how is the light reflected by a mirror different to the light reflected by a piece of paper

The difference between how light is reflected by a mirror and a piece of paper lies in the type of reflection: specular reflection and diffuse reflection.

1. Specular Reflection (Mirror): When light hits a smooth surface like a mirror, it reflects off in a single direction. This is known as specular reflection. The angle at which the light hits the surface (angle of incidence) is equal to the angle at which it leaves the surface (angle of reflection). This is why we can see clear and sharp images in mirrors, because the light rays are reflected in an organized manner.

2. Diffuse Reflection (Paper): When light hits a rough or uneven surface like a piece of paper, it scatters and reflects off in multiple directions. This is known as diffuse reflection. Even though a piece of paper may seem smooth to the naked eye, under a microscope, it has many irregularities that cause the light to scatter. This is why we cannot see a clear image reflected in a piece of paper.

In summary, a mirror reflects light in a single direction due to its smooth surface, resulting in a clear, sharp image (specular reflection). A piece of paper, on the other hand, scatters light in many directions due to its rough surface, and does not produce a clear image (diffuse reflection).