• Snell's Window pixel-art physics poster, Plate 025

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Snell's Window

Plate 025 Physics Poster

\[n_1 \sin\theta_1 = n_2 \sin\theta_2\]
$19.99 USD
$19.99 USD
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Plate 25 speaks for itself: “The whole sky, through a 97° hole.”

The Physics

Looking up from under water, the whole hemisphere of sky is squeezed into a circle bounded by the critical angle. Outside it you see total internal reflection of the water below.

θ_c = arcsin(1/n)

  • θ_c: critical angle, °
  • n: refractive index of water, dimensionless

n = 1.333: θ_c ≈ 48.6°, window 97.2°.

Sources

  • E. Hecht, Optics, 5th ed., §4.7.

On the poster

Plate 025, “Snell's Window”: the pixel-art plate with its slogan “The whole sky, through a 97° hole.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.

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The physics

Equations

\[n_1 \sin\theta_1 = n_2 \sin\theta_2\]
\[\theta_c = \arcsin\!\left(\frac{n_2}{n_1}\right) = \arcsin\!\left(\frac{1}{n}\right)\]
\[n = 1.333:\ \theta_c \approx 48.6^\circ,\ \ 2\theta_c \approx 97.2^\circ\ \text{window}\]
SymbolMeaningUnit
\(n_1\) refractive index of the incident medium (water) \(\mathrm{1}\)
\(n_2\) refractive index of the second medium (air ≈ 1) \(\mathrm{1}\)
\(n\) refractive index of water relative to air \(\mathrm{1}\)
\(\theta_1, \theta_2\) angles from the surface normal \(\mathrm{°}\)
\(\theta_c\) critical angle for total internal reflection \(\mathrm{°}\)

Sources

  1. E. Hecht, Optics, 5th ed. (Pearson, 2017), §4.7 Total internal reflection
  2. Hale & Querry (1973) Optical constants of water in the 200-nm to 200-μm wavelength region, Appl. Opt. 12, 555

Field notes

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