Real and virtual images

Two mirrors, two families of behaviour. A concave mirror curves inward like the inside of a bowl and can converge light to a real crossing point; a convex mirror curves outward like the back of a spoon and always spreads (diverges) light apart. That single geometric fact — converging versus diverging surface — governs everything about which kind of image forms.

What "real" actually means. When rays reflected by a mirror physically travel to the same point in space and cross there, an image forms at that crossing point whether or not a screen is present. Hold a sheet of paper at that spot and a sharp picture appears, because light energy genuinely arrives there. That is a real image. Every real image formed by a single concave mirror is inverted — the geometry of converging rays flips top and bottom as they cross.

What "virtual" actually means. Sometimes reflected rays leave the mirror diverging, and never cross anywhere in front of it. Your eye still perceives an image, because your brain traces the diverging rays backward in straight lines (dotted construction lines in a ray diagram) until they meet, and places the image at that backward-projected point, behind the mirror. No light energy actually reaches there, so a screen held at that spot shows nothing. That is a virtual image, always upright — the same way up as the object.

Concave mirror: the object's position decides everything. For a concave mirror the type of image swings between real and virtual depending purely on where the object sits relative to the focus (F) and the centre of curvature (C):

• Object beyond C, exactly at C, or between C and F — reflected rays are still converging when they leave the mirror, so they cross in front of it: the image is real and inverted (size varies from diminished to magnified depending on exact placement).
• Object exactly at F — rays reflect out perfectly parallel and never meet at any finite distance, so no image forms at all (the "image at infinity" case).
• Object between F and the pole (P) — the object is now too close for the rays to converge before leaving the mirror; they diverge outward, and only their backward extensions meet, behind the mirror. The image is virtual, upright, and always magnified. This is the shaving-mirror and dentist-mirror case.

Convex mirror: the object's position never matters. A convex mirror's outward curve makes every reflected ray diverge, regardless of where the object stands — near, far, it makes no difference to the kind of image, only to how small it looks. The image is always virtual, upright, and diminished (smaller than the object). This is why convex mirrors are used as vehicle side-mirrors and shop security mirrors: they can never form a real image, but they pack a wide field of view into a small, upright picture.

The whole rule rests on one idea: where light energy actually goes. A real image is simply the ordinary geometric fact that two or more reflected rays, obeying the law of reflection, happen to cross at a physical point in space. Anything placed there — a screen, a wall, your retina — receives light energy and shows a picture. That is why real images can always be projected: light genuinely arrives at that location. A virtual image is the alternative: the rays leaving the mirror are diverging rather than converging, so they never cross in front of it. Your eye still collects two of these diverging rays and, because it can only interpret light as having travelled in a straight line, extrapolates them backward until they intersect. Your brain places the image there, behind the mirror, even though no photon actually travels behind the silvered surface. No energy arrives at that backward point, so nothing can ever be photographed there — the image exists only in the act of viewing. This is also why a concave mirror can produce either kind of image while a convex mirror produces only one. A concave mirror's inward curve converges rays, but only when the object sits far enough away (beyond F). Move the object inside the focus and the geometry flips: the rays that would have converged now leave already spreading apart. A convex mirror, curving the opposite way, spreads every incoming ray no matter what — it has no converging zone at all, so a real image is geometrically impossible from it, at any object distance.

A dentist holds a small concave mirror very close to a patient's tooth to get a magnified view of it for examination. Determine whether the image seen is real or virtual, and justify the answer using ray-tracing reasoning.

Step 1. The mirror is held very close to the tooth, so the tooth lies between the focus (F) and the pole (P) of the small concave mirror — well inside the mirror's converging zone.

Step 2. Trace two rays from a point on the tooth: one parallel to the principal axis, which reflects through F; another aimed toward the centre of curvature C, which reflects straight back along itself. Because the object is closer than F, these two reflected rays emerge diverging and never cross anywhere in front of the mirror.

Step 3. Extend both reflected rays backward, behind the mirror, with dotted construction lines. They cross at a point behind the mirror — this backward crossing point is where the image appears to be.

Step 4. Since the rays only appear to meet, and the meeting point lies behind the mirror rather than in front of it, the image is virtual, upright, and larger than the tooth (magnified), matching the general rule for an object between F and P.

Final answer: the dentist sees a virtual, upright, magnified image of the tooth — exactly why a concave mirror held close to an object is useful for close inspection, just as with a shaving or makeup mirror.

Competitive stretch

Now compare this with a concave mirror used the opposite way: sunlight in a solar cooker strikes a large concave mirror and converges to a small, intensely bright, upside-down spot exactly at the focus, where food is placed. Here the "object" (the distant Sun) is effectively at infinity — far beyond C — so incoming rays arrive already parallel to the axis. Parallel rays reflecting off a concave mirror genuinely converge and physically cross at F; no backward extension is needed. Because the rays actually meet, the image (and the concentrated heat energy) is real and inverted, forming exactly at the focus — the same real-image property that torch reflectors and solar water heaters rely on. Same mirror type, opposite object distance, opposite kind of image.

• Thinking a virtual image is somehow "fake" or not really seen — it is genuinely visible to the eye; it simply cannot be projected onto a screen because no light energy actually converges there.
• Assuming a concave mirror always gives a real image — it only does so when the object is beyond the focus; between the focus and the pole it gives a virtual, magnified image instead.
• Believing a convex mirror can sometimes form a real image if the object is placed far enough away — it cannot, under any object distance, because it always diverges light rather than converging it.
• Forgetting that all real images from a single concave mirror are inverted, while all virtual images, from either mirror type, are upright.

Ask the tutor: Still unsure why the same concave mirror gives a virtual image for a dentist's tooth but a real image for a solar cooker's sunlight — ask the AI tutor to walk through both ray diagrams side by side.