The Human Eye and the Colourful World | CBSE Class 10 Science Notes

This note covers the human eye, accommodation, defects of vision and their correction, corrective-lens calculations, refraction through a prism, dispersion of white light, rainbow formation, atmospheric refraction, twinkling of stars, advance sunrise, delayed sunset, scattering of light and the blue colour of the sky.

How does the human eye form an image?

The human eye uses light to make objects and colours visible. It works somewhat like a camera: its lens system forms an image on the retina, a delicate, light-sensitive membrane at the back of the eye.

Which structures control and focus incoming light?

The eyeball is approximately spherical, with a diameter of about 2.3 centimetres, written as cm. Light enters through the cornea, a thin membrane forming the transparent bulge at the front of the eyeball.

Refraction is the change in direction of light when it passes obliquely between different media. Most refraction of light entering the eye occurs at the outer surface of the cornea. The crystalline lens provides the finer adjustment needed to focus objects at different distances.

How does the retinal image lead to vision?

The eye lens forms a real, inverted image on the retina: the light rays actually meet there, and the image is upside down. The illuminated retinal cells become active and generate electrical signals.

The optic nerves carry the signals to the brain. The brain interprets and processes the information so that objects are perceived as they are. Image formation on the retina and interpretation by the brain are therefore successive parts of seeing.

The cutaway drawing shows the cornea, pupil and iris at the front, the crystalline lens behind them, ciliary muscles around the lens, the retina lining the back and the optic nerve leaving the eyeball.

See Fig. 10.1 in your NCERT textbook

How does accommodation make near and distant objects clear?

Accommodation is the ability of the eye lens to adjust its focal length. The focal length of a lens is the distance between its optical centre, its central point, and its principal focus.

The principal axis joins the centres of the spheres of which the curved lens surfaces form parts. Rays initially parallel to this axis meet at the principal focus or appear to spread from it after passing through the lens.

The eye lens contains fibrous, jelly-like material. The ciliary muscles, which alter the shape of the lens, can modify its curvature to some extent. Changing curvature changes focal length and allows the eye to focus at different distances.

How do near and distant viewing differ?

The eye cannot decrease its focal length below a certain minimum. Holding a printed page very close may make its image blurred or cause strain. Clear near vision therefore has a limit even when the eye has normal vision.

What are the near point and far point?

The near point, or least distance of distinct vision, is the minimum distance at which objects can be seen most distinctly without strain. For a young adult with normal vision, it is about 25 cm.

The far point is the farthest point up to which objects are seen clearly. For a normal eye it is infinity, meaning an effectively unlimited distance. A normal eye can see clearly from about 25 cm to infinity.

Note: Increasing object distance does not require the retinal image to move backwards inside the eye. The lens adjusts its focal length to keep the image on the retina; the lens-to-retina image distance remains the same.

What causes myopia, and how is it corrected?

Myopia, or near-sightedness, allows a person to see nearby objects clearly while distant objects are indistinct. The far point lies nearer than infinity. Such a person may see clearly up to a distance of a few metres.

Where does the image form?

For a distant object, the myopic eye forms the image in front of the retina. The image is therefore not focused on the light-sensitive surface where it is needed for clear vision.

The defect may arise from excessive curvature of the eye lens or elongation of the eyeball. These are alternative possible causes; both need not be present together.

Why is a concave lens suitable?

A concave lens is a lens thinner in the middle than at its edges. It diverges light, meaning that it spreads the rays apart. A concave lens of suitable power corrects myopia by allowing the eye to focus the image back on the retina.

1. Light from a distant object reaches the corrective concave lens.
2. The concave lens diverges the rays before they enter the eye.
3. The eye lens refracts these rays towards the back of the eye.
4. With suitable correction, the rays form the image on the retina.

A student who has difficulty reading a blackboard from the last row could have myopia. Likewise, a myopic person unable to see objects beyond 1.2 metres distinctly requires a concave corrective lens. The symptom is difficulty with distant vision.

