I could not find the answer to my question in the physics textbooks I studied. My question is this: What is the difference, if any, between the reflection of light on a mirror and the reflection of all the colors of light on a white surface?

There is specular reflection and diffuse reflection; what you get depends on how smooth the surface is

https://micro.magnet.fsu.edu/primer/java/reflection/specular/

https://scienceprimer.com/specular-diffuse-reflection

If the surface isn’t smooth on the scale of the wavelength of the light, the reflected rays won’t be parallel and you won’t form an image

Enne Malus discovered another difference between light reflected from a smooth surface and a rough surface in about 1800. Light reflected from a smooth surface is both circularly and linearly polarized while light from a rough surface is not.

This is how polarized glasses are able to eliminate the glare reflected from smooth surfaces. Also, if circularly polarized light is reflected from a smooth surface, the direction of polarization is rotated by 90 degrees. Light polarized to the right becomes polarized to the left etc..

With linear polarization, the light is polarized in either a horizontal or vertical position, but with circular polarization, the “electro” part of the electromagnetic light wave runs slightly behind the “magnetic” part and how far it is behind makes the wave appear to rotate to either the left or the right.

The glasses used to view 3D movies use both linear and circular polarization. Both right and left lenses are linearly polarized the same as sun glasses but the right and left lenses have opposite circular polarization as does the movie projector. This way the projector can project different images for the viewer’s left and right eyes so they see the image in 3D.

There is a surprising effect if you look at your reflection in a mirror while wearing 3D movie glasses. If you look at your reflection with just one eye. Say your right eye. The light from your right eye can’t return because the mirror reverses the circular polarization so your right lens appears totally opaque while the left lens appears clear. You can see your closed left eye but not your open right eye.

16 hours ago, bangstrom said:

Light reflected from a smooth surface is both circularly and linearly polarized while light from a rough surface is not.

This is how polarized glasses are able to eliminate the glare reflected from smooth surfaces. Also, if circularly polarized light is reflected from a smooth surface, the direction of polarization is rotated by 90 degrees. Light polarized to the right becomes polarized to the left etc..

This is unclear, at best. Light reflecting from a smooth surface tends to become linearly polarized; at Brewster’s angle it is completely polarized, parallel to the surface. There’s no circular polarization involved (symmetry should tell you this - why would one handedness be preferred?) Linearly polarized light can be represented as a superposition of right- and left-handed circular polarizations, but when you say that light is circularly polarized you are implying one handedness is present.

There are left- and right-handed polarization, but “to the left” or “to the right” has a different implication. And what is the 90 degree rotation referring to? Light reflected normal to a smooth surface will change handedness (but only at normal incidence)

https://en.wikipedia.org/wiki/Circular_polarization#Reflection

 

I see, so there are two kinds of reflection. I checked diffuse and specular in my textbooks and it is there. I did not get it at first because the chapter on colors did not mention the term specular reflection. Now it is clear to me. Thanks. The part on polarized light is hard to me, but it sounds awesome.