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We can see physical objects because of reflection of light from the surface of the object.

Does the light incident on an object interfere with the light which is being reflected of its surface? Are there resultant waves produced by this interference?

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Yes. These are generally known as light-induced gratings (and related terminology) and they can be important in a wide variety of contexts.

Here is one example,

enter image description here

from this paper, where the grating that's formed near the surface as the incident and reflected waves interfere is crucial to understand the emission of photoelectrons from the surface of a metal.

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Precisely speaking, we are able to see objects not only because of reflection but rather because of scattering or absorption and reemission.

And yes, all light beams constantly interfere with each other but usually this superposition is not coherent and no stationary interference pattern can be observed.

For example, a laser (coherent light) that is incident on a surface at 90°, a standign wave will occur. For different angles, a pattern like in Emilio Pisanty's answer will occur.

Since the coherence length of e.g. sunlight is shorter than one micrometer, these effects are strongly suppressed.

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Yes, there is interference of the incident and the reflected light wave so that a standing wave is produced. This has first been demonstrated by Otto Wiener in 1890, who experimentally found a stripe pattern in a photographic plate that was put on the reflecting surface with a very small inclination. See: Otto Wiener, “Stehende Lichtwellen und die Schwingungsrichtung polarisirten Lichtes,” Ann. Phys. Chem. 38 (1890), 203-243. This also showed that the blackening of the plate ocurred at the maxima of the electric field strength. A description in English is found here.

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