Why does the far end of facing mirrors get darker and greener?
― Mirrors lose about a tenth of the light with every bounce
Mirrors look like they reflect "all" of the light that hits them. In fact, they lose a little with every single bounce, and the amount they lose varies slightly by colour. Facing mirrors simply stack that tiny difference dozens of times, until it becomes visible.
Hold a hand mirror up facing the bathroom mirror. A mirror appears inside the mirror, and inside that one another mirror appears, and so on — a tunnel stretching into the distance.
Look closely and the deeper reflections are darker. The nearest one looks whitish, but the further ones sink into a deep green.
The mirror itself shouldn't have any colour. So where do this darkness and this green come from?
Just two reasons
An ordinary mirror is thought to reflect roughly 90% of the light that hits it. You wouldn't notice that on a single bounce, but stack it dozens of times and the brightness drops off fast.
A mirror's silver coating sits on the back of the glass. Light has to travel through that glass both ways. Ordinary glass — the same kind as window glass — is slightly green-tinted, absorbing a little more red and blue than other colours.
The first reason explains the darkening; the second explains the green. Neither difference is visible on its own. Facing mirrors multiply both effects dozens of times over, until they become large enough to see.
One-tenth lost per bounce. But after 20 bounces, only a tenth remains
Say 90% of the light entering a mirror comes back out. After two bounces, that's 90% of 90%, or about 80%. With each further bounce, only 90% of the current brightness survives.
This kind of decline shrinks by the same *proportion* each time, not the same *amount*. It drops sharply at first, then more slowly, forever edging toward zero without quite reaching it. Try the slider in Figure 1 to change how much light the mirror reflects per bounce.
At 90% in Figure 1, the 10th reflection is already down to about a third of the original brightness. By around the 22nd bounce, it drops below a tenth. Raise it to 99% and it takes over 200 bounces to fall that far. In other words, a mere 10-percentage-point difference can change the tunnel's "depth" tenfold.
In practice it's hard to keep two mirrors perfectly parallel, so the tunnel curves slightly more with each reflection. Still, being able to count dozens of reflections at all shows just how high — around 90% — a mirror's reflectance really is.
The source of the green: the glass on the front of the mirror
A household mirror is a sheet of glass with a thin silver coating on the back, itself protected by a layer of paint. Light enters the glass first, bounces off the silver behind it, then passes back through the glass on its way out (Figure 2). So for every single reflection, the light crosses the thickness of the glass twice.
Ordinary sheet glass contains a trace of iron, left over from the sand it's made from. This iron absorbs slightly more of the reddish and bluish light, which is why the glass has a faint greenish tint. Looked at straight on, it appears clear — but look along the edge of a pane and it's clearly green.
The edge looks green because the light has to travel a much longer distance through the glass. The same thing happens with facing mirrors. Light that has bounced 20 times has, if the glass is 4 mm thick, effectively passed through 16 cm of glass in total. Looking into the depths of the tunnel is almost like peering into a solid block of glass.
Because a white object reflected in a mirror looks white, we tend to think of mirrors as colourless by nature. But careful measurements of how much each colour is reflected show that an ordinary mirror actually reflects the highest proportion around green. In that sense, "a mirror is a very slightly green object" is literally true.
The large mirrors in astronomical telescopes have their metal coating on the front surface of the glass, not the back. Because the light never passes through glass, this avoids colour bias and double images. The trade-off is that the coating is easily damaged, so unlike a household mirror it can't just be wiped by hand.
Summary
The far end of facing mirrors looks dark because each bounce loses about a tenth of the light, and that loss multiplies over dozens of bounces. It looks greenish because the glass on the front of the mirror absorbs slightly more red and blue, and that difference compounds too. A difference too small to notice on a single bounce grows, through repetition, into something clearly visible.
A mirror returns "almost all" of the light.
It's that "almost" that becomes a green darkness at the far end of facing mirrors.
For why mirrors flip only left and right, see "Why do mirrors flip only left and right, and not up and down?", and for how window glass becomes a mirror at night, see "Why does window glass turn into a mirror at night?".
- Stand in front of a bathroom mirror and hold a hand mirror beside your face, angled so the two mirrors face each other almost directly. You'll see a tunnel stretching into the hand mirror.
- Count how many reflections you can make out, starting from the nearest. Notice how the deeper ones get darker and greener.
- Look along the edge of a window pane or a picture-frame glass, straight on from the side. Glass that looks clear from the front should look distinctly green at the edge.
Glass edges can be sharp — look, don't run your finger along them. Also avoid reflecting sunlight off a mirror into anyone's eyes.
Want to go deeper? ― terms, formulas, and how this connects to the curriculumWe clearly mark which level each part belongs to, from junior-high science to university-level courses
- JHScovered in junior-high-school science
- HScovered in high-school "physics" or "maths"
- HS+high-school extension material, or a textbook sidebar topic
- Univ.not covered in high school — university-level specialist content (optics, materials science)
- Researchnot yet settled even at university level — something researchers are actively investigating
JHSTerminology: this phenomenon has names
- Reflectance: the fraction of incoming light that bounces back. For an ordinary mirror this is thought to be roughly 90%.
- Absorption: when a material takes in light energy and converts it into something else, such as heat. How readily this happens varies by colour.
- Back-surface and front-surface mirrors: a mirror with the metal coating on the back of the glass is a back-surface mirror (household mirrors); one with the coating on the front is a front-surface mirror (telescope mirrors).
