# Optics: White Color VS Mirror

#### Bloo_Mec

Hi, today a question crossed my mind. I was thinking about mirrors and colors, why they exist and how does light interact with them. And I always heard that white is the mix of all colors, and that white reflects all the colors. It makes sense because one points a red light to a white wall, the wall becomes red as it would with any other color. The rainbow effect also confirms this. But if white reflects all the colors, then why is not a perfectly smooth white surface a mirror? What is the difference between a mirror and a smooth white color?

Another question is, if light are photons with mass, then if one points a very powerful light source at a mirror, by Newton's second law, the mirror is being pushed away from the light. Right?

I am an engineering student and sometimes things like this cross my mind...
Can you recommend a book that answers this kind of questions? I have never studied the light or optics so I am a begginer in the subject but with good math skills. I tend to be theoretical.

Thank You.

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#### zhermes

Great questions Bloo_mec.

But if white reflects all the colors, then why is not a perfectly smooth white surface a mirror? What is the difference between a mirror and a smooth white color?
The difference is that a 'smooth' white surface isn't actually that smooth---microscopically, the surface is still very rough. Because photons are so small (optical photons ~ 500 nanometers), they are effected by those small imperfections. In particular, the photons end up being reflected in an approximately random direction---leading to the reflected image being a mix of all directions (i.e. everything in the room).

A mirror's surface is smooth even on the microscopic scale. In fact, the mirrors used by telescopes are made to be smooth down to the atomic level! This means that every photon which bounces off, bounces in the same very particular direction, allowing you to see the original image.

Another question is, if light are photons with mass, then if one points a very powerful light source at a mirror, by Newton's second law, the mirror is being pushed away from the light. Right?
Light is just photons. No mass. But light still caries momentum---and therefore you're still correct, the mirror is being pushed away by the light. This is actually a very important issue for highly sensitive optics (e.g. those used in Laser Interferometers).
With photons, the definition of momentum as $p = mv$ is no longer true.

I am an engineering student and sometimes things like this cross my mind...
Can you recommend a book that answers this kind of questions? I have never studied the light or optics so I am a begginer in the subject but with good math skills. I tend to be theoretical.
I dont know any good books to recommend in particular; but any 'physics 101' type textbook will have a discussion of basic optics and light. I'd recommend checking amazon for what gets good reviews. (Make sure the index includes the sections you're interested in).

#### Bloo_Mec

Thank you zhermes!

So isn't it possible to smoth down a white surface to atomic level so that it becomes a mirror? What you said makes total sense, but has this been done to actually confirm this?

#### zhermes

This happens all the day. That's one of the main effects of 'polishing' surfaces (besides just cleaning them), you're actually smoothing the surface (its like a very light sanding).

Most materials aren't capable of holding a pristinely smooth surface---thats why only special materials make good mirrors---specifically substances with strong crystal structure. That's also (part of) why most metals are highly reflective.

As an experimental example, its easy to show the reverse process. If you have a small mirror (that you don't care about), you can use sand-paper on the surface to make it rough---and it will become 'clouded' until it no longer shows a reflection. Generally with mirrors and glass, once it becomes extensively clouded it just appears white---because it is still generally reflective.

#### Bloo_Mec

Thank you for the quick reply zhermes!

I've just read that mirrors are made by "painting" glass with silver. Why does silver stay smooth when painted and white paint does not? It's the same polished glass surface.

This questions are killing me! I love physics..

#### zhermes

Silver is a metal---it has a hard, crystal structure with atoms arranged in a tight lattice. Glass itself is also in a strong lattice.
Something like white paint is soft, you can push your finger nail into it, it can't hold a tight smooth surface.

#### Bloo_Mec

Yes but even when the silver is still liquid, we can start seeing the mirror effect. And I suppose that the silver will dry up in whatever shape the glass has, so this means that the glass surface needs to be perfectly smooth to make a mirror. And I also suppose that when I paint it white, the white coat will also dry up in the shape of the glass. My point is, both the silver and the white paint are getting the exact same surface finish (wich is given by the glass), and the white paint does not act as a mirror.

Thank You!

#### zhermes

No. Liquids tend to have smooth surface because of surface tension---so they're automatically quite smooth. Additionally the silver will not just maintain the glass-shape for the same reason.

White paint vs. silver on a surface will be completely different. The paint would be almost a clay-like substrate (i.e. malleable and irregular), while the silver is rigid and smooth (if done appropriately). Once again, paint is not capable of maintaining a hard smooth surface.

#### Bloo_Mec

I see. Now you gave me another question, if liquids tend to have smooth surfaces, why doesn't a white liquid look like liquid mercury?

#### zhermes

Probably what you're thinking of as a white liquid (e.g. milk) is white because of the particulates inside the fluid (i.e. its just really cloudy). You're not actually seeing the surface of the fluid like you are in the case of liquid metals.

#### Bloo_Mec

I see! The difference is that a metal is opaque and white paint isn't! Thank you!

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#### Bloo_Mec

Thank you Drakkith!

I got it, it doesn't have to do with the smoothness of the surface, but with the opacity of the material.

#### Drakkith

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Thank you Drakkith!

I got it, it doesn't have to do with the smoothness of the surface, but with the opacity of the material.
It depends on the material.
For simplicity, "reflections" are spoken of here, but more generally the interface between the small particles that constitute many materials is irregular on a scale comparable with light wavelength, so diffuse light is generated at each interface, rather than a single reflected ray, but the story can be told the same way.

This mechanism is very general, because almost all common materials are made of "small things" held together. Mineral materials are generally polycrystalline: one can describe them as made of a 3-D mosaic of small, irregularly shaped defective crystals. Organic materials are usually composed of fibers or cells, with their membranes and their complex internal structure. And each interface, inhomogeneity or imperfection can deviate, reflect or scatter light, reproducing the above mechanism.

Few materials don't follow it: among them metals, which do not allow light to enter; gases, liquids; glass and transparent plastics (which have a liquid-like amorphous microscopic structure); single crystals, such as some gems or a salt crystal; and some very special materials, such as the tissues which make the cornea and the lens of an eye. These materials can reflect diffusely, however, if their surface is microscopically rough, like in a frost glass (figure 2), or, of course, if their homogeneous structure deteriorates, as in the eye lens.
My telescope mirror is coated with aluminum, and as the last paragraph states the aluminum does not allow light to enter at all, thus allowing a near total specular reflection unless the surface is not smooth.

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