The human eye & power of accommodation
A phone camera focuses on a friend close to you and then on a hill far away. Your eye does the same all day without you noticing: its lens changes shape.
The eye is a nearly round ball about 2.3 cm across. Light enters through the cornea, passes the pupil (its size is set by the iris) and is focused by the eye lens into a real, inverted image on the retina. Retina cells send signals along the optic nerve to the brain, which shows the picture upright. Most bending happens at the cornea; the lens only fine-tunes. Accommodation is the eye lens changing its focal length with the help of the ciliary muscles.
Equation / formula : Normal eye: near point 25 cm · far point infinity
In the figure : Light path: cornea, pupil, lens, retina, then the optic nerve carries the signal.
The human eye & power of accommodation
In the app you can move this figure with your finger.
Open in the appRule 1 : Parts of the eye and how we see — Light passes cornea, pupil and lens and forms a real, inverted image on the retina; the brain turns it upright. In bright light the iris makes the pupil small, in dim light large.
- Easy : Stepping from a dark hall into sunlight, the iris shrinks the pupil to protect the retina.
- Medium : The image on the retina is upside down, yet we see objects upright because the brain reads the signals and corrects the picture.
- For exams : Name the part: bends light most = cornea; image forms on it = retina; carries signals to the brain = optic nerve; controls pupil = iris.
Rule 2 : Accommodation, near point and far point — For far objects the ciliary muscles relax, the lens becomes thin and its focal length is long. For near objects they contract, the lens becomes thick and its focal length is short. The lens cannot be curved beyond a limit, so the near point is about 25 cm; the far point of a normal eye is at infinity.
- Easy : Reading a book at 25 cm: the muscles contract and the lens becomes thicker.
- Medium : Looking from a book to a distant hill: the muscles relax, the lens thins and its focal length increases.
- For exams : A page held 8 cm from the eyes looks blurred because the eye lens cannot shorten its focal length enough; a normal eye sees clearly only from 25 cm to infinity.
Eye donation: the eyes must be removed within 4 to 6 hours after death. The donor’s cornea can give sight to a corneal blind person, and donors can be of any age or sex.
Thinking the lens does most of the bending of light. Most bending happens at the outer surface of the cornea; the lens only fine-tunes the focus.
Far: muscles relaxed, lens thin. Near: muscles tight, lens thick. Memory clue : "Relax for far, tighten for near": relaxed muscles give a thin lens and a far view.
Spot the difference
| Point | Looking far | Looking near |
|---|---|---|
| Ciliary muscles | relaxed | contracted |
| Eye lens | thin, long focal length | thick, short focal length |
Practice questions
- 1Name the part of the eye that bends light the most.
- 2What kind of image forms on the retina?
- 3What is the job of the iris?
- 4When the ciliary muscles relax, can you see far or near objects clearly?
- 5Why can’t we see a page held 8 cm from the eyes clearly?
- 6A person looks from a distant hill to a book. What happens to the focal length of the eye lens?
- 7Within how many hours after death should eyes be removed for donation?
- 8Why does the pupil become small in bright sunlight?
Show answers (try them yourself first)
- 1The cornea (its outer surface).
- 2Real and inverted; the brain makes it appear upright.
- 3It controls the size of the pupil and so the amount of light.
- 4Far objects: the lens becomes thin with a long focal length.
- 5The lens cannot shorten its focal length enough; the near point is about 25 cm.
- 6It decreases, because the lens becomes thicker.
- 7Within 4 to 6 hours.
- 8The iris lets less light in, which protects the retina.
Defects of vision & their correction
A girl squints at the board yet reads her phone easily, while her grandfather holds the newspaper at arm’s length. Different eyes have different focusing problems, and spectacles fix them.
Myopia (near-sightedness): near objects are clear, distant ones blurred; the far point is nearer than infinity and the image forms in front of the retina; a concave lens corrects it. Hypermetropia (far-sightedness): distant objects are clear, near ones blurred; the near point is beyond 25 cm and the image would form behind the retina; a convex lens corrects it. Presbyopia: with age the lens stiffens and the near point recedes; reading glasses or bifocal lenses help. Cataract: a cloudy lens, treated by surgery.
Equation / formula : P = 1/f (f in metres) · concave: negative · convex: positive
In the figure : Myopia and hypermetropia are fixed with spherical lenses; cataract needs surgery.
Defects of vision & their correction
In the app you can move this figure with your finger.
Open in the appRule 1 : Myopia: cause and correction — Cause: lens too curved or eyeball too long. The spectacle lens must form a virtual image of a distant object at the far point, so a concave lens with focal length f = minus (far point distance) is used.
- Easy : Far point 100 cm: f = -1 m, so P = 1/(-1) = -1 D.
