Question
What image is formed for different object positions in convex and concave lenses? Summarise all cases with image characteristics.
Solution — Step by Step
- Parallel ray: Passes through (or appears to come from) the focus after refraction
- Central ray: Passes through the optical centre undeviated
- Focal ray: Ray through F emerges parallel to the principal axis
For a convex lens, parallel rays converge to the focus on the other side. For a concave lens, parallel rays diverge as if from the focus on the same side.
| Object Position | Image Position | Nature | Size |
|---|---|---|---|
| At infinity | At F (other side) | Real, inverted | Point-sized |
| Beyond 2F | Between F and 2F | Real, inverted | Diminished |
| At 2F | At 2F (other side) | Real, inverted | Same size |
| Between F and 2F | Beyond 2F | Real, inverted | Magnified |
| At F | At infinity | Real, inverted | Highly magnified |
| Between F and O | Same side as object | Virtual, erect | Magnified |
A convex lens behaves exactly like a concave mirror in terms of image characteristics. When the object is between F and the lens, it acts as a magnifying glass — the image is virtual, erect, and magnified.
Like a convex mirror, a concave lens always produces:
- Image on the same side as the object (between O and F)
- Virtual and erect
- Diminished
This is true for all object positions. The image is always closer to the lens than the object and smaller.
graph TD
A{Lens type?} --> B[Convex: converging]
A --> C[Concave: diverging]
B --> D{Object position?}
D -->|Beyond 2F| E["Real, inverted, diminished"]
D -->|At 2F| F["Real, inverted, same size"]
D -->|Between F and 2F| G["Real, inverted, magnified"]
D -->|Between F and O| H["Virtual, erect, magnified"]
C --> I["Always: virtual, erect, diminished"]Why This Works
The thin lens formula:
Sign convention: For a convex lens, . For a concave lens, f < 0. Object distance is always negative (object on the left).
Magnification:
Note: the lens formula has a minus sign (), unlike the mirror formula (). Students who mix these up will get every answer wrong.
Alternative Method
A parallel between mirrors and lenses helps with memorisation:
| Concave mirror | Convex lens | Both produce |
|---|---|---|
| Converging | Converging | Real images (mostly), virtual only when object is between F and surface |
| Convex mirror | Concave lens | Both produce |
|---|---|---|
| Diverging | Diverging | Always virtual, erect, diminished |
Once you master one from each pair, you automatically know the other.
For Class 10 CBSE boards, lens ray diagrams carry 3-5 marks. Practice drawing at least the convex lens cases for object at 2F, between F and 2F, and between F and O. These three cover the most common exam questions.
Common Mistake
The formula difference between mirrors and lenses trips up many students. Mirror formula: . Lens formula: . Using the wrong formula is one of the most common errors in optics. Also, magnification for mirrors is but for lenses it is (no negative sign). Double-check which formula you are using before substituting values.