Formulas & tables/Physics/Optics/Law of refraction (Snell's law)

Law of refraction (Snell's law)

sin⁡αsin⁡β=n2n1\dfrac{\sin\alpha}{\sin\beta}=\dfrac{n_2}{n_1}

Result unit: — (dimensionless ratio)

What it describes

Snell's law — describes the refraction of light at the boundary between media with different refractive indices.

Symbols

α\alpha
angle of incidence
[°]
β\beta
angle of refraction
[°]
n1,n2n_1, n_2
refractive indices of the media

Where it comes from

When light enters an optically denser medium (higher nn) it bends toward the normal and slows down. When passing into a less dense medium, total internal reflection may occur.

When to use it

Lenses, prisms, optical fibers. nn of air ≈1\approx1, of water ≈1.33\approx1.33.

Example

Light passes from air (n1=1n_1=1) into water (n2=1.33n_2=1.33) at an angle of 30°. Calculate the angle of refraction.
Substitutionsin⁡β=sin⁡30∘⋅11.33\sin\beta=\dfrac{\sin 30^\circ\cdot1}{1.33}.
Resultsin⁡β≈0.376⇒β≈22∘\sin\beta\approx0.376\Rightarrow\beta\approx22^\circ.

Related formulas

Lens equation Speed of an EM wave

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