Images in concave lenses

A lens is a transparent object, usually glass or plastic, with at least one curved surface — and unlike a mirror, we look through it rather than into it. Lenses come in exactly two basic shapes.

• A convex lens is thicker at the centre than at its edges. It converges (brings together) parallel light rays, and depending on how close the object is, it can form images that are enlarged, diminished, erect, or even inverted.
• A concave lens is thicker at its edges than at its centre — the reverse shape. It diverges (spreads apart) parallel light rays, and it forms only one kind of image, regardless of distance: erect and diminished.

That single rule — always erect, always diminished — is what separates a concave lens from every other case a Class 8 student meets in this chapter. Move the object closer or farther, the image never inverts and never magnifies; it may shrink a little more as distance increases, but it stays upright and smaller than the object throughout. The diagram below shows why the two lens shapes are named "converging" and "diverging": watch what a bundle of parallel rays does after crossing each lens.

The rule that a concave lens always produces an erect, diminished image, with no exceptions across any object distance, follows directly from the single fact that a concave lens can only spread light rays apart and never bring them together.

Step 1. A concave lens is thinner at its centre than at its edges. When a bundle of parallel rays (like sunlight, or light reflected from a distant part of an object) reaches such a lens, the thicker edges bend the outer rays away from the centre more strongly than the thin middle bends the central rays. The net effect is that the rays leave the lens spread wider apart than when they entered — they diverge.

Step 2. Because the rays diverge, they never cross and meet at a real point on the far side of the lens the way a convex lens's rays do. Your eye, receiving these spreading rays, automatically traces them backward in straight lines to figure out where they seem to have come from. Since diverging rays always appear to originate from a point closer to the lens than the object actually is, the image always appears smaller than the object — diminished.

Step 3. This backward-traced image also always sits on the same side of the lens as the object and points the same way up as the object, because the rays never cross each other before they reach your eye. Rays that cross produce an inverted image (this is what happens with a convex lens once the object is far enough away); rays that only spread apart, without crossing, always preserve the original up-down orientation — erect.

Step 4. None of this reasoning depends on how far the object is from the lens — divergence happens for every object distance, so the erect-and-diminished outcome is not a special case, it is the only case for a concave lens. A convex lens, by contrast, converges rays and can make them cross, which is why its image behaviour changes with distance while a concave lens's image behaviour never does.

Question: A student holds a concave spectacle lens close to a printed word in a book, then slowly moves the lens away from the page while looking through it. Describe what she observes at each stage, and explain why, using the diverging-rays reasoning above.

Step 1. With the lens held very close to the page, the student looks through it and sees the printed word appear smaller than its actual size — but still perfectly right-side up.

Step 2. As she slowly moves the lens farther from the page, the word remains right-side up at every position; it never flips upside down, no matter how far she moves the lens.

Step 3. The image shrinks a little further as the lens moves away, but only mildly — it does not suddenly become dramatically smaller the way a convex lens's image would change with distance.

Step 4. Explaining why: at every lens position, the concave lens diverges the light rays coming from the word. Diverging rays never cross, so by the reasoning in Step 3 above, the image the student's eye reconstructs is always erect, and by Step 2 above, it is always diminished. Because this divergence happens regardless of distance, the result cannot change as she moves the lens.

The observation, fully explained: the word stays erect and diminished throughout, because a concave lens diverges light at every distance and diverging rays can never cross to invert the image or converge to enlarge it.

Competitive stretch

If the same student now swaps the concave spectacle lens for a convex magnifying glass and repeats the experiment, holding it close to the page and slowly pulling it away, the outcome is different: very close to the page the magnified word looks bigger and still erect, but past a certain distance (once the object crosses the lens's principal focus) the image flips upside down. Spotting when an image behaviour changes with distance versus staying fixed is exactly how you tell convex and concave lenses apart in a written answer, even without doing any ray diagram.

• Thinking a concave lens can magnify an object if held close enough to the eye — it cannot; the image is diminished at every distance, unlike a convex lens which can magnify when the object is near the focus.
• Confusing "concave lens" with "concave mirror" — a lens's shape (thinner or thicker at the centre) is a completely separate idea from a mirror's curvature (curving inward or outward); don't mix the two vocabularies.
• Assuming the image through a concave lens eventually inverts at large object distances — it never does; erect and diminished is the rule at every distance, with no threshold distance at which it changes.
• Believing "diverging" describes the lens spreading the object apart — it is the light rays passing through the lens that diverge; the object itself does not move or change shape.

Ask the tutor: Want to see how this erect-and-diminished rule connects to the lens formula and ray diagrams you'll meet for concave lenses in Class 10?