Light is the same field as your magnet — just shivering fast
The last three guides in this rung were all about magnetism — dipoles, domains, hysteresis, the Curie point. This guide and the next turn to light, and here is the surprise that stitches them together: light and magnetism are the same thing. A magnet holds a steady magnetic field; light is a magnetic field, braided with an electric field, oscillating and racing through space at c = 3 x 10^8 m/s. Maxwell showed that electricity and magnetism are one electromagnetic field, and a ripple travelling through that field is a wave of light. So every optical property we are about to meet is, underneath, just how a material's electrons respond to an electric-and-magnetic field that flips back and forth hundreds of trillions of times a second.
Visible light is a razor-thin slice of the whole electromagnetic spectrum — wavelengths from about 400 nm (violet) to 700 nm (red), sandwiched between infrared below and ultraviolet above. What matters for materials is not the wavelength itself but the energy each photon carries, and there is a handy shortcut: E(eV) = 1240 / lambda(nm). Plug in the edges and the visible band spans roughly 1.8 eV (deep red) to 3.1 eV (violet). Keep that little window in mind, because whether a solid does anything interesting to light comes down to whether it owns electrons that can absorb a bite of energy somewhere inside it — which is exactly the band gap idea you carried up from the electrical rung.
Four fates of a beam: reflect, absorb, transmit
When a beam strikes a slab, its energy has nowhere to hide — it must do one of three things. Part bounces off the surface, which is reflection (fraction R). Part is soaked up inside and turned into heat or re-radiated, which is absorption (fraction A). And part sails clean through and out the far side, which is transmission (fraction T). Since energy is conserved, the three fractions must add up to the whole beam: R + A + T = 1. That single line of bookkeeping, read in different proportions, is the entire reason one material is a mirror, another a window, and another a black wall.
WHERE DOES THE LIGHT GO? R + A + T = 1 (fractions of intensity)
I0 -->|=========|--> T (transmitted, out the far side)
| slab |
reflected | | A absorbed inside -> heat or re-emit
R <----| |
window glass : R ~ 0.08 A ~ 0.01 T ~ 0.91 -> see-through
polished steel: R ~ 0.6 A ~ 0.4 T = 0 -> mirror, opaque
black rubber : R ~ 0.05 A ~ 0.95 T ~ 0 -> opaque, warms up
VISIBLE PHOTON ENERGY: E(eV) = 1240 / lambda(nm)
700 nm (red) -> 1.8 eV 400 nm (violet) -> 3.1 eV
BAND-GAP RULE OF THUMB (electronic absorption in a NON-metal):
Eg > 3.1 eV : no visible photon can be absorbed -> TRANSPARENT
diamond 5.5, silica glass ~9, alumina ~9 (eV)
1.8-3.1 eV : swallows the bluer colors -> COLORED
CdS ~2.4 eV eats blue/green -> looks yellow
Eg < 1.8 eV : every visible photon gets absorbed -> OPAQUE
silicon 1.1 eV (dark grey), metals (no gap at all)Read the extremes straight off that ledger: a window is almost all T, a polished metal is high R with zero T, and black rubber is almost all A. Two honest footnotes keep you out of trouble. First, R, A, and T each depend on wavelength — a red filter is simply a slab whose A runs high for green and blue and low for red, so only red survives to your eye. Second, reflection itself comes in two flavours: a mirror-like specular bounce off a smooth surface, and a diffuse scatter off a rough or cloudy one. That is why a polished and a sandblasted piece of the same metal look so different, and why frosted glass glows softly without ever showing you an image.
Refraction: light slows down, so it bends
Even the part of the beam that gets transmitted does not sail through untouched — it slows down. In vacuum light runs flat out at c = 3 x 10^8 m/s, but inside a material the passing wave drives the electrons, they push back, and the light crawls slower. The ratio of the two speeds is the refractive index, n = c / v. Air is about 1.0003 (just call it 1); water is 1.33; ordinary window glass is about 1.5, so light limps through glass at only c / 1.5 = 2 x 10^8 m/s; diamond is a hefty 2.42. The bigger the n, the more the material grabs and slows the light.
Why does a slower speed make light bend? Picture a marching band crossing at an angle from firm pavement onto soft mud. The row of players who reach the mud first slow first, while their neighbours still on the pavement keep striding — so the whole line pivots and turns. Light does exactly this: when a beam meets a surface at an angle, the edge that enters the slower medium first is held back, and the wavefront swings around. That pivot is refraction, and Snell's law (n1 sin theta1 = n2 sin theta2) counts the degrees. It is why a straw looks snapped at the water line, why a pool looks shallower than it is, and why a shaped lens can gather light to a focus.
