Convex and concave lenses: images and ray diagrams
A convex lens converges light and can form real or virtual images; a concave lens diverges light and always forms a small, erect, virtual image.
Lens words you must know
- Lens: a piece of transparent material with two curved surfaces, or one curved and one flat surface.
- Centre of curvature (C): the centre of the sphere of which a lens surface is a part. A lens has two.
- Principal axis: the straight line through the two centres of curvature.
- Optic centre (O): the central point of the lens. A ray through it goes straight on without bending.
- Principal focus (F): rays parallel to the principal axis meet at F after a convex lens. After a concave lens, they seem to spread out from F.
- Focal length (f): the distance between the optic centre and the principal focus. The point at twice this distance is called 2F (your textbook may label it C).
Rules for drawing ray diagrams
- Rule 1: a ray parallel to the principal axis passes through F after a convex lens. After a concave lens, it seems to come from F on the same side.
- Rule 2: a ray through the optic centre goes straight on, without bending.
- Rule 3: in a convex lens, a ray through F comes out parallel to the principal axis. In a concave lens, a ray aimed towards F on the far side does the same.
- The image forms where two refracted rays meet (a real image). If they only seem to meet when traced back with dotted lines, the image is virtual.
Images formed by a convex lens
| Object position | Image position | Nature and size | Use |
|---|---|---|---|
| At infinity | At F | Real, inverted, highly diminished (a point) | Objective of a telescope |
| Beyond 2F | Between F and 2F | Real, inverted, diminished | Camera |
| At 2F | At 2F | Real, inverted, same size | Photocopier |
| Between F and 2F | Beyond 2F | Real, inverted, magnified | Film projector |
| At F | At infinity | Real, inverted, highly magnified | Spotlight, which sends out a parallel beam |
| Between F and O | Same side as the object | Virtual, erect, magnified | Magnifying glass (simple microscope) |
Convex vs concave lens
For a concave lens, an object at infinity gives a highly diminished image at F. An object anywhere else gives a diminished image between F and O.
How to draw a convex lens ray diagram (object between F and 2F)
- 1Draw a horizontal line for the principal axis. Draw the lens as a tall thin oval at the centre and mark its centre O.
- 2Mark F and 2F on both sides of the lens at equal distances.
- 3Draw the object as an upright arrow AB between F and 2F on the left.
- 4From the top of the object, draw a ray parallel to the axis. After the lens, draw it passing through F on the right.
- 5From the top of the object, draw a second ray through O, going straight on.
- 6★Where the two rays meet, beyond 2F on the right, draw the image arrow A′B′ pointing down. Write real, inverted, magnified.
★ key step
The camera in a mobile phone uses a convex lens to form a small, real, inverted image on its sensor. Grandparents use a magnifying glass to read the small print on a medicine strip.
1 marks: “Where should an object be placed in front of a convex lens to get a real image of the same size?” At 2F; the image also forms at 2F on the other side.
2 marks: “Distinguish between a convex lens and a concave lens (two points).” Convex: thick in the middle, converging, real or virtual images. Concave: thin in the middle, diverging, always virtual, erect, diminished images.
7 marks: “Draw ray diagrams to show the image formed by a convex lens when the object is (i) beyond 2F (ii) between F and O. State the nature of each image.” Two labelled diagrams using the parallel ray and the ray through O; (i) image between F and 2F, real, inverted, diminished; (ii) image on the same side, virtual, erect, magnified.
Bring the object in, the image runs out and grows: as the object nears F, the real image moves away and gets bigger.