Snell's Law Calculator

Enter any 3 values to calculate the 4th.

Incident Refractive Index (n₁)

Index

Incident Angle (θ₁)

deg (°)

Refracted Refractive Index (n₂)

Index

Refracted Angle (θ₂)

deg (°)

Result

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How it works?

Snell's Law describes how light bends (refracts) when passing from one medium to another with a different refractive index. Depending on which variables you know, the formula can be rearranged to solve for any missing parameter.

Calculating Incident Angle ($\theta_1$)

To find the incident angle, you need the refractive indices of both media and the refracted angle.

$$ \theta_1 = \sin^{-1} \left( \frac{n_2}{n_1} \cdot \sin(\theta_2) \right) $$

Calculating Refracted Angle ($\theta_2$)

To find the angle at which light exits the interface, rearrange the formula to solve for $\theta_2$.

$$ \theta_2 = \sin^{-1} \left( \frac{n_1}{n_2} \cdot \sin(\theta_1) \right) $$

Calculating Incident Index ($n_1$)

If you know the path of the light (both angles) and the target material's index, you can determine the index of the starting medium.

$$ n_1 = n_2 \cdot \frac{\sin(\theta_2)}{\sin(\theta_1)} $$

Calculating Refracted Index ($n_2$)

This is commonly used to identify unknown materials by measuring how much they bend light from a known source (like Air).

$$ n_2 = n_1 \cdot \frac{\sin(\theta_1)}{\sin(\theta_2)} $$

Why is Snell's Law important?

Snell's Law is the foundational equation for geometrical optics. It quantifies how light rays bend when moving between materials of different densities (Refractive Index). This bending is the mechanism behind lenses, prisms, and optical fibers.

1. Fiber Optics & TIR

Snell's Law allows us to calculate the Critical Angle. If light hits the boundary between core and cladding at an angle steeper than this critical limit, it doesn't refract out—it reflects back in. This Total Internal Reflection (TIR) is what keeps data inside fiber optic cables over long distances.

2. Optical Lens Design

Every camera, microscope, and telescope relies on this formula. By knowing the refractive index of glass (n ≈ 1.5), optical engineers calculate the exact curvature needed to bend light rays to a precise focal point, correcting for aberrations.

3. Prisms & Dispersion

Refractive index actually changes slightly depending on the wavelength (color) of light. Snell's law explains why a prism separates white light into a rainbow: blue light refracts at a sharper angle than red light due to this dispersion.

4. Mirages

A mirage on a hot road is Snell's Law in action. As air heats up near the asphalt, its density (and index) decreases. Light from the sky bends gradually as it moves through these temperature layers until it refracts upward into your eye.

Deep Dive Article Snell's Law: Why Light Bends & How We Predict It

Explore the history, the derivation, and the complete physics behind refraction in our comprehensive guide.

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