Question

Do the laws of reflection hold true in the case of irregular reflection? Explain.

Answer 1

If by “the law of reflection” you mean “angle of incidence equals angle of reflection” - then no, it does not.
That is merely a “rule of thumb” for very shiny surfaces like mirrors. (“Specular reflection” - speculum being latin for “mirror”.)
Diffuse reflection(irregular reflection) follows “Lambert’s law” - which is also an approximation - saying that the amount of light reflected (equally in all directions) depends on the cosine of the angle of incidence of the light to the normal at each point on the surface.
However, just as the “law of reflection” only works for idealized perfect mirrors - “Lamberts’ law” only works for surfaces like plaster that are idealized lambertian reflectors.
Real world materials like metals reflect light in a cone who’s centerline follows the “angle of incidence equals angle of reflection” law - but with some dispersion of the light. This results in “fuzzy reflections” in less than perfectly polished surfaces. Outside of that cone, they are experiencing lamberts’ law.
But it can get even more complicated than that. Materials like gold reflect some colors more strongly than others - and materials like copper can even shift the color of the incoming light.
Then you get to hybrid materials like oil floating on water - where there is a mixture of reflection and refraction going on…that makes for even more complexity. If you think of metal that’s been wiped with oil - you can imagine the complications involved.
Very rough materials can approximate a lambertian reflector at a distance, but exhibit specular reflection close-up. Subtly textured plastics are a great example of this. Perfectly smooth plastic is highly specular - but as it gets rougher, the “micro geometry” reflects in a wide range of directions - and averages out to a lambertian reflector.
Then you get things like a music CD or a DVD where the microtexture is so small that it’s close to the wavelengths of the light itself. That makes it reflect different colors at different angles - and splits white light into a rainbow just like a prism.
Lighting is COMPLICATED.
Lots of the so-called “laws of physics” are like that though - they are true at some scales and with idealised materials that don’t exist…but fail in real world situations. The laws of friction and anything involving the concept of temperature or pressure are good examples of that.