Why does a streetlight split into a grid of dots through umbrella fabric?
― Gaps between threads bend light and rearrange it
Fabric seems like something that just blocks light. But finely woven cloth can also show you light's hidden side — as a wave. The dots ringing a streetlight are a pattern woven from waves of light that have spread through the gaps between threads and overlapped.
You're walking home on a rainy night, umbrella up. You tilt it forward, and a distant streetlight shows faintly through the fabric.
Look closely and the streetlight isn't a single point at all. Around the bright centre, small points of light sit evenly spaced above, below, and to each side, forming a grid-like pattern.
What's more, the further-out dots shimmer with rainbow colours, red spilling furthest outward. How did the fabric turn plain white light into a row of coloured dots?
Just two reasons explain it
Light is a wave, so passing through a narrow gap makes it spread out beyond it like a widening ring. When waves from many gaps overlap, only the directions where crest meets crest turn bright — producing separate dots instead of a smear.
Red light has a longer wavelength than blue. The longer the wave, the further outward its reinforcing direction shifts. So each dot stretches into a rainbow toward the edges, with red outside and blue inside.
The grid shape comes from the fabric's threads running in two directions, warp and weft. The gaps between the vertical threads spread light sideways; the gaps between the horizontal threads spread it up and down. Together they produce a grid of dots.
Light "bends" as it passes through a gap
When ripples on water pass through a gap in a breakwater, they spread out beyond it as a widening semicircle. Light, being a wave too, does the same thing. This is called diffraction. We don't usually notice it because light's wavelength is only about 1/10,000 of a millimetre — extremely short. When a gap is far wider than that, the bending is essentially invisible.
In umbrella fabric, the gaps between threads are thought to be around 0.1–0.3 millimetres. That's still hundreds of times the wavelength of light, but fine enough that the bending becomes visible to the eye.
Look at Figure 1. Light arriving from the left spreads into a ring at each gap. The spreading waves overlap with waves from neighbouring gaps. In some directions crest meets crest and it brightens; in others crest meets trough and they cancel out, going dark. This is interference. It only brightens in directions where the path difference from neighbouring gaps is exactly one wavelength, two wavelengths, and so on.
Red outward, blue inward — the reverse of a rainbow's order
The reinforcing direction is set by "path difference equals one wavelength." Red, with its longer wavelength, needs a larger diagonal angle to make that difference equal one full wavelength. Since red light's wavelength is about 1.5 times blue's, the red dot lands about 1.5 times further out than the blue one.
Figure 2 shows the pattern as seen through the fabric. The further a dot sits from the central white point, the fainter it gets, and the more its colour splits into a band.
In a prism or a raindrop, light slows down and bends inside the glass or water. There, blue bends the most. In a fabric grid, the bending direction is set by path difference, so red bends the most. Even though both are called "rainbow colours," the order the colours appear in tells you which mechanism produced them.
The size of the pattern is set by an angle. Whether the fabric is close to your eye or further away, the angular spacing between the dots stays much the same. What changes is only how fine the gaps are: finer fabric spreads the dots further apart. In mesh like a window screen, where gaps exceed a millimetre, the dot spacing nears the limit the eye can resolve, and it's often seen as crossed streaks rather than separate dots.
Fabric barely dims sunlight at all. Check the pattern using a night-time streetlight, or in daytime a reflection off a distant car's headlights — something not too dazzling. Staring at the sun risks damaging your eyes.
Summary
Umbrella fabric is a "grid" of countless narrow gaps arranged neatly in two directions. Light passing through the gaps spreads out and overlaps, and only the reinforcing directions shine as dots. Because that direction depends on wavelength, the dots form a rainbow with red outside and blue inside.
The grid of light seen through fabric
is proof, on a rainy night, that light is a wave.
The same mechanism — light waves overlapping through gaps or thin films — also produces colour in soap-bubble rainbows and opal's shimmer. For the reverse case, where bending water or light splits colours the opposite way, see our article on rainbows.
- At night, pick out one distant streetlight through a window. Hold up a fine-woven fabric — an umbrella, a thin handkerchief, a lace curtain — in front of your eye and look at the streetlight through it.
- Slowly rotate the fabric. The direction the dots line up in rotates with it — proof that the pattern's orientation is set by the weave's direction.
- Try stretching the fabric diagonally to distort the weave, or swap in fabric with a different weave fineness, and compare how the dot spacing changes. Finer fabric should spread the dots further apart.
Smaller, more distant lights show the dots most clearly separated. Larger, nearby lights tend to blur the dots into a hazy spread of light.
Want to go deeper? ― terminology, formulas, and textbook connectionsLabels below show whether this is middle-school, high-school, or university-level material
- Middle schoolcovered in middle-school science
- High schoolcovered in high-school physics
- High school+advanced or sidebar material in high-school textbooks
- Universitynot covered in high school — university-level optics/wave-optics content
- Researchnot yet settled even at university level — an active research topic
Middle schoolTerminology: this phenomenon has names
- Diffraction: when a wave passes through a gap or past an edge, it curves round into what should be a shadow region and spreads out.
- Interference: when two or more waves overlap, reinforcing where crest meets crest and cancelling where crest meets trough.
- Diffraction grating: a set of narrow, evenly spaced gaps or grooves. It splits light into fixed directions by colour. A fabric weave acts as a diffraction grating in two directions, along the warp and the weft.
Middle schoolHigh schoolChecking with a formula: how far apart do the dots appear?
