OxfordAQA International GCSE Physics: Lenses, image formation and the eye (9203)

This study guide follows the OxfordAQA International GCSE Physics (9203) specification, for exams May/June 2018 onwards, and covers section 3.3.6, Lenses and the eye, points a to l. The section is marked for the full Physics award, and the qualification is untiered. Use it with the revision notes and the practice questions. The course home is the OxfordAQA IGCSE Physics hub, and the printable checklist lets you tick each point off. Not sure where to start? Try a free 10-minute diagnostic.

What this unit covers

Points a to d cover refraction by lenses, convex and concave lenses and focal length. Points e to g cover describing images, ray diagrams and magnification. Points h to j cover the eye, range of vision and sight defects. Points k and l cover lasers and the camera.

How a lens forms an image (3.3.6 a)

A lens is a piece of transparent material with curved surfaces. Rays strike the curved surfaces at different angles, so they are bent by different amounts. This refraction lets a lens send rays from one point of an object towards one point of an image.

Convex lenses (3.3.6 b, d)

A convex lens is thicker at the middle than at the edges. It is also called a converging lens.

• Rays parallel to the principal axis meet at one point on the far side, the principal focus.
• The focal length is the gap between the middle of the lens and the principal focus.
• A lens has a principal focus on each side, equally far from it.

Three rays you can always draw

1. From the tip of the object, a ray running parallel to the axis is refracted and goes through the principal focus on the far side.
2. A ray from the top of the object aimed at the middle of the lens passes through without changing direction.
3. A ray through the principal focus on the object side leaves the lens parallel to the axis.

Any two are enough. Where they cross (or appear to cross) is the top of the image. If the foot of the object is on the axis, so is the foot of the image.

Describing an image (3.3.6 e)

Describe every image using three pairs of words.

Feature	Choices
Size compared with the object	larger (magnified), same size, smaller (diminished)
Orientation compared with the object	upright, inverted
Type	real, virtual

A real image forms where rays actually cross and can be caught on a screen. A virtual image is where rays only appear to have come from. Your eye can see it, but a screen cannot show it.

Images from a convex lens at different distances (3.3.6 b)

Let f be the focal length. The object distance is measured from the lens.

Object position	Image	Size	Orientation	Type
Further than 2f	between f and 2f on the far side	smaller	inverted	real
At 2f	at 2f on the far side	same size	inverted	real
Between f and 2f	beyond 2f on the far side	larger	inverted	real
At f	no image: emerging rays are parallel	not applicable	not applicable	not applicable
Closer than f	on the object side, behind the object	larger	upright	virtual

As the object moves towards the lens, the real image moves away from it and grows. Inside the principal focus the rays leaving the lens still spread out, so they never meet. Your eye traces them back to a larger, upright, virtual image.

The magnifying glass

A magnifying glass is a convex lens used with the object closer to the lens than the principal focus. The image is virtual, upright and larger, and it is on the same side as the object. You cannot project its image onto a wall.

Concave lenses (3.3.6 c)

A concave lens is thinner at the middle than at the edges. It is also called a diverging lens.

• Parallel rays spread out after the lens. They appear to have come from a point on the object side of the lens, the principal focus.
• The focal length is the distance from the lens to that point.
• For any object distance, the image is virtual, upright and smaller, on the same side of the lens as the object, between the object and the lens.

Draw ray 1 (parallel to the axis) spreading away from the axis, with a dotted line back to the principal focus on the object side. Ray 2 passes straight through the centre. The refracted rays never cross, so extend them backwards as dotted lines. Their intersection is the image.

Ray diagrams on graph paper (3.3.6 f)

You may be asked to draw or read a diagram on graph paper. Use the same scale on both axes unless told otherwise. Draw the lens as a vertical line, the axis as a horizontal line and mark each principal focus on the axis. A ray bends at the lens line itself. Read the image distance and height from the grid.

Worked example 1: a real image

A convex lens has a focal length of 4 cm. An object 3 cm tall stands 12 cm from the lens. Find the position and nature of the image. Take the lens at x = 0, the axis along y = 0, and the object tip at (−12, 3).

Step	Working
Ray 1 hits the lens at height 3, then passes through the principal focus at (4, 0)	Line from (0, 3) to (4, 0): y = 3 − 0.75x
Ray 2 goes through the centre from (−12, 3)	Line through (0, 0): y = −0.25x
They cross where 3 − 0.75x = −0.25x	3 = 0.5x, so x = 6, y = −1.5

The image is 6 cm from the lens on the far side and 1.5 cm below the axis. It is real, inverted and smaller (1.5 cm against 3 cm).

Worked example 2: a magnified real image

With the same lens, an object 1.5 cm tall is 6 cm away. Ray 1 runs from (0, 1.5) through (4, 0) and ray 2 from (−6, 1.5) through the centre. They cross at x = 12, y = −3: the image is 12 cm from the lens, 3.0 cm tall, real, inverted and larger.

