Question

An expert archer tried to shoot an arrow into a target lying at the bottom of a shallow pool. Even though the water did not change the direction of the arrow, the archer missed the mark by several inches. Which interaction between light and matter caused the archer to miss the target?

Answer 1

The interaction that caused the archer to miss was probably refraction.

Answer 2

Refraction is indeed the reason the archer missed.  When light passes from inside the water to the air outside, it bends causing the image of the target to appear to someone outside the pool to be in a different position.  This is due ultimately to the difference of electric permittivity between water and air.