Chopsticks in Water

Question

When you put chopsticks (or any other object) in a glass cup of water, why do the chopsticks seem curved or bent?
Is it because of the shape of the cup, the water, or the chopsticks itself?

Note:
I'm sorry I currently don't have an image of it. You can try this at home. Just put a pair of chopsticks in a glass of water. If you have an image, please edit this question and put an image in.

Answer 1

Like this:

In all materials, light travels a bit slower (with speed $v$) than their speed $c$ in vacuum. This fraction is called the refractive index or index of refraction $n$:

$$n=\frac{v}{c}$$

In the transition from one material to another, light will bend if they have different $n$.

As this picture shows the general law, called Snell's law, states that:

$$n_a \sin(\theta_a)=n_b \sin(\theta_b)$$

So when going from air (where light moves fast) to water (where light moves slower), we have $n_{air}>n_{water}$, which gives $\sin(\theta_{air})<\sin(\theta_{water}) \Rightarrow \theta_{air}<\theta_{water}$.

So the angle with a vertical line (perpendicular to the surface) in water is bigger than that in air. Therefor the chopsticks look like they bend outwards.

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To see why this is, remember than light has wave behaviour.

Consider an incoming wave from the air reaching the water surface. Like an incoming wave from the sea reaching the beachline. This wave continues, but moves slower in the water than in the air - as the wave from the sea is slowed down over the shore. This GIF here is kind of illustrative: http://en.wikipedia.org/wiki/File:Propagation_du_tsunami_en_profondeur_variable.gif

If the wave comes with an angle, it is slowed down in one end of the wave before the other end of the wave:

That is the reason for the bending.