Taking the spacing between thread gaps as 0.2 mm, we calculate the angle at which a green light dot appears from the centre. Since the angle is small, we treat the angle and its sine as roughly equal (in radians).
| In symbols | d × sinθ ＝ m × λ |
| In words | gap spacing × tilt of the visible direction ＝ order of the dot × wavelength of light |
| Where it comes from | the interference condition that when the path difference (d × sinθ) between light from neighbouring gaps is exactly a whole number of wavelengths, crest meets crest and it reinforces |
| d | spacing between thread gaps (in nanometres) |
| θ | angle of the light dot as seen from the central dot |
| m | order of the dot (1, 2, 3…) |
| λ | wavelength of the light (in nanometres) |
| Umbrella-fabric thread spacing (typical) | 0.2 mm ＝ 200000 nm |
| Wavelength of green light | 550 nm |
| Wavelengths of red and blue light | red 700 nm, blue 450 nm |
| 1 radian in degrees | about 57.3° |
| Apparent size of the full moon | about 0.5° |
| Angle of the 1st-order green dot (radians) | 550 ÷ 200000 ＝ 0.00275 |
| Converting to degrees | 0.00275 × 57.3 ≒ 0.158 |
| Compared with the moon's size | 0.158 ÷ 0.5 ≒ 0.32 |
| Angle of the 1st-order red dot (radians) | 700 ÷ 200000 ＝ 0.0035 |
| Angle of the 1st-order blue dot (radians) | 450 ÷ 200000 ＝ 0.00225 |
| How much further out red sits than blue | 0.0035 ÷ 0.00225 ≒ 1.56 |
| Spacing between dots at a streetlight 30 m away (metres) | 30 × 0.00275 ≒ 0.083 |
The dots sit about 0.16° apart — roughly a third of the moon's diameter. For a streetlight 30 metres away, it looks as if copies of the light were spaced about 8 cm apart beside it. Since the red dot sits about 1.6 times further out than blue, the outer dots are the easiest to spot as rainbow bands.
High schoolHigh school+From Young's experiment to a two-way grid
High schoolHigh-school physics covers "Young's experiment," where two slits produce light fringes, and the "diffraction grating," where many slits are lined up. The more slits there are, the narrower and sharper the bright directions become, with near-total darkness in between. The fabric's dots look crisp because light is passing through hundreds of gaps at once.
High school+Because fabric has gaps running in two directions — warp and weft — only the directions that satisfy both the left-right condition and the up-down condition at once light up. The result is a grid of dots rather than a line. Dots grow fainter toward the edges because a single gap's own width also diffracts light, capping how far the spread can reach.
UniversityThe far-field diffraction pattern is a "Fourier transform" of the gap's shape
When the light source is far away and the eye's lens focuses it as if from infinity, the diffraction involved is called Fraunhofer diffraction. In that case, the brightness pattern on the retina is the squared magnitude of the Fourier transform of the fabric gaps' shape (the aperture function). The Fourier transform of an evenly spaced grid is an evenly spaced array of dots. The shape of a single gap sets the overall brightness envelope. When you stretch the fabric diagonally to distort the grid, the pattern distorts in the opposite sense — a relationship between real space and reciprocal-lattice space. This is the same mathematics used to study atomic arrangements via X-ray diffraction through crystals.
📖 For the derivation and further reading: Diffraction grating (Wikipedia, Japanese) ／ Fraunhofer diffraction (Wikipedia, Japanese)
ResearchWhat's still not fully understood
- Weave irregularity and pattern blur. Real fabric has threads of slightly uneven thickness and spacing, and it flexes. Attempts exist to work backward from images of fabric to gauge quality from how this irregularity blurs the pattern, but no settled method is established yet.
- How living creatures build their own "gratings." Butterfly scales and beetle shells carry gratings as fine as the wavelength of light, producing colour through diffraction and interference. How living things assemble structures this precise is still an open research question.
- Differences between individual observers. Even with the same fabric, how the dots and their fringes appear is said to vary from person to person. How much this depends on pupil size or fine structures in the eye's lens is reportedly not yet well studied.
In other words, this article too reflects "what's understood so far." That said, the reason the dots form a grid at all rests on wave properties confirmed over the past 200 years.
Textbook connections (by level)
| Level | Subject / unit | Where in this article |
|---|---|---|
| Middle school | Science: "properties of light," "sound and waves" | light spreading through a gap, waves overlapping |
| High school | Physics: "interference and diffraction of light" | the diffraction-grating equation, positions of the red and blue dots |
| High school+ | Physics, advanced: "two-dimensional gratings" | why the dots form a grid, why they dim toward the edges |
| University | Optics / wave optics | Fraunhofer diffraction and the Fourier transform |
| Research | Structural colour, fabric imaging measurement | gratings in living things, weave irregularity |
| ― | Everyday connections | observing light waves with an umbrella, curtain, or handkerchief |
- Wikipedia, "Diffraction grating" (回折格子)
- Wikipedia, "Fraunhofer diffraction" (フラウンホーファー回折)
- E. Hecht, Optics, 5th ed., Pearson (chapters on diffraction gratings and Fraunhofer diffraction from two-dimensional apertures)
- High-school "Physics" textbooks (units on interference and diffraction of light, various publishers)
※This article is a general-audience science explainer. Figures given are approximations meant to aid understanding of the mechanism. The thread spacing of fabric varies greatly between products.