Two combs make a third pattern.

What you're seeing

Each comb is a ruling of fine lines. Where a bright part of one lands on a bright part of the other, light gets through. Where a bright part lands on a dark part, it does not.

Start with the two combs identical and perfectly aligned. Nothing happens. Every line sits on its twin, so the plate keeps the same spacing and direction — only the contrast deepens, because you are looking at one comb squared. No new pattern, at any scale.

Now nudge the twist off zero. Something arrives that was not there, enormously coarser than the lines: at one degree the bands are 344 pixels apart, fifty-seven times the line spacing and wider than the plate itself, so you see one broad band rather than many. Keep turning and they shrink and crowd in — four degrees puts three and a half of them across the plate.

The reason is easier to see with the twist at zero and the spacings slightly different. Set the first comb to 6.0 and the second to 6.5. Now the lines drift out of step. They start aligned, fall gradually out of phase, and come back into step 78 pixels later — thirteen lines of the finer comb, or twelve of the coarser, which is the same distance counted two ways. Bright where they agree, dark where they do not: that is the fringe, and its spacing is thirteen times the lines.

The cross-section below makes this concrete. The pale trace is what is actually on the plate, jittering at the pitch of the lines. The cyan curve is that same trace averaged along the fringes. The fast part cancels and one slow, clean wave is left. That slow wave is the envelope, and it is what dominates what you notice. At these spacings you can still make out the individual lines if you look for them; step back, squint, or photograph the plate and the fine stripes wash out while the envelope stays.

So the third pattern is a difference. Give each comb an arrow — a wavevector: its length is how tightly the comb is ruled, its direction points across the lines — and the fringe is what you get by subtracting one arrow from the other. Nearly equal arrows leave a tiny difference, and a tiny arrow means a huge spacing. That is the whole exhibit.

It also explains the direction, which is the part that catches people out. Twist a comb of vertical lines by one degree and the bands you get are almost horizontal. Both arrows point across vertical lines, so both point sideways; subtract two arrows that nearly cancel and the remainder is a small arrow at right angles to them, pointing up the plate. Fringes run across their own arrow, so they lie almost flat.

Why this matters outside a plate of glass

A vernier caliper is two rulings of slightly different pitch. You read the main scale for the coarse figure, and then, instead of trying to judge a fraction of a division by eye, you look for the one pair of marks that happens to line up. That coincidence is a fringe. It turns a difference too small to see into a position you can point at, which is the same amplification you are dragging here.

A photograph of a striped shirt or a distant brick wall can break out in ugly bands for a closely related reason, though not quite this one. There the sensor's grid of pixels is the second comb, and because it samples rather than multiplies, the coarse pattern is created at the moment of capture: it is in the file, not in the shirt. Same subtraction of two near-equal spacings, different place in the chain — which is why not every striped shirt does it, and moving the camera an inch can make it stop.

What this is and isn't

These combs are smooth sine-wave rulings, not crisp black bars. A sharp-edged bar is not one spacing but several stacked on top of each other, so real bars share the fringe spacing you see here and add a family of fainter extra fringes from the tighter ones. The spacing you can predict here is the first and strongest of them.

And the pattern is in the light, not in your eye. A camera pointed at two real gratings records the same bands. What your eye contributes is only the blurring — it averages away the fine lines, which is what leaves the fringe standing alone.