6.12 - 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.

How rays refract through a convex lens

Three rules predict where a convex (converging) lens sends any ray:

1. An incident ray parallel to the axis refracts through the lens and passes through the principal focus on the other side.
2. An incident ray passing through the principal focus refracts and then travels parallel to the axis.
3. An incident ray passing through the centre of the lens carries straight on in the same direction.

Simplifying the refraction:

• A ray actually refracts twice - once entering the lens, once leaving.
• These rules let each ray be treated as if it changes direction only once as it passes through the lens.

How rays refract through a concave lens

Three rules describe how a concave (diverging) lens refracts rays:

1. An incident ray parallel to the axis refracts so it travels in line with the principal focus, appearing to have come from the principal focus on the same side as the incident ray.
2. An incident ray heading towards the principal focus on the far side refracts and then travels parallel to the axis.
3. An incident ray passing through the centre of the lens carries straight on in the same direction.

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.

Magnifying glasses

A magnifying glass is a single convex (converging) lens used to make an object look bigger.

• The object must be placed closer to the lens than the focal length.
• The lens forms a virtual image that is upright and larger than the object, on the same side of the lens as the object.
• The closer the object is to the principal focus, the larger the image appears.

The magnification formula

Magnification compares the size of the image with the size of the object.

• Magnification is a ratio, so it has no units.
• Both heights must be in the same units (for example mm or cm).
• Magnification less than 1 means the image is smaller than the object; greater than 1 means the image is larger.

Worked example - Magnification of a magnifying lens

A coin 20 mm across is viewed through a magnifying lens. The virtual image of the coin is 50 mm across. Calculate the magnification of the lens.