Three ray drawings show the far point of a myopic eye, distant rays focusing before the retina, and a concave lens placed before the eye so that the final rays meet on the retina.

See Fig. 10.2 in your NCERT textbook

What causes hypermetropia, and how is it corrected?

Hypermetropia, or far-sightedness, allows a person to see distant objects clearly but makes nearby objects indistinct. The near point is farther away than the normal near point of about 25 cm, so reading material must be held much farther away.

Why is nearby writing blurred?

Light from a nearby object is focused behind the retina. Hypermetropia arises either because the focal length of the eye lens is too long or because the eyeball has become too small.

A convex lens, thicker in the middle than at the edges, converges light, bringing rays together. A convex lens of appropriate power supplies the additional focusing needed to form the image on the retina.

How can the two defects be distinguished?

The label N marks the hypermetropic eye’s near point; N′ marks the normal near point. The drawings show a nearby object focusing behind the retina and a convex lens bringing the final focus onto it.

See Fig. 10.3 in your NCERT textbook

For either defect, naming the lens is only part of the explanation. Link the blurred object’s distance to the image position, and then explain how the corrective lens brings the final image onto the retina.

How do presbyopia and cataract affect vision?

The power of accommodation usually decreases with ageing. For most people, the near point gradually recedes. Seeing nearby objects distinctly and comfortably becomes difficult without corrective spectacles. This defect is called presbyopia.

Presbyopia results from gradual weakening of the ciliary muscles and diminishing flexibility of the eye lens. These changes reduce the eye’s ability to adjust its lens for nearby objects.

When are bifocal lenses useful?

Sometimes a person suffers from both myopia and hypermetropia. Such people often require bifocal lenses, lenses having two portions for different viewing distances. A common type combines a concave upper portion for distant vision with a convex lower portion for near vision.

Refractive defects can also be corrected with contact lenses or surgical interventions. The correction must address the particular focusing difficulty; the presence of presbyopia does not mean that every person has the same combination of defects.

What is cataract?

Sometimes the crystalline lens in old age becomes milky and cloudy. This condition, called cataract, causes partial or complete loss of vision. It is possible to restore vision through cataract surgery.

Clouding of the lens differs from the gradual loss of accommodation. Presbyopia concerns declining adjustment of focal length; cataract concerns the lens becoming cloudy. Keeping these descriptions separate prevents the two conditions from being confused.

Corneal transplantation means transplanting donated corneal tissue to help a person with corneal blindness, blindness involving the cornea. An eye bank collects, evaluates and distributes donated eyes. Eyes unsuitable for transplantation can support research and medical education, and donor and recipient identities remain confidential.

How are corrective-lens calculations solved?

The power of a lens measures its ability to converge or diverge light and equals the reciprocal of its focal length. Let P represent power and f represent focal length. Write f in metres, abbreviated m, when calculating power.

$P = \frac{1}{f}$; therefore, $f = \frac{1}{P}$. The SI, or International System of Units, unit of lens power is the dioptre, abbreviated D. One dioptre is the power of a lens with focal length one metre: $1\,\mathrm{D} = 1\,\mathrm{m}^{-1}$.

For the lens formula, let u be object distance and v be image distance, both measured from the lens’s optical centre. Then $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$. A virtual image is an image formed where rays appear to meet when extended backwards.

Use the sign convention in which distances against the incident light’s direction are negative. An object and its corrective virtual image in front of the lens have negative distances. Convex lenses have positive focal length and power; concave lenses have negative focal length and power.

Note: For these corrective-lens calculations, treat the lens as close to the eye and neglect the small separation between them. Use consistent distance units in the lens formula, and convert centimetres into metres before finding power.

What focal lengths correspond to the prescribed powers?

Solved exercise 1. A person needs a lens of power −5.5 D for distant vision and +1.5 D for near vision. Find both focal lengths using $f = \frac{1}{P}$.

Answer: For distant vision, $f = \frac{1}{-5.5}\,\mathrm{m} \approx -0.182\,\mathrm{m}$. For near vision, $f = \frac{1}{+1.5}\,\mathrm{m} \approx +0.667\,\mathrm{m}$. The symbol $\approx$ means approximately equal to. The negative result identifies a concave lens; the positive result identifies a convex lens.

