3.12 - How Lenses Work

Convex and concave lenses

• Lenses form images by refracting light and changing its direction.
• There are two main types of lens, and they have opposite effects on the rays passing through them.

Convex (converging) lenses

• A convex lens bulges outwards, so it's thickest at its centre and thinnest at its edges.
• It brings parallel rays of light together (it converges them).
• Rays hitting the lens parallel to its axis meet at the principal focus.

Concave (diverging) lenses

• A concave lens caves inwards, so it's thickest at its edges and thinnest at its centre.
• It makes parallel rays of light spread out (it diverges them).
• Rays hitting the lens parallel to its axis appear to come from the principal focus - tracing the emerging rays back, they all appear to meet at this point.

How rays bend

• A ray bends towards the normal as it enters the lens, and away from the normal as it leaves.
• A ray that passes through the optical centre of either lens isn't bent - it carries straight on without refraction.

Axis, principal focus and focal length

Three terms describe how a lens behaves:

1. Axis - An imaginary straight line through the middle of the lens, perpendicular to it. Also called the principal axis.
2. Principal focus - For a convex lens, the point where rays hitting the lens parallel to the axis are brought together. For a concave lens, the point those rays appear to come from when traced back. There's a principal focus on each side of the lens.
3. Focal length - The distance from the centre of the lens to the principal focus.

Real and virtual images

An image forms where all the light rays from a point on an object come together, or appear to come together.

The two kinds of image

1. Real image - The light rays actually meet at the image. Because the light really is there, a real image can be captured on a screen (for example, on the retina at the back of the eye).
2. Virtual image - The light rays only appear to come from the image. Tracing the emerging rays back, they meet at a point the light never actually reaches, so a virtual image cannot be captured on a screen (for example, the image seen through a magnifying glass).

To describe an image fully, state:

• whether it's bigger or smaller than the object,
• whether it's upright or inverted,
• whether it's real or virtual.

The power of a lens

The power of a lens describes how strongly it bends light.

• The more powerful the lens, the more strongly it converges the rays, so the shorter its focal length.
• Power is measured in dioptres: power (in dioptres) = 1 ÷ focal length (in metres). Change the focal length into metres first, so a lens with a focal length of 20 cm (0.20 m) has a power of 1 ÷ 0.20 = 5 dioptres.
• A converging lens has a positive power; a diverging lens has a negative power.
• For a given material, a more strongly curved lens is more powerful.
• A material that refracts light more strongly gives the same focal length with less curvature, so a powerful lens can be made thinner.