Not to scale: distances and the focus offset are exaggerated.
Click any part, or pick one from the list
Controls
Type of eye
Readings
- Object distance
- 100cm
- Lens power P = 1/f
- 41.00D
- Focal length f
- 2.44cm
- Image distance v (lens to retina)
- 2.50cm
- Near point
- 25.0cm
- Far point
- ∞
- Pupil diameter
- 5.0mm
- Ciliary muscle
- Relaxed
- Lens shape
- Thin
- Image falls
- On the retina (sharp)
How to use this simulation
- Press play and drag the object distance slider. As the object comes closer, the ciliary muscle turns red and thickens, the suspensory ligaments go slack, the lens bulges and its power P rises. The image stays on the retina the whole time.
- Drag the light intensity slider. More light and the iris squeezes the pupil down; less light and it opens wide. The same thing happens in your own eye when you switch a room light on or off.
- Choose myopia or hypermetropia under the type of eye. The image now lands in front of or behind the retina and blurs. Tick “Wear the correcting lens”: a concave or convex lens moves the image back onto the retina.
- Click any part of the drawing, or choose it from the list. It lights up and its job appears below. On a small screen the names become numbers, with the key under the picture.
- Watch the readings for lens power, focal length, near point and far point. Slide the object to 10 cm and even the normal eye blurs: that is inside the near point.
Try this first: make a dot vanish
Draw a small plus sign on a sheet of paper and a thick dot 8 cm to its right. Hold the paper at arm’s length, close your left eye and keep your right eye fixed on the plus. Now bring the paper slowly towards your face without looking at the dot. At about 30 cm the dot suddenly disappears. Move closer still and it comes back.
The arithmetic is simple. The blind spot sits about 15° to the side of the fovea, so the dot lands on it at a distance of 8 ÷ tan 15° ≈ 30 cm. You just found a place in your own eye where there are no light sensors at all.
You never notice it in daily life because the two eyes have their blind spots in different places and the brain fills the gap from the surroundings. This page takes the eye apart. Another oddity is coming too: the picture on your retina is completely upside down, yet you see the world the right way up.
The eye is a living camera
Comparing the eye with a camera makes the parts easier to remember. Both let light into a dark box and form a picture on a screen. The difference is that the eye adjusts its own light, its own focus and its own screen.
| Camera part | Eye part | Job |
|---|---|---|
| Lens | Cornea and eye lens | Bend light to bring it to a focus |
| Diaphragm (aperture) | Iris and pupil | Decide how much light gets in |
| Film or sensor | Retina | Catch the light and make electrical signals |
| Dark box | Eyeball (sclera and choroid) | Block stray light so the image stays clear |
| Moving the lens to focus | Changing the lens shape (accommodation) | Focus on near or far objects |
| Cable | Optic nerve | Carries the signals to the brain |
| Lens cap | Eyelid | Covers the eye and wipes away dust |
Meet the parts: one job each
The human eyeball is nearly spherical, about 2.3 cm across. Let us follow the light from the outside in. Read the six groups below, then find all twelve parts in one table. You can also click each part in the simulation to check.
Sclera and choroid: the outer wall
The white of the eye is the sclera, a tough white coat that holds the eyeball’s shape and protects what is inside. Under it lies the dark choroid, rich in blood vessels. The choroid soaks up stray light so it does not bounce around and blur the picture, much like the black paint inside a camera.
Cornea and aqueous humour: the front window
The transparent dome at the front is the cornea. It has no blood vessels, which is why it is clear. Most of the bending of light happens here, about two thirds of the eye’s total power. Behind it, the space up to the lens is filled with aqueous humour, a clear watery fluid. It keeps the cornea in shape, feeds the cornea and the lens, and helps refract light a little.
Iris and pupil: the adjustable hole
The iris is a coloured sheet of muscle: brown in some people, blue in others. The round hole in its middle is the pupil. The iris holds two sets of muscle. When the circular muscles contract the pupil gets smaller; when the radial muscles contract it gets larger. In effect the iris is the eye’s light control.