Where does n come from, physically? It is the optical face of the very same electron cloud that set the dielectric constant back in the electrical rung: at optical frequencies, n is roughly the square root of the dielectric constant. Beware one honest trap, though — this uses the high-frequency dielectric constant, driven only by the nimble electrons, not the static one. Water's static dielectric constant is about 80, yet its optical n squared is only about 1.8, because at the blistering pace of light nothing but the electrons can keep up. And n is not a single number: it rises for shorter, bluer wavelengths, an effect called dispersion, which is precisely why a prism fans white light into a rainbow.
Reflection, and why metals are mirrors
At every interface where n changes, a slice of the light reflects. At straight-on incidence the reflected fraction follows a clean formula: R = ((n2 - n1) / (n2 + n1))^2. For glass in air that is ((1.5 - 1) / (1.5 + 1))^2 = (0.5 / 2.5)^2 = 0.04 — so about 4% bounces off each surface, and a windowpane with two faces loses roughly 8%. That is exactly why camera lenses and eyeglasses wear thin anti-reflection coatings. For diamond, n = 2.42 gives R = (1.42 / 3.42)^2 = 0.17, a 17% flash off every facet — that high reflection, married to diamond's strong dispersion, is a gem's famous fire.
Metals are the extreme case, and they are opaque and reflective for one and the same reason: their sea of free electrons in metallic bonding has no band gap at all. A photon of any visible energy instantly finds electrons ready to absorb it, so light cannot penetrate more than a few tens of nanometres — which is why even a thin metal foil is opaque. But those same jostled electrons re-radiate the light straight back out almost immediately, so nearly all of it returns as a reflection rather than staying as heat. Absorb-and-instantly-re-emit at the surface is, quite literally, what a mirror does.
Absorption and transparency: why glass is clear and silicon is not
Now the flip side of the ledger — what decides whether the transmitted beam survives its trip. In a non-metal, the main way to absorb a visible photon is to spend it lifting an electron across the band gap. So the whole thing is a contest between the photon's 1.8-3.1 eV and the size of the gap. If the gap is wider than 3.1 eV, no visible photon is energetic enough to make the jump, the light passes clean through, and the solid is intrinsically transparent — this is why window glass (gap around 9 eV), diamond (5.5 eV) and pure sapphire are clear. If the gap is below 1.8 eV, every visible photon can be absorbed and the solid is opaque, which is why silicon (1.1 eV) looks dark grey even though it is not a metal. In between, the material swallows the higher-energy colors and lets the rest through, so it looks colored.
- Is it a metal? If yes, its gapless free electrons absorb across the whole visible band and instantly re-radiate it — so it is opaque and reflective. Stop here.
- Otherwise, find the band gap. If it is bigger than about 3.1 eV, no visible photon can be absorbed by a band-to-band jump, so the material is intrinsically transparent (glass, diamond, sapphire).
- If the gap sits between 1.8 and 3.1 eV, it absorbs the bluer colors and passes the redder ones, so it looks colored (cadmium sulfide, gap ~2.4 eV, eats blue and green and looks yellow).
- If the gap is below 1.8 eV, every visible photon carries enough to be absorbed, so the material is opaque (silicon, 1.1 eV).
- Finally, even a wide-gap, non-absorbing solid turns cloudy if light scatters inside it — at pores, a second phase, or grain boundaries. Single-crystal sapphire is water-clear; ordinary polycrystalline alumina of the identical chemistry is a white, opaque ceramic. Transparency needs BOTH no absorption AND no scattering.
That last step deserves its own honest emphasis, because it is where the tidy band-gap rule needs a chaperone. A perfectly non-absorbing solid is only see-through if light does not scatter on the way. Every pore, second-phase particle, or grain boundary bends the beam a little, and a slab packed with them turns milky — the difference between clear sapphire and white alumina is nothing but the light-scattering boundaries inside. And the sharp band-gap cutoff is idealized in a second way too: real materials also absorb weakly below the gap through impurities and defects (the faint green in a thick pane of ordinary glass is dissolved iron), and Beer's law, I = I0 exp(-beta x), means any slab — however clear — eventually goes dark if you make it thick enough. No real material is infinitely transparent; that is the same lesson we keep meeting, that a single clean number always hides a messier truth. Guide 5 takes these same ideas into color, luminescence, lasers, and the optical fiber that carries the internet.