- Medium : Far point 40 cm: f = -0.4 m, so P = 1/(-0.4) = -2.5 D.
- For exams : A student’s spectacles are -2 D. Defect: myopia (negative power). Focal length: f = 1/(-2) = -0.5 m = -50 cm, so the far point is 50 cm.
Rule 2 : Hypermetropia and presbyopia — Cause: eye lens focal length too long or eyeball too short. A convex lens must form a virtual image of an object at 25 cm exactly at the eye’s near point N. Use 1/f = 1/25 - 1/N (distances in cm). Presbyopia is corrected the same way, or with bifocals (concave top, convex bottom).
- Easy : Spectacles of +2 D have focal length 1/2 m = 50 cm.
- Medium : Near point 50 cm, wants to read at 25 cm: 1/f = 1/25 - 1/50 = 1/50, so f = 50 cm and P = +2 D.
- For exams : Near point 40 cm: 1/f = 1/25 - 1/40 = 3/200, so f = 200/3 = 66.7 cm = 0.667 m and P = +1.5 D.
Negative power means a concave lens; positive power means a convex lens. Always check the sign before answering.
Using a convex lens for myopia. A myopic eye focuses too strongly, so it needs a diverging (concave) lens that moves the image back onto the retina.
Myopia: concave, negative P. Hypermetropia: convex, positive P. Memory clue : "Myopia = Minus": M for Myopia, M for Minus (concave) lens.
Spot the difference
| Point | Myopia | Hypermetropia |
|---|---|---|
| Blurred objects | distant objects | near objects |
| Corrected by | concave lens (negative P) | convex lens (positive P) |
Practice questions
- 1Which defect has a far point nearer than infinity, and which lens corrects it?
- 2A person reads a newspaper clearly only at 60 cm but sees far objects well. Name the defect and the lens needed.
- 3A myopic person has a far point of 20 cm. Find the power of the corrective lens.
- 4A myopic person has a far point of 1.25 m. Find the power of the lens.
- 5A student wears spectacles of -1.5 D. Name the defect and find the focal length.
- 6A hypermetropic person’s near point is 60 cm. Find the power of the lens to read at 25 cm.
- 7Why does an elderly person need reading glasses even if earlier vision was normal?
- 8Can cataract be cured with spectacles? Give a reason.
Show answers (try them yourself first)
- 1Myopia; a concave lens.
- 2Hypermetropia; a convex lens.
- 3f = -0.2 m, P = 1/(-0.2) = -5 D.
- 4f = -1.25 m, P = 1/(-1.25) = -0.8 D.
- 5Myopia (negative power); f = 1/(-1.5) = -0.667 m, about -67 cm.
- 61/f = 1/25 - 1/60 = 7/300, so f = 42.9 cm and P = +2.33 D (about +2.3 D).
- 7The ciliary muscles weaken and the lens loses flexibility, so the near point moves away (presbyopia).
- 8No. The lens itself is cloudy; it is treated by surgery.
Refraction through a prism & dispersion of light
Sunlight through a cut-glass crystal hanging at a window throws small rainbows on the wall. The glass is splitting white light into its colours.
A glass prism has two triangular bases and three rectangular side faces that lean towards each other. A ray bends towards the normal on entering and away from it on leaving, so overall it bends towards the base. Angles: i (incidence), r (refraction), e (emergence), A (angle of the prism between the two refracting faces) and D (deviation between the incident and emergent directions). Dispersion is the splitting of white light into VIBGYOR, a band called the spectrum. Red bends the least, violet the most. Newton’s second, inverted prism joined the colours back into white light, so the prism does not create colours.
Equation / formula : VIBGYOR · red bends least · violet bends most
In the figure : A narrow beam of sunlight is used so that the colour bands do not overlap.
Rule 1 : Prism compared with a glass slab — In a glass slab the two faces are parallel, so the emergent ray is parallel to the incident ray and only shifted sideways. In a prism the faces are inclined, the two bends add up, and the ray is deviated towards the base. The angle between the two refracting faces is the angle of the prism, A.
- Easy : Slab: emergent ray parallel to the incident ray. Prism: not parallel.
- Medium : A prism with angle 60 degrees means the two refracting faces make 60 degrees with each other; it is not the angle of deviation.
- For exams : Label: i = incident ray with the normal at the first face; r = refracted ray with that normal; e = emergent ray with the normal at the second face; D = between the incident and emergent directions.
Rule 2 : Dispersion and Newton’s experiment — Different colours travel at different speeds in glass, so each has its own refractive index and bends by its own angle. This separates white light into a spectrum. A second identical prism placed upside down joins the colours back into white light. A single colour passed through another prism is only bent, not split.
