Light interaction: interaction of light waves

Question

First of all, I would like to apologise for my English and I hope my question will be clear (even if I guess it is a quite basic question).

Let's assume a person is in a closed room lighted by a light bulb. This person is looking at a white wall. The other wall are painted with different colours.

The light bounce on every wall even if lots of the photon are absorbed by these walls.

If we consider the geometrical model of light I understand that the person will clearly see the wall in front of him and assuming light rays do not interact with each other he will just (only be able) to see the wall in front of him, i.e. (light rays in his cone of vision).

If we now consider wave optics, I do not understand why the light waves reflected by the wall the person is looking at do not interact with the light waves reflected by the three other wall. If it was the case, how is is possible that we only see the wall in front of us (or the person can see really accurately an object placed in front of the wall) ?

Thank you for your help.

Answer 1

The light reflected from the white wall and entering your eyes does interfere with the light reflected from other walls, but this interference happens only in the areas where the light waves actually overlap, and it does not change the light reflected from the white wall once it passed these areas of interference.

This is due to the principle of superposition, which, in application to this case, says that the light entering your eyes is equal to the sum of lights reflected from different walls, if acting alone.

For example, if the light reflected from other walls was not reaching your eyes at all, you would see just the unmodified light reflected from the white wall in front of you, although that light does interfere with the light from other walls in the areas outside your eyes.

In reality, some light reflected from other walls may reach your eyes, for instance, through the secondary reflections from the white wall, and this could indeed change your perception of the white wall color, but this would be due to the direct effect of that other light on your eyes - not because it modified the light originally reflected from the white wall.

Answer 2

Maxwell’s equations (the equations governing classical electrodynamics) are linear, meaning that light waves don’t interact just when they cross each other. Nonlinearities can occur from interaction with a medium (like in air or glass), but these are rather weak, and you wouldn’t see them with the intensity of room light. Since the air in a room is almost entirely linear to light propagation, and there are typically no gradients of refractive index (as you might see in a mirage, for example), the light won’t change direction as it travels. Thus, you only see light which originates from in front of your eyes, and you only see the wall you’re looking at.