Why Do Metals Shine?
― Free Electrons Shake Back Together With the Light and Push It Away
Your face shows up in a spoon, but not in a wooden chopstick or a pebble. Metal does not shine because something has been painted on its surface. Inside a metal are many electrons that are not tied to any atom and move about freely. These electrons throw the incoming light back.
After a meal, a child peers into a spoon and says, "Look, my face is upside down!"
Then the child asks, "Why are iron and aluminium shiny, but stones and wood aren't?"
You are tempted to say "because they're metal," but that is not an answer. Behind this question lies a big discovery in physics: electricity and light are close relatives.
There are just two reasons
Metal atoms let go of their outermost electrons. The freed electrons belong to no particular atom and roam freely through the whole piece of metal. They are also the reason metals carry electricity so well.
Light is a wave in which an electric force travels while rapidly oscillating. Free electrons respond to that shaking at once and shake back, giving off light of their own. This light cancels the incoming light and pushes it back out.
The electrons in stone or wood are firmly tied to their atoms. When light arrives, they cannot move much. So the light goes inside, where it is absorbed or scattered in all directions. Only things with free electrons can throw light back in such an orderly way that a face appears.
How do electrons push light back?
Light is a wave whose electric force reverses direction hundreds of trillions of times a second. When light hits a metal, the free electrons near the surface are pulled back and forth by this force.
A shaking electron acts like a tiny antenna. It sends out new light around itself. There are so many electrons, and they keep up with the shaking of the light. The light they send out points exactly against the light trying to move into the metal, and cancels it.
Light that cannot go in has no choice but to leave the surface. That is what "reflecting" means. Light is said to get in only a few tens of nanometres below the surface. That is several thousand times thinner than a human hair.
Can metal reflect every kind of light?
In fact, some light cannot be reflected. The electrons' shaking back has a speed limit they can keep up with. If the light shakes faster than that, the electrons cannot follow. Then the light passes straight through the metal.
This limit is set by the number of electrons. For aluminium, the limit lies in the ultraviolet, where light shakes much faster than visible light. Use the slider in Figure 1 to change the wavelength of the light (the length of one full shake). The shorter the wavelength, the faster the shaking.
In the graph on the right of Figure 1, the band of visible light lies far from the limit. To the electrons, every colour of light is a "slow shake." So aluminium reflects red and blue alike. Every colour comes back in the same proportion, which is why it looks silver.
Why are some metals gold or copper-red?
In gold and copper, electrons deeper down, besides the free ones, also react to light. In gold, these electrons are said to absorb part of the blue and green light. The reflected light is then richer in red and yellow, giving gold its colour. Copper absorbs over a wider range and looks reddish.
In silver, this absorption is shifted toward the ultraviolet, so visible light returns almost unchanged. This is one reason silver has long been used on the back of mirrors.
Aluminium foil is shiny on one side and looks dull on the other. Both are the same aluminium and reflect light equally well. What differs is how smooth the surface is. On a bumpy surface, light bounces off in all directions, so no face appears and the surface looks whitish. Grind a metal into fine powder and it looks grey or blackish. Light bounces many times among the gaps between grains and is gradually absorbed.
In 1933, the American physicist Robert Wood reported that thin films of sodium and similar metals suddenly start letting through ultraviolet light shorter than a certain wavelength. It overturned the common belief that "metals do not let light through." That same year, it was shown that the same mechanism as the limit in Figure 1 explains it.
Summary
Metals shine because a sea of electrons, free of any atom, shakes back together with the light. There are so many electrons that they easily keep up with the shaking of visible light. In this way they push light back without letting it in. The electrons in stone and wood are tied to their atoms, so they cannot do this.
The shine of a metal is not a colour on its surface.
It is the sea of electrons pushing light back.
How fish shine silver without any metal is explained in "Why do sardines and cutlassfish shine silver?", and why the far end of facing mirrors grows dark is in "Why does the far end of two facing mirrors get darker?". Metals feel cold because of the same free electrons, as explained in "Why does metal feel colder than wood?". Why the same sea of electrons lets gold be hammered out to a ten-thousandth of a millimetre without breaking is in "How thin can gold be stretched?".