- Easy : From least bent to most bent: red, orange, yellow, green, blue, indigo, violet.
- Medium : Green light from a prism is sent through a second prism: it stays green (only deviated), because one colour cannot split further.
- For exams : Suppose red deviates by 37 degrees and violet by 41 degrees. The spectrum spreads over 41 - 37 = 4 degrees, with violet nearer the base.
Newton was the first to get the spectrum of sunlight with a glass prism. Never look straight at the Sun.
Saying the prism adds colours to light. It only separates the colours already present in white light.
Prism bends towards the base; red least, violet most. Memory clue : "VIBGYOR": V is Very bent, R is Rarely bent. Violet bends most, red least.
Spot the difference
| Point | Glass slab | Prism |
|---|---|---|
| Faces | parallel | inclined to each other |
| Emergent ray | parallel to the incident ray | deviated towards the base |
Practice questions
- 1What is the angle between the two refracting faces of a prism called?
- 2Why is the emergent ray not parallel to the incident ray in a prism?
- 3Which colour bends the most and which the least?
- 4A second identical prism is placed inverted next to the first. What emerges?
- 5Green light from a prism is passed through another prism. What happens?
- 6Red deviates by 36 degrees and violet by 40 degrees. Find the angle of spread.
- 7Who first obtained the spectrum of sunlight with a glass prism?
- 8Why is a narrow beam of sunlight used in the prism experiment?
Show answers (try them yourself first)
- 1The angle of the prism, A.
- 2Its two refracting faces are inclined, so the two bends add up instead of cancelling.
- 3Violet bends the most; red bends the least.
- 4White light again, because the colours are recombined.
- 5It stays green and is only deviated; a single colour cannot split further.
- 640 - 36 = 4 degrees.
- 7Isaac Newton.
- 8So that the colour bands do not overlap and a clear spectrum forms.
Rainbow & atmospheric refraction
After a monsoon shower the Sun peeps out and a rainbow arches over the hills. At night the stars seem to wink while the Moon shines steadily.
A rainbow is a natural spectrum seen after rain, in the direction opposite to the Sun. Each raindrop acts like a small prism: sunlight is refracted and dispersed on entering, internally reflected, and refracted again on leaving. Atmospheric refraction is refraction by air whose refractive index changes gradually; hot air is lighter, with a slightly lower index. It makes stars twinkle, makes a star near the horizon look slightly higher, and makes the Sun visible about 2 minutes before actual sunrise and after actual sunset. Planets do not twinkle because they are extended sources.
Equation / formula : Day gets longer by about 4 minutes (2 + 2)
In the figure : Every drop sends different colours at different angles, so we see a band of colours.
Rule 1 : How a rainbow is formed — Sunlight needs water droplets in the air. Each drop refracts and disperses the light, reflects it from its back, and refracts it again as it leaves. The light returns to the side it came from, so the observer must have the Sun behind them and look at the opposite side.
- Easy : Stand with the Sun behind you and look at the rain in front: the rainbow appears there.
- Medium : A garden sprinkler on a sunny day, seen with the Sun behind you, can also show a small rainbow because the spray gives droplets.
- For exams : Name the three steps inside a raindrop: (1) refraction with dispersion, (2) internal reflection, (3) refraction on leaving.
Rule 2 : Effects of atmospheric refraction — Starlight bends towards the normal as it enters denser air layers, so a star seems slightly higher than it is. The air is always moving, so the apparent position and brightness keep changing: the star twinkles. A planet is a cluster of many point sources, so the changes cancel and it does not twinkle. The same bending lets us see the Sun about 2 minutes early and 2 minutes late.
- Easy : Actual sunrise at 6:30 am: the Sun is seen at about 6:28 am.
- Medium : Actual sunset at 6:40 pm: the Sun is seen until about 6:42 pm, so the day is longer by 2 + 2 = 4 minutes.
- For exams : Why do planets not twinkle? A planet is a collection of many point-like sources; if some dim, others brighten, so the total light stays steady.
Without an atmosphere there would be no twinkling, and sunrise would be about 2 minutes later.
Saying stars twinkle because they give out light in flashes. Twinkling is caused by refraction in the moving atmosphere.
Rainbow: dispersion in drops, Sun behind you. Twinkling: atmospheric refraction. Memory clue : "Sun behind, rain in front": that is how you see a rainbow.
Spot the difference
| Point | Star | Planet |
|---|---|---|
| Appears as | a point source | an extended source |
| Twinkles? | yes | no |
Practice questions
- 1Where must the Sun be for you to see a rainbow?
- 2Name the three steps that happen to sunlight inside a raindrop.
- 3Why do stars twinkle but planets do not?
- 4By about how many minutes does atmospheric refraction lengthen the day?