Lens, ciliary muscles and suspensory ligaments: the focusing team
The eye lens is transparent, flexible and convex. Once the cornea has done the heavy bending, the lens makes the fine adjustment that puts the image exactly on the retina. A ring of ciliary muscle surrounds the lens, and thin suspensory ligaments hang the lens from that ring. When you look at something near, the ciliary muscle contracts, the ligaments slacken and the elastic lens bulges by itself. When you look far, the muscle relaxes, the ligaments pull tight and stretch the lens thin.
Vitreous humour: the jelly inside
The big chamber behind the lens is full of a clear jelly, the vitreous humour. It keeps the eyeball round and firm, and light passes through it to reach the retina. Like the aqueous humour it must be transparent, or no picture would arrive.
Retina, fovea, blind spot and optic nerve: the screen and its cable
The retina lines the back wall inside the eye and holds the light-sensitive rod and cone cells. At its centre is a small pit, the fovea or yellow spot, packed with cones; the sharpest vision comes from here. That is why your eyes swivel to drop whatever you are reading onto the fovea. Close to the fovea the optic nerve leaves the eye on its way to the brain. There are no sensors at that exit, so it is the blind spot you found at the start.
| Part | What it is | Job |
|---|---|---|
| Cornea | Transparent front dome | Most of the refraction |
| Aqueous humour | Fluid between cornea and lens | Shape, nourishment, a little refraction |
| Iris | Coloured sheet of muscle | Changes the pupil size |
| Pupil | Hole in the iris | The way in for light |
| Lens | Clear, flexible convex lens | Fine focus, accommodation |
| Ciliary muscle | Muscle ring around the lens | Contracts to thicken the lens |
| Suspensory ligaments | Fibres between muscle and lens | Taut, they keep the lens thin |
| Vitreous humour | Jelly behind the lens | Keeps the shape, passes light |
| Retina | Light-sensitive inner screen | Turns the image into signals |
| Fovea (yellow spot) | Pit at the centre of the retina | Sharpest, colour vision |
| Blind spot | Where the nerve leaves | Has no sensors |
| Optic nerve | Cable from retina to brain | Carries the signals |
How the image forms
Say there is a tree in front of you. Light spreads from every point of the tree, and a part of it enters your eye. Here is the journey, step by step.
1/f = 1/v − 1/uLens formula in the cartesian sign convention: the object is to the left, so u is negative
P = 1/fPower; with f in metres the unit is the dioptre (D). With f in centimetres, P = 100 ÷ f
- Light strikes the cornea. The cornea bends it the most, and the rays start to come together.
- It passes the aqueous humour and reaches the pupil. The iris sets how much light gets through.
- The lens bends the light further and brings it to a fine focus. This is where the focus changes for near or far objects.
- Through the vitreous humour the light reaches the retina and forms a small, inverted, real image.
- Rod and cone cells turn the light into electrical signals, which the optic nerve carries to the brain.
- The brain reads the upside-down picture the right way up, and compares the two eyes to judge depth.
Accommodation: changing focus from near to far
The image distance v is fixed: 2.5 cm from lens to retina. Yet the object may be 25 cm away one moment and a hundred metres the next. The lens formula says that if v stays put and u changes, f must change too. The eye does exactly that by changing the curvature of its lens. This ability is called accommodation.
For a distant object 1/u is almost zero, so 1/f = 1/2.5 = 0.40 cm⁻¹. That gives f = 2.5 cm and a power P = 40 D. For an object 25 cm away, 1/f = 0.40 + 0.04 = 0.44 cm⁻¹, so f = 2.27 cm and P = 44 D. Over the whole range the ciliary muscles change the lens power by only 4 D. Because the cornea stays fixed, that small change is enough.