What corrects a myopic far point of 80 cm?

Solved exercise 2. The far point is 80 cm in front of the eye. To see a distant object, the corrective lens must produce its virtual image at that far point.

Answer: Here $u$ tends to negative infinity, so $1/u$ tends to zero; $v = -80\,\mathrm{cm} = -0.80\,\mathrm{m}$. Thus $\frac{1}{f} = \frac{1}{-0.80\,\mathrm{m}} - 0 = -1.25\,\mathrm{m}^{-1}$. Hence $f = -0.80\,\mathrm{m}$ and $P = -1.25\,\mathrm{D}$. The required lens is concave.

What corrects a hypermetropic near point of 1 m?

Solved exercise 3. The person’s near point is 1 m, and the normal near point is 25 cm. The lens must let an object at 25 cm appear at the person’s near point.

Answer: $u = -0.25\,\mathrm{m}$ and $v = -1\,\mathrm{m}$. Therefore $\frac{1}{f} = \frac{1}{-1\,\mathrm{m}} - \frac{1}{-0.25\,\mathrm{m}} = (-1 + 4)\,\mathrm{m}^{-1} = 3\,\mathrm{m}^{-1}$. Thus $f = +\frac{1}{3}\,\mathrm{m}$ and $P = +3\,\mathrm{D}$. A convex lens provides the required convergence.

How does a triangular glass prism refract light?

A triangular glass prism has two triangular bases and three rectangular lateral surfaces. Its refracting faces are inclined to one another. The angle between the two refracting lateral faces is the angle of the prism.

An incident ray approaches a surface, a refracted ray travels after bending at that surface, and an emergent ray leaves the prism. A normal is a line perpendicular to a surface at the point where the ray meets it.

What happens at the two faces?

At the first face, light passes from air into glass and bends towards the normal. At the second face, it passes from glass into air and bends away from the normal.

The prism’s shape makes the emergent ray inclined to the incident ray’s original direction. The angle between those directions is the angle of deviation. A rectangular glass slab instead gives an emergent ray parallel to the incident ray, though slightly displaced sideways.

How can the ray path be traced?

1. Fix white paper on a drawing board. Place the prism on a triangular base and trace its outline.
2. Draw an incident line inclined to one refracting face and fix two pins on that line.
3. View the images of these pins through the other refracting face. Place two further pins in line with the images.
4. Remove the prism and pins. Extend the marked lines to the prism outline and join their points of entry and exit.
5. Draw normals at both points. Mark the angles of incidence, refraction, emergence and deviation.

ABC labels the triangular outline; E and F are the entry and exit points. PE is the incident ray, EF the internal refracted ray and FS the emergent ray. Dashed normals and extended ray directions show the angles.

See Fig. 10.4 in your NCERT textbook

The symbol ∠ means angle. In this diagram, ∠i is incidence, measured between the incident ray and first normal; ∠r is refraction between the internal ray and first normal; ∠e is emergence between the outgoing ray and second normal. ∠A is the prism angle and ∠D is deviation.

The letter D here labels an angle; it does not represent the dioptre unit used in lens calculations. Identify a symbol from its immediate context before using it.

Why does a prism separate white light into colours?

Dispersion is the splitting of light into its component colours. The spectrum is the band of coloured components of a light beam. Dispersion names the process; spectrum names the band produced.

How can the spectrum be observed?

1. Make a small hole or narrow slit in a thick piece of cardboard.
2. Allow sunlight through the opening to obtain a narrow beam of white light.
3. Direct the beam onto one face of a glass prism.
4. Turn the prism slowly until the emerging light falls on a nearby screen, producing a band of colours.

The colours are violet, indigo, blue, green, yellow, orange and red. The acronym VIBGYOR records their initial letters in this order. You might not be able to see all the colours separately in the observed band.

Different colours bend through different angles relative to the incident ray. Red bends the least and violet the most. Their rays therefore emerge along different paths, making the colours distinct in the spectrum.

