Deeper than it Looks

Why it matters

Every swimming pool is lying to you. The floor you see is NOT where the floor is — and spear-fishers have known it for ten thousand years.

The idea in plain words

The pool's lie, quantified. Tap each term.

μ = real depth ÷ apparent depth

A tank looks 30 cm deep but is really 40 cm deep. Find μ of the liquid.

μ = 1.33 — it's water

• m: real — where the object actually is
• m: apparent — where refraction makes it SEEM to be — always shallower
• no unit: μ — refractive index of the liquid — the shrink factor
• μ = real ÷ apparent = 40 ÷ 30

Predict first

A coin lies under 2 m of water (μ = 1.33). How deep does it LOOK from above?

Rays from the coin bend AWAY from the normal as they leave the water; your eye traces them back to a raised image: apparent = real ÷ μ = 2 ÷ 1.33 ≈ 1.5 m.

• About 1.5 m — shallower than it is — correct
• Exactly 2 m — water is transparent
• About 2.7 m — deeper than it is

What you do

Slide the real depth and swap the liquid. Watch the ghost coin hover above the real one — denser liquid, bigger lie.

Check yourself

A stick half in water looks bent because…

The submerged part's image is raised by refraction, so the stick appears kinked at the waterline.

The apparent depth of a pool is 3 m. Its real depth is…

real = apparent × μ = 3 × 1.33 ≈ 4 m. Pools are always deeper than they look — a real safety fact.

In which liquid would the coin look MOST raised?

apparent = real/μ — bigger μ, smaller apparent depth, bigger lift. Depth scales both together.

• light from the underwater part refracts at the surface — correct
• water pressure bends the stick slightly
• water magnifies things
• about 4 m — correct
• about 2.25 m
• exactly 3 m
• The one with the highest μ — correct
• The clearest one
• The deepest one