The Straw Is Intact: Lacuna and Horn on Refraction

In the small hours, the glass cast a pale oval across the table. Lacuna lowered a straw into the water and held it still.

“Intact above the surface. Displaced below it,” Lacuna said. “Why does the eye accept a break that my fingers can disprove?”

Horn leaned back far enough to see the apparent kink. “Because the light changes direction on its way out. Your eye doesn't get the route it took. Just the direction it arrived from.”

“So it reconstructs the route incorrectly.”

“Straight back, when there was a bend. Light travels more slowly in water than in air. At the boundary, that speed change bends a ray crossing at an angle. Coming out of water into air, it bends away from the normal.”

Lacuna glanced up. “Define normal before this becomes a judgment.”

“A line perpendicular to the surface. Not a standard of behaviour.” Horn pointed down through the water. “Snell's law: n₁ sin θ₁ = n₂ sin θ₂. Each n is the refractive index of a medium—how much slower light travels there than in a vacuum. The angles are measured from that perpendicular line.”

“And straight along the perpendicular?”

“The speed still changes. The direction doesn't.”

Lacuna shifted to one side. The submerged section seemed to move without troubling the water.

“An unreliable witness,” Lacuna said.

“Reliable about where the light came from last. Less useful about where it started.” Horn rested a hand beside the glass. “A flat water surface does this too, without the extra complications of the glass. Look down at a fish from above and it appears shallower than it really is. Light leaves the fish, bends at the surface, reaches you. Trace that last stretch backward in a straight line and you place the fish too high.”

“So a spearfisher standing above the water must aim below the fish as seen.”

“Yes. Below the image, toward the actual fish. The spear doesn't follow the light's bent path. How far below depends on the viewing angle and depth. There's no universal correction you can mark on your thumb.”

“That would have been convenient.”

“The sea declines most convenient arrangements.”

Lacuna lifted the straw clear. Its two apparent pieces became one again.

“No damage,” Lacuna said. “Only a faulty reconstruction.”

Horn nudged the glass away from the table's edge. “Still worth correcting before you act on it.”