Quick answer
Apparent depth occurs because light bends when it crosses between materials. An object under water usually appears shallower than its true depth when viewed from air.
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When light passes from water into air, it changes speed and bends at the surface. This bending is called refraction, and it changes the direction from which light seems to reach your eyes. Because your brain assumes light travels in straight lines, a coin, fish, or rock under water appears closer to the surface than it really is.
This effect is called apparent depth, and it matters in swimming, fishing, diving, and optical design.
For viewing nearly straight down into water, the apparent depth is approximately the real depth divided by the refractive index of water. Since water has a refractive index of about 1.33, an object 1.33 m below the surface may appear about 1.00 m deep. The same refraction also causes the bent-straw illusion, where the part of a straw under water looks shifted because light rays from that section bend at the water surface.
Ray diagrams explain the illusion by tracing rays from the real object to the eye, then extending the refracted rays backward to locate the virtual image.
Understanding Physics: Refraction and Apparent Depth
The size of the shift depends strongly on viewing angle. Looking almost straight down gives the simplest result because the rays reach the surface close to the normal. The normal is an imaginary line drawn at right angles to the water surface.
At larger angles, the bending is greater and the apparent position moves sideways as well as upward. This is why a fish seen from the bank can seem to be in a different place from a fish viewed from directly above. A simple depth rule becomes less accurate when the line of sight is steeply slanted.
Ray diagrams are useful because they separate what light really does from what the eye assumes. Start at a point on the object and draw two rays to the surface. Draw the normal at each point where a ray meets the surface.
The rays change direction as they enter the air and then travel to the observer. Extend the outgoing rays backward beneath the surface. Their extensions meet at the virtual image.
No light actually comes from that image position. It is a location created by the brain's straight line interpretation of the incoming rays.
The amount of bending is controlled by refractive index. This number describes how much slower light travels in a material than in empty space. A larger refractive index means light travels more slowly.
Snell's law connects the two refractive indices with the angles measured from the normal. It states that the first refractive index times the sine of the first angle equals the second refractive index times the sine of the second angle.
Students should measure angles from the normal, not from the surface. Mixing up those two reference lines is one of the most common errors in refraction problems.
There is another important effect when light tries to leave water at a very large angle. Beyond a certain angle, light cannot pass into the air at all. Instead, it reflects back into the water.
This is called total internal reflection. A swimmer below the surface can see a bright circular region overhead where light from the sky enters the water.
Outside that region, the water surface acts more like a mirror and can reflect the underwater scene. Optical fibres use the same idea to keep light trapped inside a thin glass core.
Apparent depth has practical limits that matter outside textbook diagrams. Waves make the surface tilt in many directions, so an object can appear to jump or wobble. Murky water scatters light, which makes the object harder to locate accurately.
A person using a spear or reaching for an object underwater must aim below the apparent position when viewing from air. Cameras face the same issue, especially when photographing through an aquarium wall. When solving problems, first identify the direction of travel, draw the normal, label the real object and virtual image, then decide whether the question asks for a depth, an angle, or a position shift.
Key Facts
- Refraction is the bending of light when it crosses a boundary between materials with different refractive indices.
- Snell's law: n1 sin(theta1) = n2 sin(theta2).
- For near-vertical viewing from air into water: apparent depth = real depth / nwater.
- Water has refractive index n ≈ 1.33, while air has refractive index n ≈ 1.00.
- When light goes from water to air, it bends away from the normal because it speeds up.
- A submerged object appears shallower because the eye traces refracted rays backward in straight lines to a virtual image.
Vocabulary
- Refraction
- Refraction is the change in direction of a light ray as it passes between materials where light travels at different speeds.
- Refractive index
- Refractive index is a number that tells how much a material slows light compared with its speed in a vacuum.
- Apparent depth
- Apparent depth is the depth at which an underwater object seems to be located when viewed from above the surface.
- Normal
- The normal is an imaginary line drawn perpendicular to a surface at the point where a light ray meets it.
- Virtual image
- A virtual image is the perceived location of an object formed by extending light rays backward rather than by actual rays meeting there.
Common Mistakes to Avoid
- Using the real depth as the apparent depth, which ignores refraction at the water surface and makes underwater objects seem deeper than they appear.
- Multiplying by the refractive index instead of dividing for near-vertical viewing from air into water, which gives an apparent depth that is too large.
- Drawing the refracted ray bending toward the normal when light goes from water into air, which is wrong because the ray bends away from the normal as it enters the lower-index medium.
- Assuming the object actually moves upward, which is wrong because only its virtual image shifts while the real object stays in the same physical location.
Practice Questions
- 1 A coin is 2.00 m below the surface of a pool. Using nwater = 1.33, find its apparent depth when viewed nearly straight down from air.
- 2 A fish appears to be 0.90 m below the water surface when viewed nearly vertically. Using nwater = 1.33, estimate its real depth.
- 3 Explain why a straw partly in water looks bent at the water surface even though the straw is actually straight.