Optics
Apparent depth (flat interface)
Refraction at a flat interface makes a submerged object look shallower (apparent depth = real depth · n₂/n₁).
Apparent depth (flat interface) — interactive Optics simulation. Refraction at a flat interface makes a submerged object look shallower (apparent depth = real depth · n₂/n₁).
Apparent depth
Refraction at a flat interface makes a submerged object look shallower (apparent depth = real depth · n₂/n₁).
Rays from an underwater object bend toward the normal when exiting to air, so the eye traces them back to a shallower apparent position. Apparent depth scales as real depth × n_water/n_air, which is why a pool looks shallower than it is.
- n₁ sin θ₁ = n₂ sin θ₂
- Shallower apparent depth
Investigation brief
Plan the question before you open the lab
The brief mirrors the prerendered page: driving question, competing predictions, variable roles, governing laws, setup, analysis and extension prompts remain visible and in this order.
Driving question
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?
Predictions to weigh
- 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.
Variable roles
What you set:
- True depth d_o (cm)
What you measure:
- Apparent depth d_i (cm)
How the investigation runs
- 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.
Governing equation
Apparent Depth (Paraxial Approximation) — n₁·sinθ₁ = n₂·sinθ₂
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.
What the printable worksheet asks students to work out
- 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.
Where this shows up beyond the lab
- 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.
- AP Physics 2 — Unit 13: Geometric Optics
- General High School Physics — Light & optics
- NGSS High School Physics — Wave properties
- Welcome to Apparent Depth
- Select the object
- Press Play
- Object looks shallower
- Open the Properties panel
- You did it!
Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.