JHSHSChecking with a formula: at which bounce does brightness fall to a tenth?
With each reflection, the same fraction R of brightness survives. We work out the brightness after n repetitions, and find at which bounce it drops below a tenth.
| In symbols | In ＝ I0 × Rn |
| In words | brightness of the nth reflection ＝ starting brightness × (the per-bounce fraction, multiplied by itself n times) |
| Where it comes from | Each reflection leaves behind "R times the current brightness," repeated n times. Because the same fraction is lost each time, this forms a geometric sequence (an exponential function). |
| In | brightness of the reflection after n bounces (as a fraction of the start) |
| I0 | starting brightness (taken here as 1) |
| R | fraction of light the mirror returns per bounce (reflectance, unitless) |
| n | number of bounces |
| Reflectance of a household mirror (rough figure) | thought to be about 0.9 |
| Thickness of the sheet glass (one example household mirror) | 4 mm |
| Number of glass passes per reflection | 2 (in and out) |
| Brightness at bounce 2 | 0.9 × 0.9 ＝ 0.81 |
| Bounce 4 (square the bounce-2 value) | 0.81 × 0.81 ≒ 0.656 |
| Bounce 8 (square bounce 4) | 0.656 × 0.656 ≒ 0.430 |
| Bounce 16 (square bounce 8) | 0.430 × 0.430 ≒ 0.185 |
| Bounce 20 (bounce 16 × the 4-bounce factor) | 0.185 × 0.656 ≒ 0.121 |
| Bounce 22 (bounce 20 × the 2-bounce factor) | 0.121 × 0.81 ≒ 0.098 |
| Glass passes over 20 reflections | 20 × 2 ＝ 40 |
| Total glass thickness crossed (mm) | 40 × 4 ＝ 160 |
By bounce 22, brightness has fallen to about 0.098 of the start — below a tenth. That matches the "bounce 22" figure from Figure 1. By that point, the light has passed through roughly 16 cm of glass — about the same distance as looking along the edge of a pane, which is why the green becomes so clear.
HSHS+What "shrinking by the same proportion" means
HSA quantity that shrinks by the same proportion each time forms a geometric sequence. Taking logarithms of both sides, the number of bounces needed to fall to a tenth works out to "log of 0.1 ÷ log of R." The closer R is to 1, the closer its logarithm gets to zero, so the bounce count shoots up sharply. That's why 90% and 99% differ by roughly a factor of 10 in bounce count.
HS+Absorption inside the glass follows the same "shrinks by the same proportion" shape. The relationship where brightness falls off exponentially with the thickness traversed is known as the Beer–Lambert law. Because red, green, and blue are absorbed by slightly different amounts, the longer the path, the more it's green — the colour absorbed least — that survives.
Univ.Metal reflectance and iron ions in glass
Metals reflect light well because the electrons that move freely within them oscillate in a way that cancels out the light's electric field. This behaviour is described by the Drude model, and silver and aluminium reflect most of the visible spectrum. The green tint of sheet glass (soda-lime glass), on the other hand, is thought to come mainly from absorption by trace iron ions. Fe²⁺ ions are thought to absorb toward red and near-infrared, and Fe³⁺ ions toward ultraviolet and blue, leaving green — the "valley" between the two — to pass through.
📖 For the derivation and further reading: Beer–Lambert law (Japanese Wikipedia) ／ Mirror structure and types (Japanese Wikipedia)
ResearchWhat's still not fully understood
- How many reflections can the human eye actually see? Beyond the raw brightness ratio, factors like eye adaptation, room lighting, the shrinking size of each image, and tiny tilts in the mirrors all come into play, so there's no single fixed answer.
- How colour is perceived in dim light. In darker reflections, the eye's own colour perception changes. How far the greenness of the deepest reflections can be explained by glass absorption alone is thought to vary with conditions.
- Making mirrors with less colour bias. Research and product development continue into high-transmission glass with reduced iron content, and into coating materials, both aimed at reducing colour bias.
So the content of this article, too, reflects only "what's understood so far." Reflectance and tint vary by mirror type, so treat the numbers as rough guides.
Links to the curriculum (by level)
| Level | Subject/unit | Where in this article |
|---|---|---|
| JHS | Year-1 science, "reflection and refraction of light" | light bouncing off a mirror, passing through glass |
| HS | Maths "exponential and logarithmic functions," physics "properties of light" | brightness shrinking by a constant ratio, the bounce count to reach a tenth |
| HS+ | Chemistry extension, "absorption of light and colour" | the Beer–Lambert law, why only green survives |
| Univ. | Optics, solid-state physics, glass engineering | the Drude model, absorption by iron ions |
| Research | Vision science, optical materials | how many reflections are visible, mirrors with less colour bias |
| ― | Everyday connections | facing mirrors, the green edge of glass, telescope mirrors |
- Japanese Wikipedia, "鏡" (Mirror) — structure and types of mirrors
- Japanese Wikipedia, "ランベルト・ベールの法則" (Beer–Lambert law)
- E. Hecht, Optics, 5th ed., Pearson (chapter on reflection and absorption by metals)
- W. Vogel, Glass Chemistry, Springer (colouring of glass by iron ions)
※This article is a general-audience science explainer. The figures given are rough estimates meant to aid understanding of the underlying mechanism. The reflectance of mirrors and the tint of glass vary by product and manufacturing method.