How Many Particles of Light Does the Human Eye Need to "See" Something?
― Light from the faintest star reaches you as only about 150 particles in 0.1 seconds
Light arrives as tiny particles called photons. From the faintest star you can see on a dark night, only about 150 particles of light enter your pupil in 0.1 seconds. Your retina catches just a dozen or so of them. The human eye is so sensitive that it can, in effect, count particles of light.
You stand on a mountaintop where city lights don't reach, and look up at the night sky. At first you see only a few bright stars.
But as you wait 20 or 30 minutes, more and more stars appear. In the end, stars so faint you can hardly tell whether they are there are scattered across the whole sky.
How much light is actually reaching your eye from that faintest star? In fact, only a small "handful" of particles gets through.
Just two reasons
The cells that work in the dark (rods) can send an electrical signal after receiving just one particle of light. This is the physical limit of sensitivity; it cannot get any smaller.
Cells sometimes fire on their own, even with no light. To avoid being fooled by these false alarms, the brain decides that light was there only when several signals pile up within a short time.
In other words, the eye itself is sensitive enough to feel a single particle. Yet for us to feel that we have "seen" something, it takes several to a dozen or so particles. The combination of these two facts sets the limit of the stars we can see with the naked eye.
How many particles arrive from the faintest star?
We describe the brightness of stars in the night sky by "magnitude." The bigger the number, the dimmer the star. Under a dark sky, the naked-eye limit is about magnitude 6. Compared with a magnitude 1 star, it is only about one hundredth as bright.
The pupil of a dark-adapted eye opens to about 7 millimeters across. Particles of light from a magnitude 6 star fly into that small window. Counting them, you get about 1,500 per second.
The cells of the retina are thought to collect light for about 0.1 seconds at a time and report it all at once. Cut into 0.1-second slices, about 150 particles enter the pupil. Look at Figure 1. Change the star's magnitude with the slider and you can see how the number of arriving particles changes.
Of the 150, only a dozen or so are caught
Not all 150 particles that enter the pupil get used. Look at Figure 2. Some bounce off the surface of the cornea, and some are absorbed by the clear jelly and the lens inside the eye, so only about half reach the retina.
Even among the particles that reach the retina, only about one in five is thought to hit the light-catching pigment inside a cell properly. The rest slip through the gaps between pigment molecules. In the end, only about one tenth of the particles that entered the pupil, a dozen or so, turn into signals.
Three people who measured their own eyes confirmed it
In 1942, three American researchers pinned down this number by experiment. They let their eyes adapt in a pitch-dark room, watched very brief flashes of light, and answered "seen" or "not seen." The test subjects were the researchers themselves.
The result: they said "seen" when somewhere between a few dozen and about 150 particles reached the cornea. After subtracting the losses inside the eye, only 5 to 14 particles were absorbed. And that light was spread over about 500 cells.
A dozen or so particles, 500 cells. Most cells receive no particle at all, and any that do receive only one. From this the three concluded that "a single cell responds to a single particle of light." About 40 years later, this reasoning is said to have been confirmed by experiments that measured the signals of single cells directly.
There are almost no cells that can respond to a single particle right at the center of your gaze. They are packed in a little away from the center. That is why a faint star vanishes when you stare straight at it and pops out when you look slightly aside. This is "averted vision," a trick stargazers have used for a long time.
A story circulates that in total darkness you could see a single candle flame from dozens of kilometers away. But a study that measured a candle's brightness and worked out the numbers put the naked-eye limit at about 2.6 km. When the distance doubles, the number of particles falls to one quarter. The distance at which the particles drop below the threshold is closer than you might think.
Summary
From the faintest star visible to the naked eye, about 150 particles of light enter the pupil in 0.1 seconds. The retina catches a dozen or so of them, scattered one apiece over about 500 cells. A cell can respond to a single particle, but the brain does not say "seen" until several have arrived. This caution protects us from the mistake of seeing light that isn't there.
The faintest star in the night sky is made of a dozen or so particles of light.
The eye can count particles, yet the brain deliberately waits for several before saying "seen."
