5.16 - 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.

A concave lens always forms a virtual image

A concave (diverging) lens always produces a virtual image, wherever the object is placed. The image is always:

• upright (the right way up),
• smaller than the object,
• on the same side of the lens as the object, between the object and the lens.

The further the object is from the lens, the smaller the image becomes.

How a convex lens image depends on object distance

A convex (converging) lens forms different types of image depending on how far the object is from the lens, measured in focal lengths (F is one focal length, 2F is two).

• Object at 2F - A real, inverted image, the same size as the object, formed at 2F on the other side of the lens.
• Object between F and 2F - A real, inverted image, larger than the object, formed beyond 2F.
• Object nearer than F - A virtual, upright, larger image, formed on the same side of the lens as the object. The closer the object is to F, the larger it appears.

Correcting short sight and long sight

• The eye contains a convex lens that focuses light onto the retina at the back of the eye, forming a real image.
• If the image doesn't fall on the retina, it looks blurry.
• Lenses worn in front of the eye correct this.

Short sight

• A short-sighted person can't focus on distant objects.
• The eye is too powerful, or the eyeball too long, so the image of a distant object forms in front of the retina.
• A concave (diverging) lens spreads the light out before it enters the eye, focusing the image onto the retina.

Long sight

• A long-sighted person can't focus on near objects.
• The eye is too weak, or the eyeball too short, so the image of a near object forms behind the retina.
• A convex (converging) lens begins converging the light before it enters the eye, focusing the image onto the retina.