The nearest distance at which the eye still sees clearly is the near point, 25 cm for a normal eye (also called the least distance of distinct vision). The farthest point is the far point, which is infinity for a normal eye. So the normal eye sees clearly from 25 cm to infinity.
| Looking at a far object | Looking at a near object | |
|---|---|---|
| Ciliary muscle | Relaxed | Contracted |
| Suspensory ligaments | Taut | Slack |
| Lens | Thin, less curved | Thick, more curved |
| Focal length f | Longer, 2.5 cm | Shorter, 2.27 cm (object at 25 cm) |
| Power P | Lower, 40 D | Higher, 44 D |
The pupil reflex: sunglasses that run themselves
Walk into a dark room and at first you see nothing, then things slowly appear. Step back into the light and you are dazzled before it settles. The pupil is changing size with the light. In bright light the circular muscles contract and the pupil narrows, down to 2 mm in this simulation. In the dark the radial muscles pull the pupil wide open, up to 8 mm.
Going from 8 mm to 2 mm cuts the area of the opening by a factor of 16, because area grows with the square of the diameter. At 50% light the simulated pupil is 5.0 mm. The brain runs this reflex without thinking about it; you cannot widen or narrow your pupils on purpose.
Adapting to the dark takes much longer, around half an hour, because the pigment in the rods has to be rebuilt. The pupil answers in seconds; the pigment is the slow part.
Rods and cones: two kinds of workers in the retina
The retina has two main kinds of light-sensitive cell. Rods respond to very dim light but cannot tell colours, which is why everything looks grey in faint light at night. Cones need bright light and tell colours and fine detail. There are three kinds of cone, most sensitive to red, green and blue light, and the brain builds every colour from their mix.
| Feature | Rod cells | Cone cells |
|---|---|---|
| Number (approx.) | About 120 million | About 6 million |
| Work best in | Dim light | Bright light |
| See colour? | No | Yes |
| Where most | Towards the edge of the retina | Packed in the fovea |
| Kinds | One | Three (red, green, blue) |
| Good for | Night and side vision | Sharp, colourful vision |
Eye defects and how lenses fix them
When the image does not land exactly on the retina, vision blurs. The simulation models the two main defects in the simplest way: the focusing system is the same, only the distance to the retina differs. A correcting lens is an extra lens that changes the direction of light a little before it enters the eye.
Myopia: good near, blurred far
Suppose the retina is a little too far back, or the lens a little too curved. Light from a distant object comes together before it reaches the retina, then spreads out again. The image forms in front of the retina. In this simulation the retina is 2.58 cm from the lens, about 0.8 mm farther than normal, so the far point drops to 80 cm.
The cure is a lens that makes a distant object appear at the eye’s far point as a virtual image. That is a concave lens, whose power is negative: −1.25 D here. Wearing it, the eye sees a distant object as if it stood 80 cm away, and the eye’s own lens focuses it.
Hypermetropia: good far, blurred near
Here the retina is a little too close, or the lens a little too flat. Light from a near object reaches the retina before it has come together, so the image forms behind the retina. In the simulation the retina is 2.33 cm from the lens, about 1.7 mm closer than normal, and the near point moves out to 100 cm. Even distant objects need the eye to curve its lens in advance, which tires it.
The cure is a convex lens with positive power, +3.0 D here. A book held at 25 cm looks, through it, like a virtual image 100 cm away, which the eye can focus easily.
Three more defects in brief
With age (usually after forty) the ciliary muscles weaken and the lens stiffens, so accommodation shrinks. The near point moves away and reading small print gets hard. This is presbyopia. Bifocal glasses, concave on top and convex below, give both distance and reading in one frame.
If the cornea is not perfectly round, lines in one direction look sharp and lines in another look blurred. This is astigmatism, and a cylindrical lens corrects it. When the lens turns cloudy the condition is a cataract, treated by surgery that swaps the cloudy lens for an artificial one.
If one kind of cone does not work, the person is colour blind, most often mixing up red and green. It runs in families and is more common in males.
| Myopia (short-sight) | Hypermetropia (long-sight) | |
|---|---|---|
| Problem | Far objects blurred | Near objects blurred |
| Cause | Eyeball too long, or lens too curved | Eyeball too short, or lens too flat |
| Image falls | In front of the retina | Behind the retina |
| Correcting lens | Concave (diverging) | Convex (converging) |
| In the simulation | Far point 80 cm, near point 19.0 cm | Near point 100 cm, far point infinity |
Try it in the simulation
Each experiment takes under a minute, and each one makes an idea stick.