For how long it takes your eyes to adjust to the dark, see "Why can't you see anything for a while when you walk from a bright place into a dark room?". For why stars look whitish, see "Stars have colors, so why do most stars in the night sky look white?".
Eyes differ among creatures not only in "how many particles it takes to see" but also in "how many frames per second they see." The fly, which sees time in about four times finer detail than humans, is covered in "Why do flies escape so quickly when you try to swat them?".
- On a clear, moonless night, go somewhere where street lamps don't shine directly into your eyes. Without looking at your smartphone screen, let your eyes adapt to the dark for about 20 minutes.
- Find a faint cluster of stars (in autumn and winter, the Pleiades in the eastern sky). Compare how many stars you see when you look straight at it and when you look slightly to the side.
- Finally, glance at your smartphone screen for just a moment, then look up at the sky again. If the faint stars have vanished, that is a sign that the cells that respond to a single particle have been put to rest by the strong light.
Check that the ground is safe underfoot before you go, and don't go to dark places alone at night. Lighting your hands with a red light barely disturbs your dark-adapted eyes.
For those who want to know more ― terms, formulas, and links to textbooksShows which level each topic belongs to, from middle-school science to university courses
- Middle schoolCovered in middle-school science
- High schoolCovered in high-school physics, biology, or earth science
- High school+Advanced high-school content, or material treated as a textbook sidebar
- UniversityUniversity-level specialist courses not taught in high school (visual physiology, quantum optics, statistics)
- ResearchNot taught even at university as settled fact; researchers are still investigating it
Middle schoolTerms: this phenomenon has names
- Photon: one particle of light, seen as the smallest lump of light that cannot be divided further.
- Rod cell: a cell in the retina that picks up light in the dark. It cannot tell colors apart but is very sensitive.
- Magnitude: a number for the brightness of a star. A difference of 5 magnitudes means a 100-fold difference in brightness; the bigger the number, the dimmer the star.
- Averted vision: the trick of looking slightly away from a faint object to see it better, because the light lands where rods are plentiful.
Middle schoolHigh schoolChecking with a formula: how many particles does the retina receive from a magnitude 6 star?
Express the light arriving from a star as "how many particles fly in per second per square centimeter," then multiply by the area of the pupil and by the collection time.
| In symbols | N ＝ F × A × t × η |
| In words | Number of particles absorbed ＝ strength of the particle flow × area of the pupil × collection time × fraction absorbed |
| Where it comes from | Particles of light neither multiply nor vanish on the way, so the number passing through a window (the pupil) can be counted as "strength of flow × area of window × time." Multiply that by the fraction that is actually used inside the eye. |
| Symbol | Meaning and unit |
| N | Number of light particles absorbed in the retina (particles) |
| F | Flow of particles arriving from the star (particles / second / square centimeter) |
| A | Area of the pupil (square centimeters) |
| t | Time over which the rods collect light (seconds) |
| η | Fraction of the particles entering the pupil that are absorbed by the pigment |
| Flow of visible-light particles arriving from a magnitude 0 star | About 1 million per second per square centimeter, it is said |
| At 6 magnitudes dimmer, the brightness is | About 1/250 |
| Radius of a dark-adapted pupil | About 0.35 cm (7 mm across) |
| Time over which rods collect light | About 0.1 seconds, it is said |
| Fraction absorbed | About 0.1 (one tenth of the particles entering the pupil) |
| Number of rods the light is spread over (1942 experiment) | About 500 |
| Particle flow from a magnitude 6 star (particles / second / square centimeter) | 1000000 ÷ 250 ＝ 4000 |
| Radius squared | 0.35 × 0.35 ＝ 0.1225 |
| Pupil area (square centimeters) | 0.1225 × 3.14 ≒ 0.385 |
| Particles entering the pupil per second | 4000 × 0.385 ＝ 1540 |
| Particles entering the pupil in 0.1 seconds | 1540 × 0.1 ＝ 154 |
| Particles absorbed in the retina (N) | 154 × 0.1 ≒ 15 |
| Particles per rod | 15 ÷ 500 ＝ 0.03 |
About 15 particles are absorbed, which is about the same size as the "5 to 14" of the 1942 experiment. Per rod, the average is 0.03 particles. This works out to about 3 cells in 100 each receiving exactly one particle, and almost no cell receives two.
