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Apparent Depth (Refraction) Calculator

Enter the real depth and refractive indices to find the apparent depth.

How it is calculated

For viewing roughly straight down through a flat surface the tool uses apparent = real × (n_observer / n_medium) and shift = real − apparent. Real depth is the true depth of the object, in metres (results are labelled m). Medium index is the refractive index of the material the object is in (water is about 1.333) and Observer index is the index where the eye is (air is about 1). If Observer index is left empty, or is zero or negative, the tool uses 1. The refractive index of the medium must be above zero and the real depth cannot be negative. Both results are rounded to two decimals. A negative shift means the object looks deeper, which happens when the observer is in the denser medium.

Worked example

An object lies 2 m under water (n = 1.333) and you look straight down from air (n = 1). Step 1: Observer index / Medium index = 1 / 1.333 ≈ 0.7502. Step 2: apparent depth = 2 × 0.7502 ≈ 1.50 m. Step 3: shift = 2 − 1.50 = 0.50 m. The object appears at 1.50 m, about half a metre shallower than reality.

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Common mistakes

  • Swapping the two indices: putting water in the observer box makes the object look deeper than it is (2.67 m instead of 1.50 m).
  • Using the formula for a steep viewing angle; it holds only for looking almost straight down, and at shallow angles the error grows.
  • Entering the depth in feet or centimetres; the results are labelled in metres, so convert first.
  • Entering an angle or the speed of light instead of the refractive index; the index is a pure number like 1.333 for water.

About this calculator

When light travels from one medium into another with a different refractive index — such as from water into air — it bends at the boundary, which is why a pool or pond always looks shallower than it actually is when viewed from above. For viewing close to straight down, this can be approximated as apparent depth = real depth × (n2 ÷ n1), where n1 is the refractive index of the medium the object is in (water, ~1.33) and n2 is the medium the observer is in (air, ~1.0), so water's higher index compresses the perceived depth to about 75% of the real value.

This calculator takes the real depth and the two refractive indices and returns the apparent depth an observer would perceive. Physics students studying Snell's law and refraction, divers and spearfishers judging distances underwater, and photographers correcting for the visual distortion of shooting through water use it to understand or predict this everyday optical illusion.

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Comments (1)

  • Editorial team

    The tool goes from real depth to apparent depth, but in the field you usually know the apparent one. Reverse it by hand: real depth is the apparent depth times 1.333 for water seen from air. A pool floor that looks about 1.5 m down is closer to 2 m, so an unmarked end can be deeper than it appears. Treat that as an estimate for near-vertical views only. Have you tried it with liquids other than water, and which index did you use?

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