What did Newton’s prism experiments establish?

Isaac Newton was the first to obtain the spectrum of sunlight using a glass prism. He tried to split its colours further with another similar prism but obtained no additional colours.

He then placed a second identical prism inverted relative to the first. All the spectrum’s colours passed through it and emerged as white light. This observation led him to the idea that sunlight consists of seven colours.

Light producing a spectrum similar to sunlight’s is often referred to as white light. The first prism separates its components; the inverted second prism brings them together again.

One drawing shows white light entering a prism and emerging as a coloured fan, with red deviating least. The other shows two oppositely oriented prisms producing a white beam on a screen after the colours pass through both.

See Figs. 10.5 and 10.6 in your NCERT textbook

How do water droplets produce a rainbow?

A rainbow is a natural spectrum appearing in the sky after a rain shower. Tiny water droplets in the atmosphere disperse sunlight. The droplets act like small prisms, but reflection inside each droplet also contributes to the path of light.

What is the sequence inside a droplet?

1. Sunlight enters the water droplet and is refracted.
2. The incoming light is dispersed into its component colours.
3. The light undergoes internal reflection, meaning reflection back inside the droplet.
4. Light is refracted again as it leaves the droplet, and different colours reach the observer’s eye.

A rainbow is always formed in the direction opposite to the Sun. On a sunny day, a rainbow can also be seen through a waterfall or water fountain when the Sun is behind the observer.

Three processes belong in the explanation: refraction changes the ray’s direction at entry and exit, dispersion separates the colours, and internal reflection redirects the light within the drop. Naming dispersion alone leaves out part of the light’s journey.

Photograph: Rainbow in the sky (NCERT Class 10 Figure 10.7). The photograph shows a rainbow above a rocky landscape.

The ray drawing shows sunlight entering a raindrop, reflecting at its inside surface and emerging along separated coloured paths.

See Fig. 10.8 in your NCERT textbook

How does atmospheric refraction change apparent positions?

Atmospheric refraction is refraction of light by the Earth’s atmosphere. The refractive index of a medium is the ratio of light’s speed in vacuum to its speed in that medium. A vacuum is a space without a material medium.

Why do objects waver through hot air?

Air immediately above a fire is hotter than the air farther above it. Hotter air is lighter, or less dense, and has a refractive index slightly less than cooler air. Density means the amount of mass in a given volume.

The physical conditions of this refracting air are not stationary. The apparent position of an object seen through it therefore fluctuates. The random wavering or flickering above a fire or radiator is atmospheric refraction on a small, local scale.

Why does a star appear higher and twinkle?

Starlight undergoes continuous refraction as it crosses an atmosphere whose refractive index changes gradually. Near the horizon, the apparent boundary between sky and ground, the star appears slightly higher than its actual position because the atmosphere bends its light towards the normal.

1. Very distant stars approximate point-sized sources of light.
2. Changing atmospheric conditions make the path of incoming starlight vary slightly.
3. The apparent position fluctuates, and the amount of starlight entering the eye changes.
4. The star appears brighter at some moments and fainter at others. This varying brightness is twinkling.

Planets are much closer and appear as extended sources, sources with an appreciable apparent extent. A planet can be considered a collection of many point-sized sources. Their total variations in light reaching the eye average out to zero, nullifying the twinkling effect.

The drawing distinguishes the actual star from a higher apparent star position. A bent ray path reaches the observer, while a dashed extension indicates the apparent direction. An arrow shows refractive index increasing downwards.

See Fig. 10.9 in your NCERT textbook

Why are sunrise and sunset seen at shifted times?

The Sun is visible about 2 minutes before actual sunrise and about 2 minutes after actual sunset because of atmospheric refraction. Actual sunrise means the Sun’s actual crossing of the horizon.

The difference between actual and apparent sunset is about 2 minutes. Atmospheric refraction also causes the apparent flattening of the Sun’s disc at sunrise and sunset. This is an effect on apparent position and shape.

