Snell's Law Calculator

Snell's Law (also known as the law of refraction) relates the angles and refractive indices at an interface:

$$n_1 \sin\theta_1 = n_2 \sin\theta_2$$

Solving for the angle of refraction:

$$\theta_2 = \arcsin\left(\frac{n_1 \sin\theta_1}{n_2}\right)$$

Where:

• n₁ — refractive index of the incident medium
• θ₁ — angle of incidence (measured from the surface normal)
• n₂ — refractive index of the refracted medium
• θ₂ — angle of refraction

When light travels from a denser medium to a less dense medium (n₁ > n₂), the refracted ray bends away from the normal (θ₂ > θ₁). At a special angle called the critical angle, the refracted ray grazes along the interface (θ₂ = 90°):

$$\theta_c = \arcsin\left(\frac{n_2}{n_1}\right)$$

For angles of incidence greater than θ_c, no refraction occurs — all light is reflected back into the denser medium. This is total internal reflection (TIR), and it is the operating principle of optical fibers, which trap light inside a glass core by ensuring the incidence angle always exceeds the critical angle.

TIR only occurs when n₁ > n₂ (light going from a denser to a less dense medium). When n₁ < n₂, refraction always occurs and the light bends toward the normal.

Common refractive indices: air ≈ 1.000, water ≈ 1.333, glass ≈ 1.5–1.9, diamond ≈ 2.417. Diamond's extremely high refractive index gives a critical angle of only 24.4°, causing extensive TIR and the characteristic sparkle.

The angle of refraction θ₂ shows the direction of the transmitted ray in the second medium. If the calculator returns −1 for θ₂, total internal reflection occurs and no refracted ray exists.

The critical angle is displayed only when n₁ > n₂ (TIR is possible). It is the maximum angle of incidence for which refraction still occurs. The TIR status tells you clearly whether total internal reflection is happening at the given angle.