, describes the relationship between the angles of incidence and refraction when light passes through a boundary between two different isotropic media, such as air and glass.
Snell's Law states that the ratio of the sines of the angles of incidence and refraction is equivalent to the ratio of phase velocities (v1 / v2) in the two media, or equivalently, to the reciprocal of the ratio of the indices of refraction (n2 / n1).
Mathematically, it is expressed as:
n₁ sin θ₁ = n₂ sin θ₂
Where:
- n₁ is the index of refraction of the first medium
- θ₁ is the angle of incidence (the angle between the incident ray and the normal to the surface)
- n₂ is the index of refraction of the second medium
- θ₂ is the angle of refraction (the angle between the refracted ray and the normal to the surface)
In simpler terms: Snell's Law explains how much light bends when it goes from one material (like air) to another (like water or glass), based on the properties of those materials. The bending (refraction) occurs due to the change in the speed of light as it transitions between media with different refractive indices.
Key Implications and Applications:
- Understanding Lenses: Snell's Law is fundamental to understanding how lenses focus light, which is crucial in applications like eyeglasses, cameras, and telescopes.
- Optical Fibers: The principle of total internal reflection, which is based on Snell's Law, is used in optical fibers to guide light signals over long distances.
- Atmospheric Refraction: Snell's Law explains why the sun appears to be above the horizon even when it is geometrically below it due to the refraction of light through the atmosphere.
- Prisms: Snell's law explains how a prism separates white light into its constituent colors.
Example:
Imagine a ray of light traveling from air (n₁ ≈ 1) into water (n₂ ≈ 1.33). If the angle of incidence (θ₁) is 30 degrees, we can use Snell's Law to find the angle of refraction (θ₂):
1 sin(30°) = 1.33 sin(θ₂)
sin(θ₂) = sin(30°) / 1.33 ≈ 0.376
θ₂ ≈ arcsin(0.376) ≈ 22.1 degrees
This shows that the light ray bends towards the normal (the imaginary line perpendicular to the surface) when entering a medium with a higher refractive index (water).
In conclusion, Snell's Law is a cornerstone of geometrical optics, providing a quantitative description of refraction and its dependence on the refractive indices of the involved media and the angle of incidence.