The drawing labels Earth, atmosphere, observer and horizon. The actual Sun is shown below the horizon and its apparent position above it, with a curved light path through the atmosphere.

See Fig. 10.10 in your NCERT textbook

What is scattering, and when is the Tyndall effect visible?

Scattering of light occurs when light is redirected by particles in its path. The atmosphere is a heterogeneous mixture, a mixture that is not uniform throughout, containing smoke, tiny water droplets, suspended dust particles and air molecules.

A beam striking fine particles can become visible because diffusely reflected light reaches the eye from the particles. The visibility of a light path depends on the particles through which it passes.

How do true and colloidal solutions differ?

A true solution is a uniform mixture with very small dissolved particles. Its light-beam path is not visible. A colloidal solution contains relatively larger dispersed particles that scatter light, making the beam’s path visible.

The scattering of light by colloidal particles gives rise to the Tyndall effect. A fine beam of sunlight entering a smoke-filled room through a small hole shows this effect because the particles scatter light towards the observer.

Sunlight passing through the canopy of a dense forest can also show the Tyndall effect. In this case, tiny water droplets in the mist scatter the sunlight.

How does particle size affect scattered colour?

Wavelength is the distance between successive corresponding points of a wave. Colours of visible light have different wavelengths, and particle size affects which wavelengths are scattered prominently.

Keep the qualifications in these statements: very fine particles scatter mainly blue, while sufficiently large particles may produce a white appearance. Scattering does not imply that every visible beam must be blue.

Why is the clear sky blue, and why are danger signals red?

Air molecules and other fine atmospheric particles are smaller than the wavelength of visible light. They scatter shorter wavelengths at the blue end more effectively than longer wavelengths at the red end.

How does sunlight produce a blue sky?

Red light has a wavelength about 1.8 times that of blue light. When sunlight crosses the atmosphere, fine particles scatter blue light more strongly than red light. This scattered blue light enters the eyes and gives the clear sky its blue appearance.

The explanation requires both selective scattering and observation: the particles redirect blue light strongly, and that scattered light reaches the observer. It does not require the atmosphere to act like a prism separating sunlight into a visible band.

Why can the sky look dark?

If Earth had no atmosphere, atmospheric scattering would not occur and the sky would look dark. The sky appears dark to passengers at very high altitudes because scattering is not prominent at such heights.

The same reasoning explains a dark sky for an astronaut where there is no atmosphere to scatter sunlight towards the observer. Absence of blue scattered light is the relevant point, rather than absence of sunlight itself.

What makes red suitable for danger signals?

Red is least scattered by fog or smoke, so a red danger signal can be seen in the same colour at a distance. The application depends on the difference in scattering of different colours.

Separate the three main explanations: prisms produce a spectrum through dispersion; changing atmospheric refraction produces twinkling; scattering produces the blue sky and explains the use of red danger signals.

Glossary

• Retina — The delicate, light-sensitive membrane on which the eye lens forms an inverted real image.
• Accommodation — The ability of the eye lens to adjust its focal length for clear vision at different distances.
• Near point — The minimum distance at which an eye sees objects most distinctly without strain.
• Far point — The farthest point up to which an eye can see objects clearly.
• Myopia — Near-sightedness in which distant objects are indistinct because their images form before the retina.
• Hypermetropia — Far-sightedness in which nearby objects are indistinct because their images form behind the retina.
• Presbyopia — Difficulty with comfortable near vision as accommodation usually decreases with ageing.
• Lens power — The reciprocal of focal length, expressing the degree of convergence or divergence produced by a lens.
• Dioptre — The unit of lens power; one dioptre corresponds to a focal length of one metre.
• Dispersion — The splitting of light into its component colours, as in a glass prism.
• Spectrum — The band of coloured components produced when a light beam is dispersed.
• Atmospheric refraction — Refraction of light by Earth’s atmosphere, which can change the apparent positions of distant objects.
• Scattering — Redirection of light by particles, allowing light from a beam to reach an observer.
• Tyndall effect — The phenomenon caused by colloidal particles scattering light and making its path visible.

