Why does white paper look white even in a dim room?
― Charcoal in sunlight is tens of thousands of times brighter than paper in moonlight, yet it still looks black
White paper looks white whether it's by a sunny window or in a dim room at night. Yet the amount of light reaching your eye can differ by thousands of times depending on the setting. What your eye and brain track isn't the "amount" of light. It's the ratio to what's next to it.
At night, with the lights off, you look at a notebook on your desk. Even by moonlight alone, the page looks whitish and the pen marks look black.
By day, you take the same notebook outside into the sun. The paper becomes dazzlingly white, but you don't feel like it's "turned into a different paper."
Yet if you measure it with a light meter, the daytime paper is hundreds of thousands of times brighter than the nighttime paper. Why do we perceive the same "white" either way?
There are just two reasons
If the light shining on a scene becomes 10 times stronger, both the paper and the charcoal become 10 times brighter. Even so, the "ratio" between the paper's brightness and the charcoal's brightness doesn't change. The eye is especially sensitive to this ratio.
From shadows and the direction of light, the brain estimates "how strongly is this scene lit right now." It then discounts that amount before deciding on an object's color.
Together, these two effects mean an object's "whiteness" or "blackness" feels almost unchanged even as the lighting changes. This mechanism is called lightness constancy.
Charcoal in sunlight is tens of thousands of times brighter than paper in moonlight
The amount of light an object sends to your eye is the product of two factors: how strong the illuminating light is, and what fraction of that light the object reflects. White paper is said to reflect about 80% of the light hitting it. Charcoal reflects only a few percent.
Meanwhile, the strength of the illuminating light varies far more than the reflectance does. Direct sunlight on a clear day is roughly 100,000 lux. A full-moon night is about 0.2 lux — around one five-hundred-thousandth as much.
Try the slider in Figure 1 to change the illuminating light. The light that white paper under moonlight sends to your eye is far less than the dotted line showing "charcoal in sunlight." The gap exceeds 20,000-fold. Even so, the paper looks white and the charcoal looks black.
But the "gap" between the paper and charcoal bars is always the same. The vertical scale is marked in multiples, so the difference in bar height represents a "ratio." Whether the light is strong or weak, the paper stays 20 times brighter than the charcoal. It's this unchanging ratio that the eye picks up on.
The brain "brightens up" what's in shadow
Ratio alone doesn't explain everything. Picture a snowfield on a sunny day. Snow in the shadow of a tree should be many times darker than snow in direct sun. Yet we perceive it as "white snow in shadow," not as "gray snow."
The brain uses clues such as how blurred a shadow's edge is and the direction the light is coming from. From these it judges "this area is lit weakly," and brightens its reading accordingly before deciding on the object's color.
There's a well-known image that makes this correction vivid: comparing a white square and a black square on a chessboard, one of which sits in shadow. Measure the light actually reaching the eye, and the white square in shadow and the black square in sunlight turn out to be exactly equal. Yet to us, looking at it, they appear simply white and black. That's because the brain discounts the shadow.
Many cameras set exposure so that the average brightness of the whole frame comes out as a "middling gray." In an almost entirely white snow scene, the camera tries to pull that average down, and ends up rendering the snow gray. Our eyes discount the illumination as we look, so the snow looks white there and then. It's only the photo that comes out gray — because of this difference.
Summary
The strength of illuminating light can differ by hundreds of thousands of times between day and night. Even so, paper still looks white because the eye captures the ratio to its surroundings, and the brain discounts the amount of illuminating light. We're trying to see the properties of the object itself, not the light falling on it.
What the eye sees isn't the amount of light, but its "ratio."
That's why white paper stays white even under the moon.
For how the colors of night-sky stars vanish inside the eye, see Why do stars look white?, and for how ice and snow differ in appearance, see Why does snow look white?
- Lay a white sheet and a black sheet side by side, and compare them both at a bright window and deep inside a dim room. In either spot, white should look white and black should look black.
- Next, hold a narrow tube (like a toilet-paper roll) up to the white paper and peek at just a small patch of it through the tube. With your surroundings hidden, you'll notice the paper's brightness differs quite a bit between the window and the back of the room.
- Cast a hand-shadow over half a sheet of white paper. Confirm that even though less light reaches your eye from the shadowed part, it doesn't look like "gray paper."
In step 2, "hiding your surroundings" removes the thing you're comparing against, making it harder for the brain's correction to kick in. Don't point the tube at direct sunlight or a lightbulb — avoid aiming it at anything bright.
Want to go deeper? ― terms, formulas, and textbook connectionsWe mark which level each part belongs to, from middle-school science up to university specialist courses
- MSCovered in middle-school science
- HSCovered in high-school physics or biology
- HS+Advanced high-school content, or textbook sidebar material
- UnivNot covered in high school — university-level specialist content (vision science, perceptual psychology)
- ResearchNot yet settled even at university — an area researchers are actively investigating
MSTerms: this phenomenon has a name
- Lightness constancy: the way an object's whiteness or blackness feels the same even as the strength of the illuminating light changes.
- Illuminance: the strength of light falling on an object. Measured in lux.
- Reflectance: the fraction of incoming light an object reflects back. White paper is said to be about 80%, charcoal only a few percent.
