There are two things at play. The first is “do you reflect all the light”, the second is “what direction do you reflect in”. A mirror reflects the light coming in in the same direction, so you can see an image. A white surface reflects light in lots of different directions, so you don’t get a sharp image. Think about flattening out a disco ball. If you make the little mirrors point in slightly different directions, you won’t get a clean picture, but instead will get lots of little pictures all jumbled together. As you make those mirrors tiny, the jumbled images become so small you can’t make them out any more and just get a white surface.
There are two main types of light reflection. Direct reflection and diffuse reflection.
Direct reflection is what a mirror does. Light reflects off the surface at the opposite angle from which it came (angle of incidence equals angle of reflection). Thus, we can see an image when we look at a mirror.
A white surface (like paper) has the property of diffuse reflection. It reflects the light in all directions, pretty much equally. The result of this is a ‘normal’ looking object, not a mirror.
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