Images by Lenses & Magnification
Three easy rays and one ratio describe every image a single lens can make.
Lesson at a glanceShow the key points
- Near the optical centre the lens is like a thin parallel slab, so a ray through the optical centre goes straight on.
- A ray parallel to the axis passes through (or seems to come from) F₂; a ray through F₁ emerges parallel.
- Lateral magnification m = h₂/h₁ = v/u (18.18); negative means inverted.
- A convex lens gives real inverted images of distant objects and a magnified, erect virtual image of objects inside F; a concave lens always gives a diminished, erect virtual image of a real object.
A camera, a projector and a magnifying glass can all use the same convex lens. Only the object’s distance changes, and with it the size, position and orientation of the image.
Three easy rays
To find the image of the tip of an object, trace any two of these rays:
- Through the optical centre: straight on. Near its centre a thin lens is like a thin slab with parallel faces, so the ray is neither turned nor noticeably shifted.
- Parallel to the axis: emerges through F₂ (convex), or as if from F₂ (concave).
- Through F₁ (or heading for it, for a concave lens): emerges parallel to the axis.
Where the emerging rays cross (or seem to cross, traced back) is the image of the tip; drop a perpendicular to the axis for the whole image.
Magnification
The ray through the optical centre makes similar triangles of object and image, with PO = −u and PO′ = +v:
A 3.0 cm object is 15 cm from a convex lens of focal length 20 cm. Find the image.
An object is 15 cm from a convex lens of focal length 10 cm. Where is the image and what is the magnification?
A summary
| Convex lens, object at | Image |
|---|---|
| Very far (∞) | At F₂: real, inverted, tiny |
| Beyond 2F₁ | Between F₂ and 2F₂: real, inverted, smaller (camera, eye) |
| At 2F₁ | At 2F₂: real, inverted, same size |
| Between F₁ and 2F₁ | Beyond 2F₂: real, inverted, larger (projector) |
| At F₁ | At infinity |
| Inside F₁ | Same side: virtual, erect, larger (magnifying glass) |
A concave lens always gives a virtual, erect, smaller image of a real object, lying between the lens and F.
- 1Ray through the optical centre: straight on. Parallel ray: through (or from) F₂. Ray through F₁: emerges parallel.
- 2m = v/u for lenses; negative m means inverted.
- 3Convex lens: real inverted images for objects beyond F, virtual magnified erect image inside F.
- 4Concave lens: always virtual, erect, diminished (for real objects).
Check yourself
Keep exploring
Hand-picked videos, simulations and readings that explain this idea from a different angle.