Why does a straight stick seem bent when part of it is pushed into a swimming pool?

John Campbell, a physicist at the University of Canterbury, responded.

Because when a ray of light passes from water into air the light ray speeds up.

This was explained to me at school through the analogy of a long column of soldiers marching several abreast. (In those days all males at school were in the military cadets and 18 year-olds had compulsory military training so we were all familiar with marching.) Their maximum speed is when they are marching along a smooth road. If the column marches in a ploughed field it is harder marching so their stepping distance is smaller than on the smooth road. Because they march at the same rate of steps per minute they travel slower in the field.

If the ray meets the interface between the transparent material and the air other than at right angles then the ray changes direction. In the marching analogy the soldier on one side of the column will exit from the plowed field onto the smooth road, and therefore speed up, before the person beside him does hence the whole column will pivot at that point and change direction.

So the light rays from the part of the stick in the water change direction on leaving the water and appear to our eyes to come from a different direction to the light rays from the part of the stick in air. The stick appears to bend at the surface of the water.

The new direction depends on the the angle at which the ray meets the interface and the ratio of the speeds. You can test this by partially immersing a pencil in a glass of water and in a glass of cooking oil. The apparent bending of the pencil will be different because light travels in water at three-quarters of its speed in air while in oil it travels at about two-thirds of its speed in air.