Pool Depth
A swimming pool always looks shallower than it is — and the further away you stand, the shallower it looks. Find how deep the bottom appears from where you stand, and drag your eye around the pool to watch the illusion change.
Why Does Water Look Shallow?
Your brain assumes light travels in straight lines. Light from the bottom of a pool bends away from the normal as it leaves the water, so when you trace it back in a straight line it seems to come from a point higher up. Looking straight down, everything seems to be at 1/n ≈ 75% of its real depth.
Seen at a slant the effect is much stronger: from the far side of a pool the deep end can look only knee-deep. That is why people misjudge depths when they jump in, and why a spear fisher must aim below the fish they see.
Side View
to scaleApparent Depth Formulas
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Worked Techniques
For nearly vertical rays, tan and sin are almost equal, so Snell’s law turns directly into the familiar depth ratio.
The light leaves the water at one point x on the surface. Its two straight pieces must cover the horizontal distance s, and Snell’s law links their angles; the calculator finds x by narrowing it down step by step.
Seen from under water, the whole sky is squeezed into a bright circle of 97° across. Outside it, the surface works as a mirror reflecting the pool floor.
Sources & Verification
- E. Hecht, Optics, 5th ed., Pearson, 2017 — Ch. 4 (The Propagation of Light) and Ch. 5 (Geometrical Optics).