MSHSChecking it with a formula: paper in moonlight vs. charcoal in sunlight
The strength of light reaching the eye from a matte white surface (its luminance) is the product of the illuminating light and the reflectance. This formula lets us calculate the dashed line and bar heights in Figure 1.
| In symbols | L ＝ E × R ÷ π |
| In words | Light reaching the eye ＝ strength of illuminating light × fraction reflected ÷ pi |
| Where it comes from | It follows from conservation of light: the reflectance's share of the incoming light spreads out evenly in every direction from a matte surface. The ÷ π converts that spread into an amount per single direction. |
| L (symbol) | Luminance. Units: candela per square meter |
| E (symbol) | Illuminance. About 100000 lux for direct sunlight on a clear day, and about 0.2 lux for a full-moon night |
| R (symbol) | Reflectance. About 0.8 for white paper, about 0.04 for charcoal |
| Charcoal in sun (E × R) | 100000 × 0.04 ＝ 4000 |
| Charcoal in sun, luminance (÷ π) | 4000 ÷ 3.14 ≒ 1274 |
| Paper in moonlight (E × R) | 0.2 × 0.8 ＝ 0.16 |
| Paper in moonlight, luminance (÷ π) | 0.16 ÷ 3.14 ≒ 0.051 |
| Charcoal in sun ÷ paper in moonlight | 1274 ÷ 0.051 ≒ 24980 |
| Paper ÷ charcoal under the same light (E and π cancel) | 0.8 ÷ 0.04 ＝ 20 |
Charcoal in sunlight sends roughly 25,000 times more light to the eye than white paper does in moonlight. If white and black were decided by light amount alone, charcoal would end up "white." But the ratio between paper and charcoal under the same light is always 20, regardless of the illuminating light. The eye and brain use this unchanging ratio as their clue.
HSHS+The retina emphasizes "edges" when sending its signal
HSThe retina is lined with light-receiving cells, and their signals are gathered by ganglion cells before being sent to the brain. The eye also adapts to darkness, adjusting its sensitivity up or down to keep pace even as overall brightness changes.
HS+Many ganglion cells respond strongly to the difference between the "center" and "surround" of the area they cover. This mechanism, where neighboring cells cancel out each other's signal, is called lateral inhibition. Because the difference signal survives even when brightness rises or falls uniformly, the ratio of light and dark at edges reaches the brain more readily.
UnivRetinex theory and estimating the illumination
In 1971, the photographer-scientist Edwin Land proposed that stitching together the light-dark ratios at edges across the whole scene could recover a reflectance that doesn't depend on the illumination. This is called Retinex theory. Later, Edward Adelson's "checker-shadow illusion" and other work showed that the brain estimates illumination not just from ratios but from shadows and depth cues as well. The same mechanism operates for color too, and is called color constancy.
📖 For the derivation of the formula and further reading: Land and McCann's original paper (Retinex theory) ／ Color constancy - Wikipedia (Japanese)
ResearchWhat's still not fully understood
- Is the brightest thing taken as "white"? One idea holds that the brain sets its white reference to the brightest surface in the visual field. But it's also known that this reference shifts depending on how much area the bright surface covers, and no fixed rule has been worked out yet.
- At what stage does the correction happen? How much is handled in the retina versus how much involves the brain estimating illumination at a higher stage is still debated.
- The correction differs from person to person. The famous 2015 photo of "the dress" appeared blue-and-black to some people and white-and-gold to others. This is thought to stem from individual differences in how people estimate the illumination, but where that difference comes from is still being studied.
In other words, even this article's explanation reflects "what's understood so far." The mechanism for capturing ratios is now fairly well understood, but the full picture of how the brain estimates illumination is still being worked out.
Textbook connections (by level)
| Level | Subject / unit | Where in this article |
|---|---|---|
| MS | Science: "reflection of light," "stimulus and response (structure of the eye)" | Fraction reflected, light reaching the eye |
| HS | Biology: "receptors and nerves" | Retinal cells, dark adaptation |
| HS+ | Advanced biology: "lateral inhibition" | How light-dark ratios at edges reach the brain |
| Univ | Vision science, perceptual psychology, photometry | Retinex theory, the luminance/illuminance formula |
| Research | Visual neuroscience | The white reference point, individual differences in illumination estimation |
| ― | Everyday connections | Photos of snowy scenes, reading in dim light |
- Land, E. H. & McCann, J. J. (1971) Lightness and Retinex Theory. Journal of the Optical Society of America 61, 1–11.
- Gilchrist, A. (2006) Seeing Black and White. Oxford University Press.
- Adelson, E. H. (2000) Lightness perception and lightness illusions. In: The New Cognitive Neurosciences, 2nd ed., MIT Press.
- Lafer-Sousa, R., Hermann, K. L. & Conway, B. R. (2015) Striking individual differences in color perception uncovered by 'the dress' photograph. Current Biology 25, R545–R546.
- Wikipedia (Japanese): "Color constancy" (色の恒常性)
※ This article is a general-audience science explainer. The figures given are approximations meant to aid understanding of the underlying mechanism. Illuminance and reflectance vary considerably with weather, time of day, and material.