Common errors and misconceptions

• Misconception: The eye lens produces all the refraction in the eye. Correct: Most occurs at the cornea’s outer surface; the crystalline lens supplies finer focusing adjustments.
• Misconception: The pupil changes lens curvature for near vision. Correct: Ciliary muscles alter lens curvature; the iris controls pupil size and hence incoming light.
• Misconception: Myopia needs a convex lens because distant objects are blurred. Correct: Myopia forms distant images before the retina and requires a suitable concave lens.
• Misconception: Every ageing person needs the same bifocal spectacles. Correct: Accommodation usually decreases with ageing; people with both myopia and hypermetropia often require bifocals.
• Misconception: The lens-power formula can use centimetres directly to give dioptres. Correct: In P = 1/f, focal length must be expressed in metres for power in dioptres.
• Misconception: Red light deviates most in a prism. Correct: Red deviates least and violet most, so different colours emerge along different paths.
• Misconception: A rainbow requires dispersion alone. Correct: Sunlight also undergoes refraction at entry and exit and internal reflection within water droplets.
• Misconception: Twinkling and the blue sky have the same cause. Correct: Twinkling involves changing atmospheric refraction; the blue sky results from stronger scattering of blue light.

Exam-style questions with model answers

Q1. Define accommodation and state what happens to the eye lens and its focal length when viewing a nearby object. [2 marks]

1. Accommodation is the ability of the eye lens to adjust its focal length to focus objects at different distances.
2. For a nearby object, ciliary muscles contract, increasing lens curvature and thickness and decreasing its focal length.

Q2. A student sees nearby objects clearly but cannot read the blackboard from the last row. Identify the likely defect, give two possible causes and explain its correction. [3 marks]

1. The likely defect is myopia, or near-sightedness. The student’s distant vision is indistinct, while nearby objects remain clear.
2. It may result from excessive curvature of the eye lens or elongation of the eyeball. The distant object’s image forms in front of the retina.
3. A concave lens of suitable power diverges incoming light so that the eye forms the final image on the retina.

Q3. A person requires −5.5 D for distant vision and +1.5 D for near vision. Using f = 1/P, where P is power in dioptres and f is focal length in metres, calculate both focal lengths and name both lens types. [4 marks]

1. For distant vision, the supplied power is −5.5 D. Substitution gives f = 1/(−5.5) m ≈ −0.182 m.
2. The negative focal length identifies the distant-vision corrective lens as concave, which diverges light.
3. For near vision, the supplied power is +1.5 D. Thus f = 1/(+1.5) m ≈ +0.667 m.
4. The positive focal length identifies the near-vision corrective lens as convex, which converges light.

Q4. A hypermetropic eye has its near point at 1 m. Find the lens power needed to read at the normal near point of 25 cm. Neglect the lens-to-eye distance. Use 1/f = 1/v − 1/u and P = 1/f, with distances in metres and distances in front of the lens negative; u is object distance, v image distance, f focal length and P power in dioptres. [4 marks]

1. The lens must form a virtual image at the person’s near point. Therefore u = −0.25 m and v = −1 m.
2. Substituting the signed distances gives 1/f = 1/(−1) − 1/(−0.25) = −1 + 4 = 3 m⁻¹.
3. Hence f = +1/3 m and the required lens power is P = +3 D.
4. The positive power indicates a convex lens. Its additional convergence allows the eye to focus the nearby object on the retina.

Q5. Explain how a glass prism produces a spectrum from sunlight and how Newton recombined the colours into white light. Give the colour sequence and the relative deviation of red and violet. [5 marks]

1. A narrow beam of sunlight enters a glass prism and splits into component colours. This splitting is dispersion, and the coloured band obtained is a spectrum.
2. The colour sequence is violet, indigo, blue, green, yellow, orange and red. VIBGYOR is the acronym used to remember this sequence.
3. Different colours bend through different angles relative to the incident ray. Red bends least and violet most, producing separate emerging paths.
4. Newton first obtained sunlight’s spectrum with a prism. He tried using another similar prism to split the colours further but obtained no additional colours.
5. He placed an identical second prism inverted relative to the first. The separated colours passed through it and emerged as white light, supporting the idea that sunlight contains seven colours.

