Curved Enough to Fool Your Own Reflection

At a science centre, a girl named Meena looked into a row of unusual mirrors: in one, her face appeared unusually large; in another, her brother, standing farther away, looked upside down; in a third, she saw a tiny version of herself. Nothing like this had happened with the plane (flat) mirrors from her earlier lessons, which always showed an image the same size as the object, right way up. A guide explained that these were spherical mirrors, curved either inward or outward, and that the curve itself was exactly what changed everything. A simple shiny metal spoon demonstrates the same effect directly: looking into its inner, hollowed-out surface shows an inverted image, while flipping it over to the outer, bulging surface shows an image that is erect but smaller. A spherical mirror whose reflecting surface curves inward, like the spoon's inner side, is called a concave mirror; one whose reflecting surface curves outward, like the spoon's outer side, is called a convex mirror. Spherical mirrors are not, in fact, cut from a hollow glass sphere despite their name; they are made by grinding and polishing a flat piece of glass into a curved shape, then coating one side with a thin reflective layer, the outer curved surface for a concave mirror, the inner curved surface for a convex mirror. Viewed side-on, at eye level, a concave mirror's curve is easy to tell apart from a convex mirror's, bending the opposite way.

Placing an object close to a concave mirror, just a few centimetres away, shows an image that is erect and clearly larger than the object itself, enlarged; slowly moving the object farther away, the image changes character entirely, becoming inverted, and its size, after growing for a while, starts shrinking again the farther the object moves. A convex mirror behaves far more simply: the image is always erect and always smaller than the object, diminished, at every single distance tested, only shrinking very slightly further as the object moves away. This is a genuine, useful difference from a plane mirror, which always shows an erect, same-size image no matter the distance; spherical mirrors, concave or convex, change the image's size, and sometimes its orientation, depending on how far away the object sits. These properties are put to real, everyday use. Concave mirrors, which can produce an enlarged image, are used as the reflectors inside torches and vehicle headlights (concentrating light forward) and as dental mirrors, giving a dentist a magnified view of teeth when held close inside a patient's mouth; large concave mirrors are also the main mirror inside most modern reflecting telescopes. Convex mirrors, always giving a smaller image, are used as the side-view mirrors on vehicles, giving a wider view of the traffic behind, exactly why they carry the familiar warning that objects in the mirror are closer than they appear; the same wide-view property makes convex mirrors useful at blind road intersections, and for surveillance in large stores.

Light is usually drawn as straight lines with arrowheads, called rays, showing the exact path light travels along. The ray that falls on a mirror is called the incident ray, and the ray that bounces back off it is the reflected ray. At the exact point where the incident ray strikes the mirror, a line drawn perpendicular, at exactly 90 degrees, to the mirror's surface is called the normal. The angle between the incident ray and the normal is the angle of incidence, and the angle between the reflected ray and the normal is the angle of reflection. Shining a thin beam of torchlight (made using a comb with all but one gap covered) onto a plane mirror at different angles, then carefully drawing and measuring both angles for each trial, reveals a genuine, exact rule: the angle of incidence always equals the angle of reflection. This is the first law of reflection. A second activity, bending part of a flat sheet of paper on which the mirror sits, shows the reflected beam disappearing the moment the sheet is bent, but reappearing once it is flattened again, confirming that the incident ray, the normal, and the reflected ray must all lie in exactly the same flat plane, the second law of reflection. Neither law is limited to plane mirrors alone: both hold true for concave and convex mirrors too, wherever the incident ray happens to strike the curved surface.

Sending several parallel beams of light onto a mirror all at once, using a comb with many gaps uncovered instead of just one, reveals a difference plane and curved mirrors do not share. Off a plane mirror, the multiple reflected beams stay parallel, exactly like the beams that arrived. Off a concave mirror, though, the reflected beams bend inward and meet, or converge, at a single point. And off a convex mirror, the reflected beams instead spread apart, or diverge. Every individual ray still obeys the same two laws of reflection at the exact point it strikes the mirror; it is simply the mirror's curved shape, changing the normal's direction at every different point on the surface, that bends the overall beam inward or outward. A concave mirror's converging power is genuinely strong: angled carefully to catch direct sunlight and focused onto a sheet of paper, the concentrated light produces enough heat at that single point to make the paper smoke and eventually burn, a real demonstration that must only ever be done under adult or teacher supervision, focusing the reflected light onto paper alone, never toward anyone's face or eyes, and never looking directly at the Sun or its reflection. This same converging trick, scaled up considerably, is used in solar concentrators, devices using mirrors and lenses to focus sunlight into enough concentrated heat to produce steam for generating electricity, for large-scale cooking, or even for solar furnaces hot enough to melt steel. Long before any of this was understood in writing, astronomers working around the time of the great Indian mathematician Bhaskara II, over 800 years ago, used shallow bowls of water as curved reflectors, observing the reflected images of stars and planets through angled tubes to measure their positions in the sky, a method that strongly suggests a working, practical understanding of reflection, even without the laws being written down.

A flat glass window pane never changes how objects behind it look, but curve that same transparent surface, and everything changes. Placing a single drop of water on a lightly oiled or waxed strip of glass makes the water bead into a round drop with a curved outer surface; peering down through that drop at printed text beneath it, the letters appear noticeably enlarged, a direct demonstration that a curved transparent surface, not just a curved mirror, can change how objects appear. This is exactly the working principle behind a magnifying glass, which is simply a lens designed to make small print look bigger. A lens is a piece of transparent material, usually glass or plastic, with at least one curved surface. Like mirrors, lenses come in two basic shapes: a convex lens, thicker in the middle than at its edges, and a concave lens, thicker at its edges than in the middle. Lenses behave fundamentally differently from mirrors in one crucial respect: light passes THROUGH a lens rather than bouncing back off it, so objects are seen through a lens, never in it the way a reflection appears in a mirror.

Placing a small object close behind a convex lens and looking through it from the other side shows an image that is erect and enlarged; moving the object farther away changes the image, first still enlarged, then shrinking, and eventually flipping to inverted, closely mirroring how a concave mirror's image changes with distance. A concave lens behaves altogether more simply, and much like a convex mirror: the image seen through it is always erect and diminished, at every distance the object is placed, only shrinking a little further as the distance grows. Testing both lenses with multiple parallel beams of light, sent through a thin flat glass plate for comparison first, confirms the underlying reason for this: a flat glass plate passes the parallel beams straight through, unchanged, while a convex lens bends the beams inward until they converge at a point, and a concave lens spreads the beams apart so they diverge, exactly the same converging and diverging behaviour already seen in concave and convex mirrors, just now happening as light passes through the lens rather than reflecting from it. Because of this, a convex lens is also called a converging lens, and a concave lens a diverging lens.

A convex lens's converging power is genuinely strong enough to demonstrate the same way a concave mirror's is: angled to focus sunlight onto a sheet of paper, held under adult or teacher supervision and never looked at directly, it produces enough concentrated heat at a single point to burn the paper, direct proof that a converging lens really does gather light to a point exactly the way a concave mirror does. Lenses show up constantly once you start looking: eyeglasses, worn to correct blurry vision, are simply carefully shaped lenses; cameras, telescopes, and microscopes all rely on lenses to work; and remarkably, the human eye has its very own convex lens inside it, one capable of subtly changing its own shape, which is exactly what allows a single eye to focus clearly on both a nearby book and a distant view. Whether the curve belongs to a mirror or a lens, and whether light bounces off it or passes through it, the same two possibilities keep reappearing throughout this entire chapter: light converging to a point, or light diverging apart, both arising from nothing more than the direction a surface happens to curve.