1. Bring the object closer and watch the lens bulge
Start with the distance slider at the far end (500 cm). The ciliary muscle is almost relaxed, the lens is thin and the power is about 40 D. Now slide slowly down to 25 cm. The ciliary muscle thickens, the ligaments go wavy and slack, the lens bulges, and the power climbs to 44 D. Through all of it the image stays on the retina.
2. Go inside the near point
With the normal eye, drop the distance below 25 cm. The image slides behind the retina and blurs, because the power is stuck at its maximum of 44 D. A sharp image at 10 cm would need 50 D, more than the eye can make. This is why print blurs when you hold a book too close.
3. Dim and brighten the light
Set the light to 0%: the pupil opens to 8 mm and the ray bundles are wide. Raise it to 100%: 2 mm, a thin bundle. The reflex signal is instant but the pupil responds smoothly, as in real life.
4. Switch on myopia
Choose myopia and send the object far away (500 cm). The image is in front of the retina: the rays meet early and spread again, leaving a blur on the retina. Now bring the object to 80 cm and it turns sharp. That is this eye’s far point.
5. Wear the concave lens
Tick “Wear the correcting lens”. A concave lens appears in front of the eye and spreads the rays slightly. The image returns to the retina and the far point goes to infinity. Reading at 25 cm still works, because the corrected eye’s near point is back at 25 cm.
6. Hypermetropia and the convex lens
Choose hypermetropia and place the object at 25 cm: the image falls behind the retina. Now add the lens. The convex lens pre-converges the rays, the image lands on the retina and the near point moves from 100 cm to 25 cm.
Solved problems
Every answer is computed from the simulation’s own model. In the cartesian sign convention the object is to the left of the lens, so u is negative; the image is on the retina, so v = +2.5 cm.
Problem 1: lens power at the near point
In a normal eye the retina is 2.5 cm behind the lens. What power does the lens need to see an object 25 cm away?
u = −25 cm, v = +2.5 cm. 1/f = 1/v − 1/u = 1/2.5 + 1/25 = 0.40 + 0.04 = 0.44 cm⁻¹. So f = 2.27 cm and P = 100 ÷ 2.27 = 44 D.
Problem 2: an object at infinity
What power does the same eye need to see a far mountain?
For u = −∞, 1/u = 0. 1/f = 1/2.5 = 0.40 cm⁻¹, f = 2.5 cm, P = 40 D. Here the ciliary muscle is relaxed and the lens is at its thinnest.
Problem 3: the range of accommodation
A student looks from a page at 25 cm to a distant hill. By how much does the lens power change?
44 D at 25 cm, 40 D at infinity. Change = 44 − 40 = 4 D. At the halfway distance of 50 cm, P = 42 D and f = 2.38 cm.
Problem 4: the simulation’s default distance
The object is 100 cm away. Find the lens power and focal length.
1/f = 0.40 + 0.01 cm⁻¹. P = 41 D and f = 2.44 cm. When you start the simulation, the readings panel shows the same values.
Problem 5: how big is the image of a tree?
A tree 5 m tall stands 50 m away. How tall is its image on the retina? (v = 2.5 cm)
Magnification m = v ÷ u, so image height = object height × v ÷ distance = 500 × 2.5 ÷ 5,000 = 0.25 cm = 2.5 mm. Such a tiny image can carry so much detail because the fovea is packed with cones.
Problem 6: glasses for myopia
A person’s far point is 80 cm. What lens lets them see distant objects clearly?
Light from a distant object is parallel, so u = −∞. The lens must form its image at the far point, v = −80 cm. 1/f = 1/v − 1/u = −1/80 − 0, so f = −80 cm and P = −1.25 D. A concave lens.
Problem 7: stronger myopia
What power is needed if the far point is 200 cm? And if it is 50 cm?
P = −100 ÷ far point. For 200 cm, P = −0.50 D; for 50 cm, P = −2.00 D. The nearer the far point, the stronger the lens.
Problem 8: glasses for hypermetropia
A person’s near point is 100 cm. What lens lets them read a book at 25 cm?
