Optics

Snell's Law

n1sin⁡θ1=n2sin⁡θ2n_1 \sin\theta_1 = n_2 \sin\theta_2

Describes how light bends when passing between media with different refractive indices.

Variables

n1
Refractive index of medium 1
Allowed values: 1 or more
unitless
θ1
Angle in medium 1
°
n2
Refractive index of medium 2
Allowed values: 1 or more
unitless
θ2
Angle in medium 2
°

Derivation

Derived from Fermat's principle of least time or from the wave nature of light at boundaries.

Your notes

0/5000

Check value

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  • n1 = 1.5 (Refractive index of medium 1)
  • θ1 = 3 ° (Angle in medium 1)
  • n2 = 3.5 (Refractive index of medium 2)

Result: θ2 = 1.2852347 °

Other optics formulas with the same quantities

  • Brewster's Angle (Polarization) shares Refractive index of medium 1, Refractive index of medium 2

Where this formula is listed

Common questions

What is the Snell's Law formula?

Snell's Law is written n₁ sin θ₁ = n₂ sin θ₂. Describes how light bends when passing between media with different refractive indices. It belongs to Optics, under Refraction.

What are the units in n₁ sin θ₁ = n₂ sin θ₂?

In SI units, n₁ is refractive index of medium 1 (dimensionless); θ₁ is angle in medium 1, measured in °; n₂ is refractive index of medium 2 (dimensionless); θ₂ is angle in medium 2, measured in °.

How is the Snell's Law formula derived?

Derived from Fermat's principle of least time or from the wave nature of light at boundaries. The result is n₁ sin θ₁ = n₂ sin θ₂.