Lenses (Physics-only)
A lens refracts light to form an image. Two main shapes:
- Convex (converging) — fatter in the middle. Bends parallel rays toward a focal point.
- Concave (diverging) — thinner in the middle. Spreads parallel rays as if from a virtual focal point.
📖Definition— Key terms
- Optical centre — middle of the lens.
- Principal axis — line through the centre, perpendicular to the lens.
- Focal point (F) — where parallel rays converge (convex) or appear to diverge from (concave).
- Focal length (f) — distance from optical centre to focal point.
Three rays for image construction
To draw a ray diagram for a lens:
- Parallel ray → refracts through F (focal point on far side for convex; appears from F on same side for concave).
- Centre ray → goes through optical centre, undeviated.
- Focal ray → ray through F (or aimed at F for concave) emerges parallel to axis.
The image forms where the rays cross.
Real vs virtual images
- Real image — light actually converges; can be projected on a screen. Occurs when object is beyond F (convex lens).
- Virtual image — light only appears to come from a position; can't be projected. Always with concave lenses; with convex when object is closer than F (magnifying glass).
Magnification
$\text{Magnification} = \dfrac{\text{image height}}{\text{object height}} = \dfrac{h_i}{h_o}$
A magnification > 1 means the image is larger; < 1 means smaller. Sign convention: negative for inverted (real) images.
✦Worked example
Object 4 cm tall, image 12 cm tall (real, inverted). Magnification?
- Magnification = 12/4 = 3.
Common image positions for convex lens
| Object position | Image |
|---|---|
| Beyond 2F | Real, inverted, smaller |
| At 2F | Real, inverted, same size |
| Between F and 2F | Real, inverted, larger |
| At F | No image (rays parallel) |
| Inside F | Virtual, upright, larger (magnifying glass) |
⚠Common mistakes
- Drawing parallel ray without refracting at the lens.
- Forgetting that concave lenses always form virtual images.
- Mixing up object position descriptions ("beyond 2F" means farther from lens than 2F).
- Confusing magnification (ratio) with magnification factor in optics formulas.
AI-generated · claude-opus-4-7 · v3-deep-physics