The book is at u = −25 cm. The lens must form a virtual image at the near point, v = −100 cm. 1/f = 1/v − 1/u = −1/100 + 1/25 = 0.03 cm⁻¹. f = 33.3 cm and P = +3.0 D. A convex lens.
Problem 9: another hypermetropic eye
The near point is 50 cm. What lens is needed to read at 25 cm?
P = 100 ÷ 25 − 100 ÷ 50 = +2.0 D, so f = 50 cm. Convex.
Problem 10: the pupil’s area
The pupil narrows from 8 mm to 2 mm. By what factor does the light entering fall?
Area ∝ diameter². Ratio = (8 ÷ 2)² = 16. The light let in drops by up to 16 times.
Common mistakes
Most lost marks on this topic come from the same few slips. Check your answers against them before you hand in.
- Drawing the retinal image upright. It is inverted, real and diminished; the brain turns it round.
- Saying the lens moves in accommodation. It does not move; its curvature changes.
- Saying the ciliary muscle relaxes for near vision. For near vision it contracts and the lens thickens.
- Writing a convex lens for myopia. Myopia needs a concave lens; hypermetropia needs a convex one.
- Thinking myopia means “cannot see near”. It is the reverse: near is clear, far is blurred.
- Giving the lens most of the refraction. Most of it happens at the cornea; the lens only fine-tunes.
- Mixing up the fovea and blind spot. The fovea has the most cones and the sharpest vision. The blind spot has no sensors at all.
- Swapping rods and cones. Rods handle dim light with no colour; cones handle bright light and colour.
- Getting the unit wrong. One dioptre is 1 ÷ focal length in metres. With f in centimetres use 100 ÷ f.
- Giving a concave lens a positive power. A concave lens has a negative f and a negative P.
Looking after your eyes
These are textbook-level tips, not medical advice. If you think something is wrong with your eyes, see an eye doctor.
Long close work tires the ciliary muscles. Every 20 minutes, look at something far away for 20 seconds; the muscle relaxes and rests. Read in good light with the book about 25 cm from your eyes. Reading lying down or in a moving vehicle keeps changing the distance and strains the eyes.
Never look straight at the Sun or at very bright light; it can burn the retina. Do not rub your eyes with dirty hands, because the cornea scratches easily. If something gets into your eye, rinse it with clean water.
Eat foods rich in vitamin A, such as carrots, sweet pumpkin, eggs, liver and leafy greens. A check-up once a year catches short or long sight early.
Donated eyes can give sight to another person through a cornea transplant. Only the cornea is transplanted, and it must be done within a few hours of death. It is worth talking to your family about it beforehand.
Exam corner: board exams
The eye is a topic where biology and physics meet, so questions can come from both. Biology asks for structure and function; physics asks about refraction, lens power and the defects of vision.
Recall questions: “Define accommodation”, “What is the blind spot?”, “What is the unit of lens power?”. Diagrams: a vertical section of the eye with the cornea, iris, pupil, lens, ciliary muscle, vitreous humour, retina, fovea and optic nerve labelled. Name the parts in the order light meets them and the labels fall into place.
Reasoning questions: “Why does the ciliary muscle contract for near vision?”, “Why does the pupil widen in the dark?”, “Why do we see upright when the retinal image is inverted?”. Numerical questions: glasses power from the far point or near point. Write 1/f = 1/v − 1/u first, put in the signs, and finish with the unit D. Higher-order questions: explain why a given person needs a concave or convex lens.
Multiple-choice items come back again and again: where most refraction happens, where the cones are concentrated, which lens cures which defect. In comparison tables keep a row each for myopia and hypermetropia: cause, where the image falls, which lens. Always add a diagram and a unit.
Quick revision
Read this the night before the exam; every line is a likely question.
- Path of light: cornea, aqueous humour, pupil, lens, vitreous humour, retina.
- The retinal image is inverted, real and diminished; the brain interprets it upright.
- Most refraction is at the cornea; the lens fine-tunes the focus. The image distance is fixed near 2.5 cm.
- Accommodation: for near objects the ciliary muscle contracts, ligaments slacken, the lens thickens and P is higher (44 D); for far ones it is the reverse (40 D).
