Question
Describe all cases of image formation by convex and concave lenses. What are the nature, position, and size of the image for each object position?
(CBSE 10 and 12 boards ask this alongside mirrors; NEET combines lens and mirror problems)
Solution — Step by Step
Convex lens (converging) — 6 cases
At infinity → Image at F₂, real, inverted, point image.
Beyond 2F₁ → Image between F₂ and 2F₂, real, inverted, diminished.
At 2F₁ → Image at 2F₂, real, inverted, same size.
Between F₁ and 2F₁ → Image beyond 2F₂, real, inverted, magnified.
At F₁ → Image at infinity, real, inverted, highly magnified.
Between F₁ and O (optical centre) → Image on same side as object, virtual, erect, magnified. This is how a magnifying glass works.
Concave lens (diverging) — always the same type
For any object position:
- Image is always on the same side as the object (between O and F₁)
- Image is always virtual, erect, and diminished
- As object approaches, image gets slightly larger but remains diminished
Concave lenses always diverge light — that is why they cannot form real images of real objects.
The lens formula
Sign convention: Convex lens = positive, Concave lens = negative. Object distance = negative (object on left side).
Magnification: . Positive = erect, negative = inverted.
Power: in dioptres (D). Convex lens has positive power, concave has negative.
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Why This Works
A convex lens converges parallel rays to the focal point. Objects at different distances create diverging rays with different angles — the lens bends them to converge at different image points. The closer the object gets to the lens, the farther the image forms (until the object is inside F, where the diverging rays can no longer be converged — producing a virtual image).
The parallel between lenses and mirrors: convex lens behaves like concave mirror (both converge). Concave lens behaves like convex mirror (both diverge).
Alternative Method
💡 Expert Tip
For lenses, the same "crossover at F" rule applies as with concave mirrors. For a convex lens: object outside F gives a real image on the other side. Object inside F gives a virtual image on the same side. This one rule handles 90% of MCQ questions about convex lenses.
Common Mistake
⚠️ Common Mistake
Students confuse the sign conventions for mirrors and lenses. The mirror formula is (plus sign), while the lens formula is (minus sign). Also, the magnification formula differs: mirror , lens . Mixing these up is the single most common computational error in optics.