- Tear off a piece of aluminium foil and look at your face in the shiny side and the dull side. The amount of light reflected is the same, yet the reflections look completely different.
- Crumple the foil into a ball, then gently open it out. In every wrinkle you will see a small bright spot. It is like many tiny mirrors lined up.
- Place a 10-yen coin and a 1-yen coin side by side on white paper and compare them by a bright window. The copper 10-yen coin looks reddish, and the aluminium 1-yen coin a whitish silver. You can see that copper absorbs some colours.
If the 10-yen coin is dull and brown, a film of another substance has formed on its surface. The newer the coin, the closer it looks to the true colour of copper.
For those who want to know more ― terms, formulas, and links to textbooksEach part is labelled by level, from junior high science to university specialist courses
- Junior highCovered in junior high school science
- High schoolCovered in high school physics or chemistry
- High school+Advanced high school material, or textbook sidebars
- UniversityUniversity specialist courses not taught in high school (electromagnetism, solid-state physics)
- ResearchTopics researchers are still investigating, not yet taught even at university as settled
Junior highTerms: this phenomenon has names
- Metallic lustre: the distinctive glossy shine seen on metal surfaces. It is taught in junior high as one property that identifies metals.
- Free electrons: electrons that are tied to no particular atom and can move freely inside a metal. They are also why metals conduct electricity and heat well.
- Plasma frequency: the upper limit on how fast a group of free electrons can shake back together. Light that shakes more slowly than this is reflected.
Junior highHigh schoolChecking with a formula: what is the limit of light aluminium can reflect?
From the number of free electrons, we estimate the limiting wavelength below which aluminium can no longer reflect light. If this is shorter than visible light, aluminium should reflect all visible light.
| In symbols | ωp ＝ √( n × e² ÷ ( ε0 × m ) )、λp ＝ 2π × c ÷ ωp |
| In words | Upper limit of electron shaking speed ＝ the square root of (number of electrons × square of the electron's charge) divided by (permittivity of vacuum × electron mass). Limiting wavelength ＝ 2π × speed of light ÷ that upper limit |
| Where it comes from | If the electrons shift slightly, an electric force arises from the displacement and pulls them back (Gauss's law). The shaking speed at which this restoring force balances the electrons' inertia (the equation of motion) is ωp |
| Symbol | Meaning and unit |
| ωp | Plasma frequency (angular frequency). Unit: radians per second |
| n | Number of free electrons per cubic metre |
| e | Charge of one electron (elementary charge). 1.6×10⁻¹⁹ coulombs |
| ε0 | Permittivity of vacuum. 8.85×10⁻¹² farads per metre |
| m | Mass of an electron. 9.11×10⁻³¹ kilograms |
| λp | Limiting wavelength. Light with a longer wavelength is reflected |
| Free electrons in aluminium (3 per atom) | 18×10²⁸ per cubic metre |
| e² divided by the product of ε0 and m | About 3200 (found from the three constants above) |
| Speed of light | 3.0×10⁸ metres per second |
| Wavelength of visible light | About 380–780 nanometres |
| ωp squared (counting in units of 10²⁸) | 18 × 3200 ＝ 57600 |
| Its square root is ωp | The square root of 57600 is 240, and the square root of 10²⁸ is 10¹⁴, so about 2.4×10¹⁶ |
| 2π × speed of light | 6.28 × (3.0×10⁸) ≒ 1.88×10⁹ |
| Limiting wavelength λp (metres) | (1.88×10⁹) ÷ (2.4×10¹⁶) ≒ 7.8×10⁻⁸ |
| In nanometres | About 78 nanometres (on the quite short side, even for ultraviolet) |
| Ratio to the shortest violet light | 380 ÷ 78 ≒ 4.9 |
Even violet, the fastest-shaking visible light, still has about a five-fold margin before the limit. That is why aluminium reflects every colour of the rainbow. Measurements put aluminium's actual limit at around 80 nanometres, which agrees well with this simple estimate.