- A normal eye has a near point of 25 cm and a far point at infinity.
- The iris changes the pupil: small in bright light, large in the dark.
- Rods: dim light, no colour. Cones: bright light, colour. The fovea has the most cones.
- The blind spot has no sensors, because the optic nerve leaves there.
- Myopia: image in front of the retina, concave lens, negative power.
- Hypermetropia: image behind the retina, convex lens, positive power.
Frequently asked questions
Why is the image on the retina inverted?
The cornea and lens act together as a convex lens, and a convex lens forms an inverted real image. The retina only sends signals, and since birth the brain has learned to read them as an upright picture.
What is accommodation of the eye?
It is the ability of the eye to change the focal length of its lens so that objects at different distances form sharp images on the retina. The ciliary muscles contract or relax to make the lens thicker or thinner.
What are the near point and far point of a normal eye?
The near point (least distance of distinct vision) is about 25 cm and the far point is infinity. A normal eye sees clearly from 25 cm to infinity, and the near point moves farther away with age.
What is the difference between myopia and hypermetropia?
In myopia near objects are clear and far ones blurred; the image falls in front of the retina and a concave lens corrects it. In hypermetropia far objects are clear and near ones blurred; the image falls behind the retina and a convex lens corrects it.
What is the difference between the fovea and the blind spot?
The fovea (yellow spot) is the small pit at the centre of the retina with the most cone cells, so it gives the sharpest vision. The blind spot is where the optic nerve leaves the eye. It has no light-sensitive cells, so an image falling there is not seen.
What do rods and cones do?
Rods work in dim light and do not detect colour. Cones work in bright light and detect colour and fine detail. There are three types of cone, sensitive to red, green and blue light.
Why does the pupil get smaller in bright light?
Too much light can damage the retina. In bright light the circular muscles of the iris contract and shrink the pupil, letting in less light. In the dark the radial muscles widen it. It is an automatic reflex controlled by the brain.
What is a dioptre?
A dioptre (D) is the unit of lens power. Power is 1 divided by the focal length in metres, so a lens with f = 1 m has power 1 D. Convex lenses have positive power and concave lenses negative power.
How do glasses correct blurred vision?
A glasses lens changes the vergence of light slightly before it enters the eye, so the eye’s own focusing system can put the image exactly on the retina. A concave lens spreads light out; a convex lens brings it together.
Keep studying this topic
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Pollination and fertilisation
Follow pollen from anther to stigma, down the pollen tube and into the ovule. Watch double fertilisation make the 14-chromosome zygote and 21-chromosome endosperm, then seed and fruit.
Animations in other subjects
Physics
Refraction of light
Physics
Ohm's law
Physics
Projectile motion
Physics
Simple pendulum
Physics
Electric field
Physics
Wave interference
Physics
Free Fall
Physics
Lens ray diagrams
Physics
Newton's Laws of Motion
Physics
Spherical mirror ray diagrams
Physics
Electromagnetic Induction
Physics
Conservation of Momentum and Collisions
Physics
Work, Energy and Power
Physics
Inclined Plane
Physics
Uniform circular motion
Physics
Transverse and Longitudinal Waves
Physics
Levers and moments
Physics
Centre of mass
Physics
Spring-mass SHM
Physics
Vector addition: triangle and parallelogram laws
Physics
Relative velocity: trains and river crossing
Physics
Kepler's laws and elliptical orbits
Physics
Newton’s law of gravitation, g and satellites
Physics
Standing waves in strings and pipes
Physics
Resonance tube and the speed of sound
Physics
Beats: when two close notes pulse
Physics
Doppler effect: moving sources, listeners and sonic booms