Worked example 3: a magnifying glass

A convex lens has focal length 5 cm. An object 2 cm tall is 3 cm from the lens, inside the principal focus. Put the tip at (−3, 2).

• Ray 1 leaves the lens along the line from (0, 2) through (5, 0), which has equation y = 2 − 0.4x. The rays spread, so extend it backwards to the left of the lens.
• Ray 2 goes through the centre: y = −(2/3)x.
• They cross when 2 − 0.4x = −(2/3)x. This gives x = −7.5, y = 5.

The image is 7.5 cm from the lens, on the same side as the object, and 5 cm tall. It is virtual, upright and larger.

Worked example 4: a concave lens

A concave lens has a focal length of 6 cm. An object 3 cm tall is 12 cm away, tip at (−12, 3). Ray 1 spreads as if from (−6, 0), so its line is y = 3 + 0.5x. Ray 2 is y = −0.25x. They meet at x = −4, y = 1: the image is 4 cm from the lens on the object side, 1 cm tall, virtual, upright and smaller.

Magnification (3.3.6 g)

magnification = image height ÷ object height

Magnification has no unit. Both heights must be in the same unit before you divide. Above 1 means a larger image, below 1 a smaller one.

For the examples above: example 1 gives 1.5 ÷ 3 = 0.5, example 2 gives 3.0 ÷ 1.5 = 2.0, example 3 gives 5 ÷ 2 = 2.5 and example 4 gives 1 ÷ 3 = 0.33.

Rearranged, image height = magnification × object height, and object height = image height ÷ magnification.

Worked example 5

A slide shows a cell 0.040 mm across. A lens system produces an image 6.0 mm across. magnification = 6.0 ÷ 0.040 = 150.

The eye (3.3.6 h)

The eye detects only visible light, a limited range of the electromagnetic waves. Light is refracted by the cornea (mostly) and then by the lens.

Structure	Function
Cornea	Transparent front surface. It refracts light entering the eye
Pupil	The opening that lets light in
Iris	Ring of muscle that changes the size of the pupil, so controls how much light enters
Lens	Variable focus lens. It fine-tunes the focusing so the image is sharp on the retina
Ciliary muscle	Ring of muscle that changes the shape of the lens
Suspensory ligaments	Fibres connecting the ciliary muscle to the lens. They pull the lens thinner when the muscle relaxes
Retina	Layer at the back with light-sensitive cells. The image must be focused here; signals pass to the brain

Accommodation

Changing the power of the lens so that objects at different distances are in focus is accommodation.

	Looking at a near object	Looking at a distant object
Ciliary muscle	contracts	relaxes
Suspensory ligaments	slacken	pulled tight
Lens shape	thicker, more curved	thinner, less curved
Effect on focal length	shorter	longer

A near object sends in strongly diverging rays, which need more bending. A distant object sends in almost parallel rays, which need less.

Range of vision (3.3.6 i)

The near point is the closest distance at which the eye can form a sharp image. For a typical eye it is about 25 cm. The far point is the furthest distance, which for a typical eye is infinity. The distance between the near point and far point is the range of vision: from about 25 cm to infinity.

Correcting long and short sight (3.3.6 j)

Long sight

The eyeball is too short, or the eye lens cannot focus a sharp image. Light from near objects would focus behind the retina, so near objects are blurred and the near point is further away than normal. A convex lens in front of the eye converges the rays slightly before they enter, so the eye can focus them on the retina.

Short sight

The eyeball is too long, or the eye lens cannot focus a sharp image. Light from distant objects focuses in front of the retina, so distant objects are blurred and the far point is closer than infinity. A concave lens spreads the rays slightly before they enter, so the eye can focus them on the retina.

	Long sight	Short sight
Blurred objects	near	distant
Image forms	behind the retina	in front of the retina
Corrective lens	convex	concave

Lasers (3.3.6 k)

A laser is a concentrated source of light. Because its energy is concentrated, it can be used for cutting, cauterising (sealing tissue by heating it) and burning. In eye surgery, lasers can be used to correct visual defects, for example by reshaping the cornea so that it refracts light differently. You do not need to know how a laser works.

The eye and the camera (3.3.6 l)

Eye	Camera
Lens focuses light	Lens focuses light
Image falls on the retina	Image falls on film or a CCD sensor
Focus by changing the shape of the lens	Focus by changing the distance between lens and film or sensor

The film or CCD sensor in a camera is the equivalent of the retina.

Common errors

• Writing that a concave lens forms a real image of a real object. It does not.
• Saying you cannot see a virtual image. You can. A screen cannot catch it.
• Saying the lens moves in the eye. The lens changes shape.
• Using a concave lens for long sight, or the reverse.
• Dividing heights measured in different units when finding magnification.

Next: the revision notes, the practice set and the exam preparation page.

Official syllabus

OxfordAQA International GCSE Physics (9203), for exams May/June 2018 onwards, Version 5.2, published by OxfordAQA. This page follows section 3.3.6, Lenses and the eye.