Snell's Law Calculator

Snell's Law, also recognized as the law of refraction, describes the mathematical relationship between the angle of incidence and the angle of refraction when a wave passes through a boundary separating two different isotropic media. The foundational formula is expressed as:

n₁ * sin(a₁) = n₂ * sin(a₂)

Where n₁ represents the refractive index of the initial medium, a₁ is the angle of incidence measured from the normal line, n₂ is the refractive index of the second medium, and a₂ is the angle of refraction. When light travels from a less dense medium into a denser medium (e.g., air to glass), it bends toward the normal line, meaning a₂ is smaller than a₁.

Imagine a light ray traveling through air and striking a flat glass surface at an angle of incidence (a₁) of 30 degrees. The refractive index of air (n₁) is approximately 1.00, and the refractive index of standard crown glass (n₂) is 1.52. To find the angle of refraction (a₂), we apply Snell's Law:

1. Set up the equation: 1.00 * sin(30°) = 1.52 * sin(a₂)

2. Calculate sin(30°), which is 0.50: 1.00 * 0.50 = 1.52 * sin(a₂)

3. Isolate the sine of the second angle: sin(a₂) = 0.50 / 1.52 ≈ 0.3289

4. Take the inverse sine (arcsin) to find the angle: a₂ = arcsin(0.3289) ≈ 19.2 degrees.

Thus, the light ray bends inward, resulting in an angle of refraction of 19.2 degrees.

Always measure angles relative to the normal line (an imaginary line perpendicular to the boundary surface), never relative to the surface itself. Additionally, watch out for total internal reflection: if you calculate a sine value greater than 1 when moving from a high-index to a low-index medium, the wave cannot refract out and will instead reflect entirely inside the material.