Why does an iron rod, partially held in water, appear to be deformed?

Answer

Dear Makaya,

This is due to the refraction of light rays at the transition between media of different refractive index.

As you may have seen in Physics classes, the concept of a refractive index is introduced to describe the propagation of light through materials. After all, the phase speed of light is different in different materials. In vacuum it is equal to the speed of light c. The refractive index n of a given material is then defined as the ratio of the speed of light c to the phase speed of light in that material v: n = c/v_.

For the air on Earth, the refractive index is approximately equal to 1. Water has a higher refractive index (n_water ≈ 1.3).

You may also have heard of Snellius-Descartes’ law. This determines how a light beam is refracted when transitioning between two media with a different refractive index. As shown in the first figure attached, a ray of light breaks away from the normal to the interface when transitioning from a medium with a high refractive index to one with a lower refractive index.

This now allows us to understand why an object appears bent when submerged in water. In the attachment you see some rays of light that leave the rod, submerged in water, towards the observer. At the surface between the water and the air, these rays of light are refracted, according to Snellius-Descartes’ law. As a result, they will reach the observer at a different angle.

In our perception, however, we forget that the rays of light have followed a curved trajectory and they seem to have come straight at us, departing from another point; a point (y in the figure) that is higher than the point where the rod actually is (x in the figure). This reasoning can be repeated for each point of the rod and therefore explains why this rod seems to bend under water towards the water surface.

The same effect occurs when we see a fish swimming in a pond. The light rays are also now refracted at the water surface. An inexperienced fisherman is not aware of this and will think that the fish is swimming in line with the beam of light that is coming towards him. This makes the fish appear to be higher than it really is.