Do perpendicular lights interfere on a surface? In the following experiment, we have an observer looking at a material illuminated by a light.
Imagine that the lights are similar to a laser (coherent?) so that all of the photons follow the direction of the coloured lines, and the observers have to be in the correct place on the diagram to see the material take on that colour.
When the lights are toggled on and off do the observers notice any difference in the colour or intensity of their lights? Is there any mixing inside of the material?
(There are quite a lot of duplicate questions, but almost all of them talk about lights crossing in space/air/vacuum, whereas I'm interested in them both reflecting from the same point, and if that makes any difference.)


 A: The light needs to be mutually coherent to produce interference. Two separate light sources (as shown) are in generally not mutually coherent.
Now, let's assume the two light sources in the diagrams are produced by the some original source of coherent light that was split and redirected to illuminate the surface as shown in the diagrams. Then there would be interference. The light would produce fringes that are perpendicular to the difference in the propagation vectors of the two light beams.
The light can now be reflected from the surface. There's two types of reflection: specular reflection and diffuse reflection. Specular reflection is what one gets with a mirror. It would cause the light from the two sources to be separated again. Hence, no more interference.
Diffuse reflection is what you see coming from any illuminated surface. It can be seen from all directions. Since the interference fringes cause a variation in illumination on the surface, these fringes can be seen from any direction as a result of the diffuse reflection.
A: Imagine the surface was a mirror. If you stood on one side and viewed the reflection of the blue light, it would be blue. If you stood at the other location and viewed the reflection of the red light, it would be red. They would not mix at the surface of the mirror, even if the two reflection points were at the same exact spot.
A: In QED and even in CED the two sources are considered (by Maxwell equations) as one source; it is just not point-like, but distributed in space. Now, the pattern observed at a point $\vec{r}$ at a time $t$ is the square of the sum of fields from the source parts. Depending on the source parts radiation correlations, we may obtain quite different "interference" (=resulting) patterns.
A: Ok here is an advanced explanation but it is fairly easy to follow.  Firstly the word "interference" is from like 200 years ago but we still use it today because it is very good at getting across the basics.  In truth 2 photons never interfere with each other or cancel as that would be violation of conservation of energy .... this is taught in Quantum Optics.  Many famous scientists like Dirac and Feynman (and probably Einstein) knew/stated that every photon determines its own path.
For your experiment with lasers (coherent light) another phenomenon comes into play ...it's called laser speckle. Even with one laser shining you will observe a speckley pattern on the surface .... we say this is due to "interference" (which is kinda wrong because it implies cancelling) but in fact what is happening is that the rough surface has distances from the laser that are good for pathways (close to integer wavelength of light distance ) for light (bright spots) ... and paths that are not probable, dark spots (close to .5 wavelength distances).
When we have 2 lasers we just get 2 speckle patterns overlapping ... which kind of averages to reduce the speckle somewhat.  If one laser was split as in the answer above there's no averaging of the speckle as the light is more coherent than if 2 independent sources were used.
All of the above assumes a rough surface like paper .... for a mirror everything is independent ... also a little dangerous as you are observing the last directly in your eye!
