The reason we can see images in mirrors but not in paper is primarily due to the differences in the surfaces of these materials and how they interact with light.
Mirrors have a smooth and highly reflective surface, typically made of a thin layer of metal, such as aluminum or silver, deposited on a glass substrate. When light waves encounter a mirror, they undergo a process called specular reflection. In specular reflection, the incident light waves bounce off the mirror's surface as a coherent beam, preserving the angles of incidence and reflection. This coherent reflection allows the light to form a clear and sharp image. Mirrors reflect most of the incident light, resulting in a highly reflective surface.
On the other hand, paper has a rough and non-reflective surface composed of fibers and irregularities. When light waves encounter paper, they undergo a process called diffuse reflection. In diffuse reflection, the incident light waves scatter off in various directions due to the unevenness of the paper's surface. This scattering causes the light to be reflected in many different angles, resulting in a loss of coherence and the inability to form a clear image. Instead of a well-defined reflection, the light is dispersed in multiple directions, making it difficult to perceive a distinct image.
So, while both paper and mirrors reflect light, the smooth and highly reflective surface of mirrors allows for coherent and specular reflection, enabling the formation of clear images. The rough and non-reflective surface of paper, however, scatters the light in multiple directions, leading to diffuse reflection and the absence of a well-defined image.