High schoolHigh school+Light is an electromagnetic wave, and metal is a conductor
High schoolIn high school physics you learn that light is an "electromagnetic wave," a travelling oscillation of electric and magnetic fields. Inside a conductor, an applied electric field moves the free electrons, and they arrange themselves to cancel it. The idea you meet in the electrostatics unit, "the electric field inside a conductor is zero," also holds for fast oscillations like light, as long as the electrons can keep up.
High school+Even in a material like glass, where electrons are bound, some light is reflected at the surface. For glass with a refractive index of 1.5, about 4% of light hitting it head-on is said to be reflected. That is an order of magnitude below the 90% or more that metals reflect.
UniversityThe Drude model and the dielectric function
In university electromagnetism and solid-state physics, the motion of free electrons is described by the "Drude model." From it follows the dielectric function of a metal, ε(ω) ＝ 1 − ωp² ÷ ω². When the light's angular frequency ω is below ωp, the dielectric function is negative and the refractive index is purely imaginary, so the light cannot go in and is totally reflected. The depth to which it seeps in is called the skin depth, on the order of tens of nanometres. The colours of gold and copper are explained by absorption through interband transitions of d-orbital electrons, in addition to the free electrons. Figure 1 is an idealisation that ignores damping from electron collisions. The same mechanism is at work in the sky. The ionosphere high above has sparse electrons, so its plasma frequency is far lower; it lets light pass but reflects AM radio waves (see Why can you hear distant AM radio stations at night?).
📖 For derivations and further reading: Wikipedia, "Drude model" (Japanese edition) ／ Wikipedia, "Plasma oscillation" (Japanese edition)
ResearchWhat is still not well understood
- The colour of nanosized metals. Gold grains a few tens of nanometres across look red or purple. This comes from "surface plasmons," collective shaking of electrons at the grain surface. Exactly how shape and size change the colour is still being studied in detail.
- Brighter mirror materials. For ultraviolet telescopes and similar instruments, the thin rust-like film that forms on aluminium lowers reflection, which is a known problem. Research continues on film materials and ways of making them.
- New materials that act like metals. Using materials whose electron number can be changed freely, researchers are working to move the reflection limit close to visible light and to switch colour and transparency.
So this article, too, is "an explanation within what is known today." The interplay of electrons and light connects the shine of an everyday spoon to cutting-edge optical materials.
Links to textbooks (by level)
| Level | Subject and unit | Where in this article |
|---|---|---|
| Junior high | Year 1 science, "Materials around us" (properties of metals) | Metallic lustre, conducting electricity |
| High school | Physics "Electromagnetic waves" and "Static electricity and conductors"; chemistry "Metallic bonding" | Free electrons, light as shaking electric field |
| High school+ | Advanced physics, "Reflection and refraction of light" | Difference in reflectance from glass |
| University | Electromagnetism; solid-state physics (optical properties) | Plasma frequency, Drude model, skin depth |
| Research | Plasmonics, optical materials | Colour of nanoparticles, ultraviolet mirrors |
| ― | Connections to daily life | Mirrors, aluminium foil, colours of 10-yen and 1-yen coins |
- N. W. Ashcroft, N. D. Mermin, Solid State Physics (1976), Chapter 1: Drude theory; AC electrical conductivity and optical properties of metals.
- C. Kittel, Introduction to Solid State Physics (Japanese edition: 固体物理学入門, Maruzen), chapter on plasma oscillation and the transmission of light through metals.
- R. W. Wood, "Remarkable Optical Properties of the Alkali Metals", Physical Review 44, 353 (1933)
- E. Hecht, Optics (Japanese edition: ヘクト 光学, Maruzen), section on reflection of light by metals.
- Wikipedia, "Drude model" (Japanese edition)
*This article is a popular-science explanation. The figures given are guides and rough estimates meant to help you understand the mechanism. The reflectance in Figure 1 is an idealised calculation that ignores losses from electron collisions; the actual reflectance of aluminium for visible light is said to be about 90%.