Snell's Law Calculator

Snell's law describes how light bends when entering a new medium.

How the Math Works

Snell's Law describes how light bends when moving between different media. The formula n₁ sin θ₁ = n₂ sin θ₂ relates the refractive indices (n₁ and n₂) of two media to the angles of incidence (θ₁) and refraction (θ₂). To find the refraction angle, rearrange the equation to θ₂ = arcsin[(n₁/n₂) sin θ₁]. This calculation requires knowing the refractive indices of both materials and the incoming angle, then applying trigonometric functions to solve for the unknown angle.

Practical Applications

This calculation is essential in designing optical instruments like lenses, prisms, and fiber optic cables. Engineers use Snell's Law to determine light paths in camera systems, telescopes, and laser equipment. In physics labs, students apply it to verify how different materials affect light behavior. Manufacturers rely on these calculations to optimize LED displays, microscope objectives, and underwater imaging systems where light transitions between air, water, and glass.

Day-to-Day Use

You encounter Snell's Law in daily life whenever light moves through different materials. It explains why a straw appears bent in a glass of water, why you squint differently when looking at objects through a window, and how corrective lenses reshape light entering your eyes. It also governs the functionality of smartphone cameras, car headlights, and even the way rainbows form after rain - making this fundamental optical principle essential to technologies we use every day.

Worked example

Air (1) → water (1.33) at 30° → 22.1°.

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