- 5The actual sunset is at 7:05 pm. Until about what time is the Sun seen?
- 6Why does a star near the horizon look higher than its true position?
- 7Why do objects seen above a hot road seem to shimmer?
- 8Would stars twinkle when seen from the Moon? Give a reason.
Show answers (try them yourself first)
- 1Behind you, so the rainbow is seen in the opposite direction.
- 2Refraction with dispersion, internal reflection, refraction on leaving.
- 3Stars are point sources, so changes show; a planet is an extended source and the changes average out.
- 4About 4 minutes.
- 5Until about 7:07 pm.
- 6The refractive index rises towards the ground, so starlight keeps bending towards the normal and the apparent position is raised.
- 7Hot air is lighter with a lower refractive index and keeps moving, so light bends by changing amounts.
- 8No. The Moon has no atmosphere, so there is no atmospheric refraction.
Scattering of light, Tyndall effect & blue sky
A sunbeam through a small hole in a dusty room shows as a bright streak, and a torch beam is visible in fog. Tiny particles throw some of the light sideways into our eyes.
Scattering is the spreading of light in all directions by tiny particles. The Tyndall effect is the scattering by colloidal particles that makes a light beam visible (smoky room, mist in a forest); in a true solution the beam is not visible. The colour of scattered light depends on particle size: very fine particles scatter mainly blue, larger ones scatter longer wavelengths, and big enough ones give white. The sky is blue because air molecules are smaller than the wavelength of light and scatter the short wavelengths more; red has about 1.8 times the wavelength of blue. With no atmosphere the sky would be dark. Red is scattered least, so it is used for danger signals, and the Sun looks red at sunrise and sunset.
Equation / formula : Shorter wavelength scatters more: blue is scattered more than red
In the figure : Short blue waves scatter easily; long red waves travel straight on.
Rule 1 : Tyndall effect and particle size — A beam is seen from the side only when particles scatter it. Colloids (smoke, dilute milk, mist) do; a true solution such as salt water has particles too small to scatter noticeably. Very fine particles give bluish scattered light; coarser particles give whitish light.
- Easy : A torch in water with a few drops of milk shows its beam; in clear salt water it does not.
- Medium : Sunlight through forest mist shows bright shafts because tiny water droplets scatter the light.
- For exams : Why do clouds look white? Their droplets are large, so they scatter all colours nearly equally, and the mixture looks white.
Rule 2 : Colour of the sky, the Sun and danger signals — Blue has a shorter wavelength than red, so air scatters blue more and the sky looks blue. At noon the sunlight takes a short path through air and looks white. At sunrise and sunset the path is long, most blue is scattered away and mainly red reaches us. Red is scattered least by fog and smoke, so it is seen from far and is used for danger signals. High above the air the sky is dark.
- Easy : Blue is 450 nm and red 720 nm. Red is 720/450 = 1.6 times longer, so blue is scattered more.
- Medium : At noon the Sun looks white because its light crosses a short path; at sunset the path is long, blue is scattered out and the Sun looks reddish.
- For exams : An astronaut high above the air sees a dark sky because there is very little air to scatter sunlight.
Violet is scattered even more than blue, but the sky looks blue because the Sun gives less violet and our eyes are less sensitive to it.
Saying the sky is blue because it reflects the sea. The colour comes from the scattering of sunlight by air molecules.
Short waves scatter more: blue sky. Red scatters least: signals and sunset. Memory clue : "Blue Bounces, Red Runs on": blue scatters away, red goes straight through.
Spot the difference
| Point | Noon Sun | Sunrise or sunset Sun |
|---|---|---|
| Path in air | short | long |
| Sun looks | white | reddish |
Practice questions
- 1What is the Tyndall effect? Give one example.
- 2Why is the path of a light beam not visible in a salt solution?
- 3Why does the sky look blue?
- 4Why are danger signals red?
- 5Why is the sky dark for an astronaut high above the air?
- 6Why does the Sun look red at sunset?
- 7Red light has wavelength 700 nm and blue light 450 nm. Which scatters more, and how many times longer is the red wavelength?
- 8Why do clouds look white?
Show answers (try them yourself first)
- 1Scattering of light by colloidal particles that makes the beam visible, such as a sunbeam in a smoky room.
- 2Its particles are too small to scatter light noticeably.
- 3Air molecules scatter the short blue wavelengths more than red.
- 4Red is scattered the least by fog and smoke, so it can be seen from far away.
- 5There is very little air, so scattering is negligible.
- 6The light travels a long path in air; most blue is scattered away and mainly red reaches us.
- 7Blue scatters more; 700/450 = about 1.6 times longer.
- 8Their drops are large and scatter all colours nearly equally, giving white.