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

These are condensed revision notes for OxfordAQA International GCSE Physics (9203), for exams May/June 2018 onwards, covering section 3.3.6, Lenses and the eye (points a to l). The section is for the full Physics award and the course is untiered. For explanations and worked ray diagrams, read the study guide first. Then test yourself with the practice questions. Other routes: the course hub, the printable checklist and the free 10-minute diagnostics.

Key definitions

Term	Meaning
Lens	Curved transparent object that forms an image by refracting light (3.3.6 a)
Convex (converging) lens	Thicker in the middle. Parallel rays are brought to a focus at the principal focus (b)
Concave (diverging) lens	Thinner in the middle. Parallel rays diverge, appearing to come from the principal focus (c)
Focal length	Distance from the lens to the principal focus (d)
Real image	Rays actually meet. Can be shown on a screen
Virtual image	Rays seem to diverge from it but never meet there. Cannot be shown on a screen
Nature of an image	Its size relative to the object, upright or inverted, real or virtual (e)
Accommodation	The eye changing the shape of its lens to focus on objects at different distances
Near point	Closest distance at which the eye focuses a sharp image, about 25 cm
Far point	Furthest distance at which the eye focuses a sharp image, infinity for a typical eye
Range of vision	The distance between near point and far point (i)

The equation

Quantity	Equation	Unit
Magnification	image height ÷ object height	none (a ratio)

Rearrangements: image height = magnification × object height; object height = image height ÷ magnification. Convert both heights to the same unit first.

Convex lens: image summary

Use f for the focal length and measure the object distance from the lens.

Object distance	Image
More than 2f	real, inverted, smaller
Exactly 2f	real, inverted, same size
Between f and 2f	real, inverted, larger
Exactly f	no image (emerging rays parallel)
Less than f	virtual, upright, larger (magnifying glass)

Memory hook: if the object is outside the principal focus the image is real and inverted. Inside the principal focus it is virtual and upright. A real image grows as the object moves closer to the lens, and it is larger than the object once the object is nearer than 2f.

Concave lens: image summary

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.

Drawing ray diagrams: method in steps

1. Draw the axis, then the lens as a straight vertical line. Mark the principal focus on each side at the focal length.
2. Draw the object as an upright arrow on the axis.
3. From the tip, draw ray 1 parallel to the axis up to the lens.
4. Convex lens: refract ray 1 through the principal focus on the far side. Concave lens: refract it so that it spreads away from the axis, and draw a dotted line back to the principal focus on the object’s side.
5. From the tip, draw ray 2 straight through the centre of the lens, undeviated.
6. Mark the tip of the image where the two rays cross. If they only appear to cross (virtual image), extend both backwards with dotted lines.
7. Draw the image arrow from the axis to that point. Read its height and distance from the grid.
8. State the nature of the image: size, upright or inverted, real or virtual.

On graph paper, use the same scale on both axes and read values from the squares rather than estimating by eye.

Worked reminders

Real image, convex lens. Focal length 4 cm, object 3 cm tall at 12 cm. The rays meet 6 cm beyond the lens, 1.5 cm below the axis. Image: real, inverted, smaller. Magnification = 1.5 ÷ 3 = 0.5.

Magnifying glass. Focal length 5 cm, object 2 cm tall at 3 cm (inside the principal focus). The rays appear to come from 7.5 cm on the object side, 5 cm tall. Image: virtual, upright, larger. Magnification = 5 ÷ 2 = 2.5.

Concave lens. Focal length 6 cm, object 3 cm tall at 12 cm. Image 4 cm from the lens on the object side, 1 cm tall. Image: virtual, upright, smaller. Magnification = 1 ÷ 3 = 0.33.

Magnification. A cell 0.040 mm across appears 6.0 mm across: 6.0 ÷ 0.040 = 150.

The eye: parts and functions

Part	Function
Cornea	Transparent front of the eye. Refracts light entering the eye
Pupil	Opening through which light enters
Iris	Muscle around the pupil. Changes the pupil size to control the light entering
Lens	Variable focus lens. Adjusts focusing so the image is sharp on the retina
Ciliary muscle	Changes the shape of the lens
Suspensory ligaments	Connect the ciliary muscle and lens, and pull the lens thinner when the muscle relaxes
Retina	Contains light-sensitive cells. The image must be focused on it

Light is refracted by the cornea as well as by the lens. The eye detects only visible light, a limited range of the electromagnetic waves.

