Apparent Depth: Why a Pool Looks Shallower Than It Is
1 · Predict
Looking straight down into water from air, an object at the bottom appears shallower than its true depth. Does this apparent-depth effect scale in direct proportion to the true depth?
- Yes — apparent depth is always a fixed fraction of true depth, set by the ratio of the two refractive indices.
- The apparent depth stays the same regardless of true depth.
- There's no simple relationship between true and apparent depth.
2 · Set Up
- Open the apparent-depth preset and press Reset. Water's index is fixed at n₁ = 1.33 (looking out into air, n₂ = 1.0).
- Enable the apparent-depth readout.
- Set the true depth for each trial and record the apparent depth.
3 · Collect Data
| True depth d_o (cm) | Apparent depth d_i (cm) |
|---|---|
| 20 | |
| 40 | |
| 60 |
Plot apparent depth d_i (y-axis) against true depth d_o (x-axis) for your three trials. Is the line straight through the origin?
4 · Analyze
- For one trial, compute d_i = −d_o·(n₂/n₁) using n₁ = 1.33, n₂ = 1.0. Compare to the table.
- Explain why looking from a denser medium (water) into a less dense one (air) always makes objects appear closer (shallower) than they really are — the n₂/n₁ ratio here is less than 1.
5 · Extend
- If you were underwater looking UP at something in the air above the surface, the ratio would flip (n₁ = 1.0, n₂ = 1.33 from the water side), making things appear farther/deeper than they really are. Explain why the direction you're looking through the interface matters.
- Someone spearfishing needs to aim below where a fish visually appears to be, because of this apparent-depth (really, apparent-position) effect. Explain, using your data, why a fish that looks 1 m deep might actually be considerably deeper.
The Physics Behind This Experiment
Apparent Depth (Paraxial Approximation)
Looking nearly straight down through a flat interface, an object's apparent depth is scaled by the ratio of refractive indices: d_apparent = d_true·(n_viewing/n_object). Denser-to-less-dense viewing (like water to air) makes objects look shallower.