Refraction through lenses

Just as a mirror's image depends on whether it is convex or concave and on the object's distance, a lens's image depends on the type of lens and how far the object sits from it. There are only two lens shapes to keep track of at this level, and each has its own rulebook.

Convex lens (converging lens). When the object is close to the lens, the image is erect (right-side up) and enlarged (bigger than the object). This is exactly the magnifying-glass effect: a convex lens held near text makes the letters look bigger. As the object moves farther away, the image flips to inverted (upside down). Just after the flip it may still look fairly large, but as the distance keeps increasing, the inverted image becomes progressively smaller (diminished).

Concave lens (diverging lens). The image is always erect and always diminished, at every object distance, without exception. Moving the object closer or farther only changes how small the image looks slightly — it never flips upside down and never grows larger than the object. A useful shortcut is to notice the lens-mirror parallel: a convex lens behaves exactly like a concave mirror (erect and enlarged up close, inverted and shrinking farther away), while a concave lens behaves exactly like a convex mirror (always erect, always diminished). The "convex" and "concave" labels do not carry over directly between lenses and mirrors — a convex lens pairs with a concave mirror, and vice versa — so this parallel is worth memorising precisely, not loosely. Why does a lens even form an image at all? Light bends — refracts — as it enters the curved glass, bends again inside, and bends once more on the way out. This double bending redirects the light rays so they meet (or appear to meet) at a point, forming an image. That is fundamentally different from a mirror, which works purely by reflecting light off a surface with no bending involved. At this level, the exact geometry of that bending — the angles, the refractive index, Snell's law — is not part of the syllabus; only the resulting qualitative behaviour of the image is expected.

At Class 8 level there is no formula to derive — no lens equation, no magnification calculation — so the goal here is to reason through why the erect/inverted, enlarged/diminished pattern behaves the way it does, using only the idea of light-bending you already know.

The convex lens is a converging lens. A convex lens is thicker in the middle than at the edges, and it bends light rays inward, toward each other, so that rays passing through it tend to converge. When the object is very close, the rays entering the lens from any one point on the object are still spreading apart quite steeply; the lens can only bend them enough to make them appear to come from a larger, upright position behind the object — hence erect and enlarged, much like looking through a magnifying glass. As the object is pushed farther away, the rays entering the lens are more nearly parallel, and the lens now has enough bending power to make them actually cross and meet on the far side, forming a real image that is inverted. The farther the object moves, the more tightly that meeting point is squeezed toward the lens's focal region, and the smaller the resulting image becomes.

The concave lens is a diverging lens. A concave lens is thinner in the middle than at the edges, and it bends light rays outward, away from each other, so rays that enter it spread out even more than before, never converging on the far side. Because they never cross, there is no way for a real, inverted image to form — the eye, looking back along the diverging rays, always perceives a virtual image that is upright and, since the rays have been spread apart rather than focused down, always smaller than the object. This diverging behaviour does not depend on how close or far the object is; it is a direct consequence of the lens's shape, which is why the concave lens's erect-and-diminished rule holds at every distance. This is also why the mirror parallel works: a concave mirror converges reflected rays like the convex lens converges refracted rays, and a convex mirror diverges reflected rays like the concave lens does — different mechanisms, same geometric consequence.

Question. A student holds a convex lens very close to a small ant on a leaf and sees an enlarged, right-side-up image. She then slowly moves the lens farther and farther from the ant. Describe how the image changes, and then state what she would see if she repeated the whole experiment with a concave lens instead.

Step 1. Start from the rule for a convex lens at close range: object close means image erect and enlarged. This matches her first observation of the ant.

Step 2. As she moves the lens away, the object is no longer "close," so the convex-lens image behaviour shifts. Following the rule, at some point the image flips to become inverted.

Step 3. Just after the flip, the inverted image may still look fairly large, but moving the lens farther still makes the inverted image become progressively smaller. So the full convex-lens sequence is: erect and enlarged (close) leads to inverted and still large (medium distance) leads to inverted and smaller (far) — the same pattern a concave mirror would show.

Step 4. Now switch to the concave-lens rule: a concave lens is always erect and always diminished, at every distance, with no inversion ever happening. So with a concave lens she would see the ant small and right-side up when the lens was close, and it would stay small and right-side up as she moved the lens farther away — never flipping upside down, never growing bigger than the ant itself.

Answer: with the convex lens, the image goes erect and enlarged, then inverted and large, then inverted and smaller as distance increases; with the concave lens, the image stays erect and diminished at every distance.

• Assuming a convex lens always magnifies — it only enlarges the image when the object is close; farther away the image inverts and eventually shrinks.
• Forgetting that a concave lens never flips the image upside down, unlike a convex lens at large object distances (or a concave mirror at any distance beyond the focus).
• Mixing up which lens behaves like which mirror — a convex lens behaves like a concave mirror, and a concave lens behaves like a convex mirror; the labels do not match up directly between lenses and mirrors.
• Reaching for Snell's law, refractive index, or ray-diagram construction to explain this behaviour — at this level only the qualitative erect/inverted, enlarged/diminished description is expected, not the bending-angle rules behind it.

Ask the tutor: want to try a few more object-distance scenarios and predict the image type for both convex and concave lenses?