How a lens changes the path of light

1. A lens is a shaped piece of transparent glass or plastic with curved surfaces that changes the direction of light by refraction.
2. Light refracts once as it enters the lens and again as it leaves, so each ray changes direction at both surfaces.
3. The surfaces are curved, so rays striking different parts of the lens meet the surface at different angles and are bent by different amounts.
4. Rays striking near the edge of a lens are bent the most, while a ray passing through the very centre carries straight on without changing direction.
5. The principal axis is the line through the centre of the lens at right angles to it, and ray diagrams for lenses are built around this line.
6. In a ray diagram, a lens is drawn as a vertical line with a symbol at each end, and each ray is shown changing direction once at that line to keep the diagram clear.
7. Every ray is drawn as a straight ruled line with an arrowhead showing the direction in which the light travels.

Convex lenses make rays converge

1. A convex lens bulges outwards, so it is thicker at its centre than at its edges.
2. It is also called a converging lens, because it refracts rays that are parallel to the principal axis inwards so that they converge.
3. After passing through the lens, these parallel rays all meet at one point on the principal axis called the principal focus, labelled $F$.
4. The distance from the centre of the lens to the principal focus is the focal length.
5. A lens has a principal focus on each side, at the same distance from its centre, because light can pass through it in either direction.
6. A fatter, more strongly curved convex lens bends light more, so it has a shorter focal length.
7. In a ray diagram, a convex lens is drawn as a vertical line with outward-pointing arrowheads at both ends.
8. Light really does pass through the principal focus of a convex lens, so a convex lens can focus light onto a screen.

Concave lenses make rays diverge

1. A concave lens curves inwards, so it is thinner at its centre than at its edges.
2. It is also called a diverging lens, because it refracts rays that are parallel to the principal axis outwards so that they spread apart.
3. If the spreading rays are traced backwards with dashed lines, they all appear to come from one point on the same side of the lens as the incoming light.
4. This point is the principal focus of the concave lens, and it is a virtual focus because no light actually passes through it.
5. In a ray diagram, a concave lens is drawn as a vertical line with inward-pointing arrowheads at both ends.
6. The rays leaving a concave lens never meet, so a concave lens cannot focus light from a distant object onto a screen.

Images formed by lenses

1. An image forms where rays of light from one point on an object meet again, or where they appear to have come from.
2. A real image forms where rays actually meet, so it can be caught on a screen.
3. A virtual image forms where rays only appear to come from, so you can see it by looking through the lens but you cannot catch it on a screen.
4. Three standard rays are used to find the image formed by a convex lens.
   1. A ray parallel to the principal axis is refracted through the principal focus on the far side of the lens.
   2. A ray through the centre of the lens carries straight on without changing direction.
   3. A ray through the principal focus on the near side of the lens leaves the lens parallel to the principal axis.
5. The point where these rays cross on the far side of the lens marks the top of the image, and any two of them are enough to locate it.
6. An object more than two focal lengths from a convex lens forms a real image that is inverted and diminished, which is how a camera forms an image on its sensor.
7. An object between one and two focal lengths from a convex lens forms a real image that is inverted and magnified, which is how a projector throws a large picture onto a screen.
8. An object closer to a convex lens than its principal focus forms a virtual image that is upright and magnified, which is how a magnifying glass works.
9. As an object moves from far away towards the principal focus, its real image moves further from the lens and becomes larger.
10. A concave lens always forms a virtual image that is upright and diminished, wherever the object is placed.

Comparing convex and concave lenses

1. Similarities between the two types of lens are listed below.
   1. Both lenses change the direction of light by refraction at their two surfaces.
   2. Both lenses have a principal axis and a principal focus on each side at the same distance from the centre.
   3. Both lenses let a ray through their centre pass straight on without bending.
2. Differences between the two types of lens are listed below.
   1. A convex lens is thickest at its centre, while a concave lens is thinnest at its centre.
   2. A convex lens makes parallel rays converge, while a concave lens makes them diverge.
   3. A convex lens has a real principal focus, while a concave lens has a virtual principal focus.
   4. A convex lens can form real or virtual images, while a concave lens forms only virtual images.

Correcting vision with lenses

1. The eye contains its own convex lens, which focuses light from an object onto the retina at the back of the eye to form a sharp image.
2. In a short-sighted eye, light from distant objects comes to a focus in front of the retina, because the eyeball is too long or the eye lens is too strongly curved.
3. A concave lens placed in front of a short-sighted eye makes the light diverge slightly before it enters, so the eye lens then brings it to a focus on the retina.
4. In a long-sighted eye, light from near objects would come to a focus behind the retina, because the eyeball is too short or the eye lens is too weak.
5. A convex lens placed in front of a long-sighted eye makes the light converge slightly before it enters, so it comes to a focus on the retina.
6. You can tell the two kinds of glasses apart by feeling them, because lenses for short sight are thicker at the edges and lenses for long sight are thicker in the middle.