Apparent Depth

d' = \frac{d}{n}

d′ =

d =

n =

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Learning zone

Rays leaving a submerged object bend away from the normal as they exit the water, and your brain traces them back in straight lines to a shallower virtual image. For water, n = 1.333, so everything appears at three-quarters of its true depth — a pool that looks 1.5 m deep is actually 2 m. Spear fishers learn to aim below the fish they see; the fish, looking up, sees the world compressed the opposite way into a 97°-wide circle called Snell's window.

Apparent Depth

d' = \frac{d}{n}

Where

$d'$ = Apparent depth
$d$ = Real depth
$n$ = Index of refraction

Missing one of these? Work it out first, then come back

Apparent depth — Hydrostatic Pressure (P = ρgh), Speed, Distance & Time
Real depth — Hydrostatic Pressure (P = ρgh), Speed, Distance & Time
Index of refraction — Index of Refraction (n = c/v), Snell's Law of Refraction

Part of this formula set

Refraction and total internal reflection

5 formulasSnell's law and the refractive index, with the critical angle, Brewster's angle and apparent depth that follow from bending light at a boundary.