• Pixel-art sticker of Trappa, personifying Total Internal Reflection, with the caption "Past My Angle, No Exit."

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Trappa

Total Internal Reflection Physics

\[\sin\theta_c = \frac{n_2}{n_1}\]
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Meet Trappa, who offers no exit: light inside a denser medium that hits the boundary beyond the critical angle, sin θc = n₂/n₁, is fully reflected. That is how optical fibres guide light. For water to air (n = 1.333), the critical angle is about 48.6°. Pixel-art kiss-cut sticker in 2, 3, 4 and 6 inches; equation, symbols and sources in the physics panel below.

Size
Surface

Flat $6 shipping worldwideMade to order, ships in 2–5 business days

Details

Size3″ × 3″

3″ × 3″ kiss-cut sticker.

Shipping

Flat $6 shipping on every order, worldwide, whatever's in it.

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

Meet Trappa, light inside glass or water who, past a certain angle, cannot get out.

When light passes from a denser medium (higher refractive index n₁) to a less dense one (n₂), it bends away from the normal. The steeper the angle of incidence, the more it bends, until at the critical angle θ_c the refracted ray skims along the surface. Beyond θ_c no light is transmitted at all. Every bit is reflected back inside: total internal reflection. The critical angle comes from Snell's law: sin θ_c = n₂/n₁.

For water (n = 1.333) to air, θ_c ≈ 48.6°. A fish looking up sees the whole sky squeezed into a cone of about that half-angle, with reflections of the underwater world beyond it.

Optical fibres guide light over many kilometres by total internal reflection, carrying most internet traffic. Binocular prisms and the sparkle of cut diamonds use it too.

The reflection is total, but a weak evanescent field leaks a tiny distance past the surface. Bring another medium within about a wavelength and light can tunnel across.

Equations

\[\sin\theta_c = \frac{n_2}{n_1}\]
Symbols
SymbolMeaningUnit
\(\theta_c\) critical angle, measured from the normal \(\mathrm{rad}\)
\(n_1\) refractive index of the denser medium —
\(n_2\) refractive index of the less dense medium (n₂ < n₁) —