An expert archer tries to shoot an arrow into a target lying at the bottom of a shallow pool. even though the water does not change the direction of the arrow, the archer misses the mark by several inches. what interaction of light and matter caused the archer to miss the target?

The water causes diffraction of the light so that the light rays get bent for an image in the water so that could throw off the archer in hitting the target

The archer misses his target due to the phenomenon of diffraction. During diffraction, light waves bend as they travel from one medium to another due to the difference of densities of the two mediums. Therefore, when one observes the position of an object underwater from above water, the object is actually in a different position than where it seems to be.
The phenomenon of diffraction can easily be demonstrated by dipping a pencil in a glass of water and looking at it from the side. The pencil seems bent, and this is a result of diffraction.