High schoolHigh school+Light is a wave, and also a particle
High schoolIn high-school physics you learn that light behaves as a wave, yet exchanges energy in lumps called "photons" (the photoelectric effect). The energy of one photon is proportional to the frequency. For green light, the energy per photon is tiny; even a small light bulb emits many quintillions of photons every second. The eye can sense just one of them.
High school+The magnitude scale expresses the ratio of brightnesses on a logarithmic scale, and is described by Pogson's formula. Since 5 magnitudes is a factor of 100, one magnitude is a factor of about 2.5. Six magnitudes is that figure to the 6th power, about 250. This builds into the numbering the fact that human senses feel brightness as a ratio.
UniversityThe Hecht–Shlaer–Pirenne experiment and the Poisson distribution
The heart of the 1942 experiment was to use the fact that particles of light arrive "one by one at random times." When the average number arriving is some value, the actual number fluctuates according to a Poisson distribution. Look at the shape of the curve showing how the probability of answering "seen" rises with light intensity, and the threshold number needed to see can be read off without depending on the fine details of physiology. The threshold found this way was about 5 to 7 particles. That a single rod responds to a single photon is said to have been confirmed in 1979 by Baylor and colleagues, by directly measuring the electric current of rods. The reason the brain waits for several is thought to be to tell real light apart from the "dark noise" produced when the pigment rhodopsin reacts on its own because of heat, with no light at all.
📖 Derivations and further reading: Poisson distribution (Wikipedia, in Japanese) ／ Rod cell (Wikipedia, in Japanese)
ResearchWhat is still not clear
- Can people notice even a single particle of light? In 2016 there was a report that, using a source that emits particles one at a time, people guessed correctly slightly more often than chance even with a single particle. But the effect is small, and follow-up checks are continuing.
- Where in the brain is "seen" decided? At which stage inside the retina the mechanism that gathers cell signals and filters out noise operates is still being investigated in detail.
- How much do limits differ between people? The naked-eye limit for stars is said to change not only with the darkness of the sky but also with age and experience. Which factors matter, and by how much, has not yet been fully sorted out.
In short, what this article says is also "an explanation of what is known so far." The numbers in the calculation above are rough guides that can change by several times depending on pupil size and sky conditions.
Links to textbooks (by level)
| Level | Subject / unit | Where in this article |
|---|---|---|
| Middle school | Science: "Structure of the eye," "Properties of light" | Retinal cells, pupil size |
| High school | Physics: "Photons"; Biology: "Receptors and photoreceptor cells" | Rods that respond to a single particle |
| High school+ | Earth science: "Brightness of stars (magnitude)" | About 1/250 at 6 magnitudes |
| University | Visual physiology, probability and statistics (Poisson distribution) | How to read the 1942 experiment |
| Research | Vision science, quantum optics | Detecting a single photon, handling dark noise |
| ― | Links to daily life | Averted vision in stargazing, why red light is used at night |
- Hecht, S., Shlaer, S., & Pirenne, M. H. (1942). Energy, quanta, and vision. Journal of General Physiology, 25(6), 819–840.
- Baylor, D. A., Lamb, T. D., & Yau, K.-W. (1979). Responses of retinal rods to single photons. Journal of Physiology, 288, 613–634.
- Wikipedia, "Magnitude (astronomy)" (等級 (天文), in Japanese)
- Tinsley, J. N. et al. (2016). Direct detection of a single photon by humans. Nature Communications, 7, 12172.
- Krisciunas, K., & Carona, D. (2015). At what distance can the human eye detect a candle flame? (an estimate of the distance at which a candle flame can be seen)
*This article is a popular-science explanation for general readers. The figures given are rough guides to help you understand the mechanism. When stargazing, make sure the ground is safe underfoot, and go to dark places with other people.