Storyboard

Electromagnetic (EM) radiation is the most information-rich sensory channel: it covers 20 orders of magnitude in frequency, from radio waves (f 10 Hz) to gamma rays (f 10² Hz). Biological eyes primarily access the visible range (380780 nm), although many species detect UV (insects, birds), near-infrared (pit snakes), or thermal infrared (some fish, vampires).

The photon energy E = hf determines which photons can trigger photochemical reactions in photoreceptors: in the human eye, opsins absorb photons in the visible (E 2.53.5 eV). A UV photon has too much energy (cell damage); a thermal infrared photon (E << 0.1 eV) is insufficient to activate the photochemicals of visual photoreceptors, which is why we do not see heat directly.

Planck and Wien's law explain the spectrum of the sun (T 5778 K, _max 500 nm) and the human body (T 310 K, _max 9.5 m): the eye evolved sensitive to the sun's peak; pit snakes and infrared drones capture radiation from the human body. The atmospheric window at 814 m coincides with the emission maximum of warm-blooded animals.

The Beer-Lambert law I = I·exp(-_a·x) governs the absorption of light in tissues, water, and atmospheres. In water, _a is minimal in the blue-green ( 480 nm), explaining why the underwater vision of fish is blue-shifted. The human eyeball has very high _a for UV (retinal protection) and low for visible.

Fraunhofer diffraction sets the resolution of any eye: the pupil of diameter D acts as a circular aperture, producing the Airy pattern on the retina. Airy's disk has radius 1.22/D: at D = 3 mm and = 550 nm, the angular minimum is 2×10 rad, which coincides with the separation of the foveal cones (25 m with focus at 17 mm). This is evidence that the eye operates at the diffraction limit.

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