Snell's Law of Refraction

Also known as law of refraction · n₁sinθ₁ = n₂sinθ₂

n_1 \sin\theta_1 = n_2 \sin\theta_2

n₁ =

θ₁ =

n₂ =

θ₂ =

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Light crossing into a denser medium slows down, and to keep its wavefronts connected it must bend toward the normal — by exactly the amount that keeps n sin θ constant. A ray entering water (n = 1.333) from air at 45° refracts to arcsin(sin 45°/1.333) ≈ 32°, which is why a pool's floor looks shallower than it is and a straw appears kinked at the surface.

Run the light the other way, from dense to thin, and Snell's law eventually fails to give an answer: past the critical angle the sine would exceed 1 and the ray reflects totally instead — the trick that traps light inside optical fibers.

Snell's Law of Refraction

n_1 \sin\theta_1 = n_2 \sin\theta_2

Where

$n_1$ = Index of refraction (medium 1)
$\theta_1$ = Angle of incidence
$n_2$ = Index of refraction (medium 2)
$\theta_2$ = Angle of refraction

Missing one of these? Work it out first, then come back

Index of refraction (medium 1) — Index of Refraction (n = c/v), Apparent Depth
Angle of incidence — Critical Angle for Total Internal Reflection, Brewster's Angle
Index of refraction (medium 2) — Index of Refraction (n = c/v), Apparent Depth
Angle of refraction — Critical Angle for Total Internal Reflection, Brewster's Angle

Part of this formula set

Refraction and total internal reflection

5 formulasSnell's law and the refractive index, with the critical angle, Brewster's angle and apparent depth that follow from bending light at a boundary.