Why Does Your Face Look Upside Down in a Spoon?
― A Hollow Mirror Gathers Light to One Point, Then Lets It Cross
Look into the inside of a spoon and you see a small, upside-down version of your face. Turn the spoon over and the face is the right way up. The inside of a spoon is a "hollow mirror" that gathers light to one point. Once the light passes that point, top and bottom swap places. The upside-down face is the result of that crossing.
Halfway through a meal, you idly hold a shiny spoon up in front of your face. In the hollow, a tiny version of you is standing on its head.
Flip the spoon over, and the bulging side shows your face the usual way up. It is a funny face, with an oddly big nose.
Now bring your eye very close to the inside of the spoon. What happens? Past a certain distance, the upside-down face suddenly snaps back to the right way up. Why does one spoon show you such different pictures?
There are just two reasons
A hollow mirror pulls the light it reflects together into one point in front of it. This point is called the "focal point". Light crosses at the focal point, so beyond it, light from the top heads down and light from the bottom heads up.
If your face is closer than the focal point, the light has not finished gathering. It reaches your eye still spreading out. Nothing crosses, so the image looks upright and enlarged. The bulging back of the spoon spreads light out, so it always looks upright.
In an ordinary flat mirror, light does not cross. That is why your face always looks the right way up. The only special thing about a spoon is that its surface is curved. That curve changes the path of the light a great deal.
Light crosses in an X at the focal point
Look at Figure 1. The curved line on the right is a side-on slice through the inside of the spoon. The arrow on the left is your face, and the tip of the arrow is the top of your head.
Of the light leaving the top of your head, a ray that travels straight to the mirror bounces back through the focal point. A ray that passes through the focal point before hitting the mirror bounces back straight to the left. The image of the top of your head forms where these two rays meet.
Both rays cross the central line before they meet. So the image of the top of your head forms below the line. Light from your chin does the opposite and gathers above the line. Top and bottom swap, and your face looks like it is standing on its head.
Left and right swap by the same logic. The spoon's image is like the flat-mirror image turned through a half turn.
Why does it flip back when you move closer?
Try moving the slider in Figure 1 all the way to the left. Once your face is inside the focal point, the reflected light no longer gathers to a point. It reaches your eye spreading out a little.
When your eye receives spreading light, your brain traces the light backwards. It feels as if the light came from deep behind the mirror. At that "apparent source" you see a large face, the right way up. For an ordinary teaspoon, the focal point is said to be about 2 cm from the mirror. It is hard to bring your eye that close, so you normally see only the upside-down face.
There is an everyday tool that uses this property: the magnifying mirror for make-up or shaving. A magnifying mirror is hollowed out much more gently than a spoon. Its focal point is tens of centimetres away, so when you lean in normally, you are inside the focal point and see a large, upright face.
By contrast, a bulging mirror like the back of a spoon always spreads light outward. So the image looks upright and small from anywhere. In exchange for being small, it fits a wide area into one view. This is why the road mirrors at junctions are made from bulging mirrors.
A bulging mirror shows the scene smaller. People tend to feel that small things are far away. A car in a road mirror often looks farther away and slower than it really is. If you see a car in the mirror, it is safer to assume it is closer than it seems and wait.
Summary
The inside of a spoon is a hollow mirror that gathers light to one point. Light crosses at the focal point, so the image beyond it is flipped top-to-bottom and left-to-right. If you bring your face inside the focal point, no crossing happens and you get a large, upright image. The bulging back spreads light out, so it always shows a small, upright image.
An upside-down face is how you look
after the light has crossed at one point.
For why a flat mirror seems to flip only left and right, see Why does a mirror flip left and right but not up and down?. Gathering light to one point is also what the lens does in Why can a magnifying glass set paper on fire?.
- Hold a well-polished, large spoon at arm's length and look into the inside. Check that your face looks upside down.
- Close one eye and slowly bring the spoon closer to your eye. The image becomes blurry and larger, then at a certain distance it turns the right way up. That distance is roughly the position of the focal point.
- Turn the spoon over and move it closer and farther in the same way. Check that the orientation never changes at any distance.
Compare a tablespoon with a teaspoon: the gentler the hollow, the farther away the flip happens. Move slowly so the tip of the spoon does not hit your eye.
For those who want to know more ― terms, formulas and links to textbooksFrom middle-school science to university-level courses, each part is marked with its level
- Middle schoolCovered in middle-school science
- High schoolCovered in high-school physics
- High school+Advanced high-school material, or a textbook sidebar
- UniversitySpecialist university material (optics) not taught in high school
- ResearchNot yet settled even at university level; what researchers are studying now
Middle schoolTerms: this phenomenon has names
- Concave mirror: a mirror hollowed inwards. The inside of a spoon, a magnifying mirror, the main mirror of a reflecting telescope, and so on.
- Convex mirror: a mirror that bulges outwards. The back of a spoon, a road mirror, part of a car's side mirror, and so on.
- Real and virtual images: an image formed where light actually gathers is a real image (upside down). An image you only see by tracing light backwards is a virtual image (upright).