Accommodation at a glance

	Near object	Distant object
Ciliary muscle	contracts	relaxes
Suspensory ligaments	slack	taut
Lens	thick, strongly curved	thin, weakly curved
Bending of light	more	less

Say all four links in your answer: muscle, ligaments, lens shape, focal length.

Range of vision

Typical near point is about 25 cm and the far point is infinity. The eye focuses on objects between these two points. So the typical range of vision is from about 25 cm to infinity.

Sight defects

	Long sight	Short sight
Cause	eyeball too short, or lens unable to focus a sharp image	eyeball too long, or lens unable to focus a sharp image
Problem	near objects blurred	distant objects blurred
Image without correction	behind the retina	in front of the retina
Near or far point	near point further than normal	far point nearer than infinity
Correction	convex lens	concave lens

Method for an explanation: state where the image forms without correction, say which lens is used, and say what the lens does to the rays before they reach the eye.

Lasers and the camera

• A laser is a concentrated source of light. Uses: cutting, cauterising and burning.
• Lasers can be used in eye surgery to correct visual defects. How lasers work is not required.

Eye	Camera
Retina	Film or CCD sensor
Image focused by changing the shape of the lens	Image focused by changing the distance between lens and film or sensor

Must-know distinctions

• Real versus virtual: a real image can be projected, a virtual image cannot.
• Convex versus concave: convex converges the rays, concave diverges them.
• Long sight versus short sight: the lens used is opposite in each case, and the blurred distance is near for long sight and far for short sight.
• Cornea versus lens: both refract light. The lens is the one that changes shape.
• Eye versus camera: the eye changes the lens shape, the camera moves the lens.

Quick self-test

1. What is the principal focus of a convex lens?
2. A convex lens has a focal length of 8 cm. An object is 24 cm from it. Describe the image.
3. An image is 36 mm tall and the object is 12 mm tall. Find the magnification.
4. A lens gives a magnification of 0.50 and the image is 2.5 cm tall. How tall is the object?
5. An object is placed 3 cm from a convex lens of focal length 5 cm. Describe the image and say what the arrangement is used as.
6. Describe the image formed by a concave lens.
7. Explain how the eye focuses on a book held close.
8. A person cannot see distant road signs clearly. Name the defect and the lens used to correct it.
9. State the usual range of vision.
10. Give one similarity and one difference in focusing between the eye and a camera.

Answers

1. The point where rays parallel to the axis are brought together after passing through the lens.
2. The object is further than 2f (16 cm). The image is real, inverted and smaller (it is 12 cm from the lens, half the height).
3. 36 ÷ 12 = 3.0.
4. Object height = 2.5 ÷ 0.50 = 5.0 cm.
5. The object is inside the principal focus. The image is virtual, upright and larger (magnification 2.5). The lens is used as a magnifying glass.
6. Virtual, upright and smaller, on the same side as the object.
7. The ciliary muscle contracts, the suspensory ligaments slacken, and the lens becomes thicker and more curved. It refracts light more, so the image falls sharply on the retina.
8. Short sight. A concave lens spreads the rays so the image forms on the retina rather than in front of it.
9. From about 25 cm (near point) to infinity (far point).
10. Similarity: both have a lens that focuses an image onto a light-sensitive surface (retina, or film or CCD sensor). Difference: the eye changes the shape of its lens, while a camera changes the distance between lens and film or sensor.

Where marks are usually lost

• Describing an image with only one word. Give size, orientation and real or virtual.
• Writing that the image formed by a convex lens is always real. It is virtual when the object is inside the principal focus.
• Saying the eye lens moves back and forth like a camera lens. The shape of the lens changes.
• Mixing up the lenses for long sight and short sight.
• Saying the pupil focuses light. The pupil is an opening, and the iris changes its size.
• Giving a magnification with a unit, or dividing heights in different units.
• Drawing ray 1 so that it does not pass through the principal focus, or drawing ray 2 bent at the lens.
• Forgetting dotted construction lines for a virtual image.
• Forgetting that light is refracted by the cornea as well as by the lens.
• Naming laser eye surgery without saying that it is used to correct a visual defect.

Official syllabus

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