Q6. Explain why stars twinkle but planets do not show the same twinkling effect. [3 marks]

1. Stars are very distant and approximate point-sized sources. Their light is continuously refracted through atmospheric layers with gradually changing refractive index.
2. Atmospheric conditions keep changing, so the ray paths, apparent positions and amounts of starlight entering the eye vary slightly. Stars therefore appear alternately brighter and fainter.
3. Planets are closer and act as extended sources. Variations from their many point-sized parts average out to zero, nullifying the twinkling effect.

Q7. Explain the blue colour of a clear sky, the dark sky at very high altitudes and the use of red danger signals. [3 marks]

1. Fine atmospheric particles scatter shorter blue wavelengths more strongly than longer red wavelengths. Scattered blue light enters our eyes, making the clear sky appear blue.
2. At very high altitudes, scattering is not prominent, so the sky appears dark. Without an atmosphere, there would be no atmospheric scattering.
3. Red light is least scattered by fog or smoke. A red danger signal can therefore be seen in the same colour at a distance.

Q8. Describe rainbow formation, including the role of droplets, the sequence of optical processes and the rainbow’s position relative to the Sun. [5 marks]

1. A rainbow is a natural spectrum seen after a rain shower. Tiny water droplets in the atmosphere act like small prisms on incident sunlight.
2. Sunlight is refracted when it enters a droplet. The light is also dispersed into its component colours as part of this entry process.
3. The light then undergoes internal reflection, being reflected back within the water droplet before it reaches the surface from which it emerges.
4. On leaving the droplet, the light is refracted again. Dispersion and internal reflection allow different colours to reach the observer’s eye.
5. A rainbow is always formed opposite the Sun. It can also be seen through a waterfall or fountain on a sunny day with the Sun behind the observer.

Key takeaways

• Most refraction occurs at the cornea; the eye lens adjusts focusing so that a real, inverted image forms on the retina.
• Accommodation changes lens focal length. A young adult’s normal near point is about 25 cm, while the far point is infinity.
• Myopia forms distant images before the retina and needs concave correction; hypermetropia forms nearby images behind it and needs convex correction.
• Accommodation usually decreases with ageing. Presbyopia involves weakening ciliary muscles and diminishing lens flexibility, while cataract involves a cloudy lens.
• Lens power equals reciprocal focal length in metres. Its sign distinguishes a positive convex lens from a negative concave lens.
• A prism disperses white light because different colours deviate differently; red deviates least and violet most.
• Rainbow formation includes refraction, dispersion and internal reflection within droplets, with the rainbow appearing opposite the Sun.
• Changing atmospheric refraction explains twinkling; stronger scattering of blue light explains the blue sky, while red signals experience least scattering.

Test yourself

Which part of the eye produces most of its refraction?

Most refraction occurs at the outer surface of the cornea; the lens provides finer focusing adjustment.

What happens to the ciliary muscles when viewing a distant object?

They relax, allowing the lens to become thinner and its focal length to increase.

Why is a page held too close difficult to read clearly?

The eye cannot reduce its focal length below a certain minimum, limiting its ability to focus very nearby objects.

Which lens corrects a myopic eye unable to see beyond 1.2 m?

A concave lens of suitable power corrects this myopic eye by bringing the final image onto the retina.

Which portions of a common bifocal lens serve distant and near vision?

The upper concave portion facilitates distant vision, while the lower convex portion facilitates near vision.

Which colour bends least and which bends most in a glass prism?

Red light bends least, while violet light bends most relative to the incident ray.

What particles show the Tyndall effect in a dense forest’s mist?

Tiny water droplets in the mist scatter sunlight passing through the forest canopy.

Why is the Sun visible before it actually crosses the horizon?

Atmospheric refraction makes the Sun visible about 2 minutes before actual sunrise by changing its apparent position.