Middle schoolHigh schoolCheck with a formula: how small is a face held 30 cm from the spoon?
Let's calculate where the image forms and how big it is when your face is 30 cm from the spoon. We assume the hollow of the spoon has a radius of 4 cm (the real value depends on the shape).
| In symbols | 1 ／ a ＋ 1 ／ b ＝ 1 ／ f （f ＝ R ／ 2, magnification m ＝ −b ／ a） |
| In words | (1 ÷ distance to the face) + (1 ÷ distance to the image) = 1 ÷ focal length. The focal length is half the radius of the hollow |
| Where it comes from | The law of reflection (angle in equals angle out), applied to light near the centre of the mirror and built from the similar triangles of the two rays in Figure 1 |
| Radius of the hollow R (assumed) | 4 cm |
| Distance to the face a | 30 cm |
| Height of the face (chin to head) | 20 cm |
| Focal length f | 4 ÷ 2 ＝ 2 (cm) |
| 1 ÷ focal length | 1 ÷ 2 ＝ 0.5 |
| 1 ÷ distance to the face | 1 ÷ 30 ≒ 0.033 |
| 1 ÷ distance to the image | 0.5 − 0.033 ≒ 0.467 |
| Distance to the image b | 1 ÷ 0.467 ≒ 2.14 (cm) |
| Size of the magnification | 2.14 ÷ 30 ≒ 0.071 |
| Height of the image | 20 × 0.071 ≒ 1.4 (cm) |
The image forms about 2.1 cm in front of the mirror, just outside the focal point. The magnification formula carries a negative sign, so the image is upside down. A face 20 cm tall shrinks to about 1.4 cm, roughly one-fourteenth, and fits in the hollow of the spoon. If you move your face farther away, the image stays near the focal point and just gets smaller.
High schoolHigh school+Image orientation, and the link to flat mirrors
High schoolThe formula above is also called the "mirror equation", and it has the same form as the convex lens equation. For a convex mirror, you treat the focal length as negative and the same formula gives the image position. In that case the image distance is always negative, and the image is an upright virtual image behind the mirror.
High school+If you make the radius of the hollow endlessly large, the focal length also grows endlessly, and the mirror approaches a flat one. The formula then becomes "image distance = −distance to the face", and the magnification is +1. The image in a flat mirror is included as a special case of the concave-mirror formula.
UniversityThe paraxial approximation and spherical aberration
The formula above holds in the "paraxial approximation (Gaussian optics)", which considers only light passing near the centre of the mirror. In a spherical mirror, light nearer the edge gathers closer to the mirror than the focal point, so it does not come together at a single point. This error is called "spherical aberration". With a parabolic surface, light parallel to the axis gathers to one point with no aberration. That is why the main mirrors of reflecting telescopes are polished to a parabola. The distortion in a spoon's image comes from this aberration and from "astigmatism", because the hollow curves differently along its length and across it.
📖 Derivation of the formula, and further reading: Spherical mirror (Wikipedia, in Japanese) ／ Aberration (Wikipedia, in Japanese)
ResearchWhat is still not clear
- How does the brain turn the image in a curved mirror into "distance"? The way people misjudge distance and speed in road mirrors has been studied in traffic psychology, but which cues matter most gives different results depending on the conditions.
- How do animals see curved mirrors? There are many experiments on whether animals recognise themselves in a mirror, but responses to distorted images have been little studied.
- Lighter curved mirrors with less distortion. For space telescopes and similar instruments, research continues on techniques that reshape a thin mirror precisely with machines to cancel aberrations.
In other words, this article too is "an explanation of what is known so far". The path of the light itself is certain, but how people see it still holds some mysteries.
Link to textbooks (by level)
| Level | Subject and unit | Where in this article |
|---|---|---|
| Middle school | Science, year 1: "Reflection of light", "Images from a convex lens" | Law of reflection, focal point, real and virtual images |
| High school | Physics: "Reflection and refraction of light (spherical mirrors)" | Mirror equation, magnification, negative focal length of a convex mirror |
| High school+ | Advanced physics | Treating a flat mirror as a spherical mirror of endlessly large radius |
| University | Optics | Paraxial approximation, spherical aberration, astigmatism, parabolic mirrors |
| Research | Traffic psychology, adaptive optics | Misjudging distance with curved mirrors, mirrors that can change shape |
| ― | Links to daily life | Spoons, make-up magnifying mirrors, road mirrors |
- Spherical mirror (球面鏡) - Wikipedia (in Japanese)
- Aberration (収差) - Wikipedia (in Japanese)
- Mirror (鏡) - Wikipedia (in Japanese)
- General descriptions of spherical mirrors and the mirror equation in high-school physics textbooks (高等学校「物理」教科書).
- E. Hecht, Optics (Pearson), on spherical mirrors, paraxial rays and aberrations.
* The radius and focal length of the spoon's hollow are assumptions made to explain the mechanism. Real values depend on the shape of the spoon.
* This article is a general-audience science explainer. The figures given are rough guides to help you understand the mechanism. At junctions, do not rely on a road mirror alone; check for safety with your own eyes.