IndexKräfte & FelderMug

Refracta

Snell’s Law Physics

\[n_1\sin\theta_1 = n_2\sin\theta_2\]
$21.99 USD
$21.99 USD
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Why does a straw look broken in a glass of water? Refracta bends the light. Light travels at different speeds in different materials, so it changes direction at a boundary. Snell’s law, n1 sin θ1 = n2 sin θ2, gives the new angle. Lenses, prisms and rainbows all depend on it. Pixel-art black ceramic mug in 11 or 15 oz; equation, symbols and sources in the physics panel below.

Shipping calculated at checkout by destinationMade to order, ships in ~10 days

Details

Size & material11oz · 15oz

Black glossy ceramic mug with a C-handle. Lead- and BPA-free.

  • 11oz: 0.33 l
  • 15oz: 0.44 l
CareDishwasher & microwave safe

Dishwasher safe (top rack) or hand wash. Microwave safe.

ShippingBy destination

Shipping calculated at checkout by destination.

Made to order: about 10 days of production and handling before it ships.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

When light passes into a different material it bends, because its speed changes. The refractive index n is the speed of light in vacuum divided by the speed in the material, and n sin θ is the same on both sides of the boundary.

Refracta changes direction every time she changes medium. She never breaks.

Light travels more slowly in water or glass than in air; the refractive index n measures by how much. When a ray crosses a boundary at an angle, the change of speed bends it, toward the normal going into the slower medium and away from it coming out. Snell's law, on this mug, gives the new angle. Willebrord Snell found it in 1621.

That is why a straw in a glass of water looks broken at the surface: light from the submerged part bends as it leaves the water, and your eye traces it back along a straight line to the wrong place.

Lenses focus light by refraction at curved surfaces. Prisms and raindrops split white light into colours because the index differs slightly from colour to colour. And going from glass into air at a steep enough angle, the ray cannot bend enough to get out at all, and reflects completely, which is how optical fibres carry light.

I BEND. I DON'T BREAK. Refracta just takes the fastest way through.

Equations

\[n_1\sin\theta_1 = n_2\sin\theta_2\]
\[n = \frac{c}{v}\]
SymbolMeaningUnit
\(n_1, n_2\) refractive indices of the first and second medium \(\mathrm{1}\)
\(\theta_1, \theta_2\) angles of the ray from the normal, before and after the boundary \(\mathrm{rad}\)
\(c\) speed of light in vacuum \(\mathrm{m/s}\)
\(v\) speed of light in the medium \(\mathrm{m/s}\)

Sources

  1. HyperPhysics — Refraction of Light
  2. Encyclopaedia Britannica — Snell’s law
  3. Feynman Lectures on Physics Vol. I Ch. 26: Optics: The Principle of Least Time

Source Descartes, R. (1637). La Dioptrique, Discours second (De la réfraction). Published with Discours de la méthode. Leiden: Jan Maire.

Field notes

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