Physics
Prism, dispersion of light and the rainbow
Physics
Kirchhoff’s laws: junction rule and loop rule
Physics
Wheatstone bridge and metre bridge
Physics
Single-slit diffraction
Physics
Defects of the human eye and their correction
Physics
Polarisation of light: Malus’s law and Brewster’s law
Physics
Charging and discharging a capacitor: the RC time constant
Physics
Magnetic field lines: bar magnet, current-carrying wire and solenoid
Physics
AC generator
Physics
Transformer
Physics
Heat transfer: conduction, convection and radiation
Physics
Photoelectric effect: Einstein’s equation and the stopping potential
Physics
Motor effect: force on a current-carrying wire and the DC motor
Physics
Gas molecules and kinetic theory: pressure, temperature and speed
Physics
The semiconductor diode: p–n junction, I–V curve and rectifier
Physics
Radioactive decay: half-life, the decay law and penetration
Physics
The Bohr atom: orbits, energy levels and the hydrogen spectrum
Chemistry
Structure of the atom
Chemistry
Acids, Bases and the pH Scale
Chemistry
Electron configuration
Chemistry
Gas laws: Boyle, Charles, Gay-Lussac, Avogadro and PV = nRT
Chemistry
How an Ionic Bond Forms
Chemistry
Electrolysis and Faraday’s Laws
Chemistry
Covalent Bond
Chemistry
Periodic Trends
Chemistry
Reaction rate and collision theory
Chemistry
States of matter: solid, liquid, gas and the heating curve
Chemistry
Atomic orbitals: the shapes of s, p and d, quantum numbers and nodes
Chemistry
Molecular shapes and VSEPR theory: bond pairs, lone pairs and angles
Chemistry
The mole concept: molar mass, Avogadro’s number and molar volume
Chemistry
Diffusion and effusion: Graham’s law of gases
Chemistry
Balancing chemical equations: method, examples and practice
Chemistry
Chemical equilibrium: the equilibrium constant Kc and Le Chatelier’s principle
Chemistry
Titration: finding an unknown concentration with a burette and an indicator
Chemistry
Galvanic cell: the Daniell cell, EMF and the Nernst equation
Chemistry
Redox reactions: oxidation numbers, electron transfer and half-equations
Chemistry
Hydrocarbons: alkanes, alkenes, alkynes and structural isomers in 3D
Chemistry
Functional groups: alcohols, aldehydes, ketones, acids, esters and amines
Chemistry
Polymerisation: addition and condensation polymers, polythene and nylon
Chemistry
Separation techniques: filtration, distillation, chromatography, crystallisation
Chemistry
Crystal lattice: SC, BCC and FCC unit cells, packing efficiency and density
Chemistry
Radioactivity: Alpha, Beta, Gamma Decay and Half-Life
Mathematics
Pythagorean Theorem
Mathematics
Trigonometric Ratios and the Unit Circle
Mathematics
Quadratic functions and their graphs
Mathematics
Circle theorems
Mathematics
Heights and distances: elevation and depression angles
Mathematics
Probability: experimental vs theoretical probability
Mathematics
Arithmetic and Geometric Sequences
Mathematics
Mean, Median and Mode
Mathematics
Sets and Venn Diagrams
Mathematics
Linear equations: graphs, slope and simultaneous pairs
Mathematics
Graphs of sin, cos and tan
Mathematics
Completing the Square and the Quadratic Formula
Mathematics
Area of a Circle: Proof, Formula and Solved Problems
Mathematics
Volume and Surface Area of Solids: Cube, Cuboid, Cylinder, Cone, Sphere
Mathematics
Similar Triangles: Scale Factor, AA, SSS, SAS and Shadow Heights
Mathematics
Coordinate Geometry: Distance, Midpoint, Slope, Section Formula and Locus
Mathematics
Conic Sections: Circle, Ellipse, Parabola and Hyperbola
Mathematics
Function Transformations: Shifts, Stretches and Reflections
Mathematics
Derivative as the Slope of a Tangent: Secant to Tangent
Mathematics
Riemann Sums and Integration: Area Under a Curve
Mathematics
Limits and the ε–δ Definition: A Visual Guide
Mathematics
3D Vectors: Sum, Dot Product and Cross Product
Mathematics
Matrix Transformations: Rotation, Reflection, Shear and the Determinant
Mathematics
Complex Numbers: Sum, Product, Powers and Roots on the Argand Plane
Mathematics






















