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Human Eye and Colourful World Exercise Solutions | KalviGavani

NCERT solutions for CBSE Class 10 Science Ch 11 — human eye, vision defects, dispersion, atmospheric refraction with full numericals.

Updated 15 June 202622 min read

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These are complete NCERT Solutions for CBSE Class 10 Science Chapter 11 — The Human Eye and the Colourful World. Every intext question and every chapter-end exercise question (Q1–Q13) is answered in detail.

How to study effectively: 1. Attempt each question on your own first. 2. Check your answer against the solution provided. 3. For numerical problems on corrective lenses, follow the Given → Formula → Substitution → Calculation → Answer format exactly as shown. 4. Pay special attention to sign conventions — they are the most common source of errors. 5. Use the Key Concepts section for a quick revision before exams.

Key Concepts (Quick Recap)

Structure of the Human Eye

  • Cornea: Thin, transparent outer covering at the front of the eye. It performs the main refraction of light entering the eye (about 70% of total refraction).
  • Iris: Coloured muscular diaphragm behind the cornea. It controls the size of the pupil to regulate the amount of light entering the eye. In bright light, the iris contracts the pupil; in dim light, it expands the pupil.
  • Pupil: The small opening in the centre of the iris through which light passes into the eye.
  • Eye lens: A crystalline, biconvex lens behind the iris. It provides fine adjustment of focal length. The ciliary muscles change its curvature — this is accommodation.
  • Retina: The light-sensitive screen at the back of the eye. It contains photoreceptor cells: rods (respond to dim light, give black-and-white vision) and cones (respond to bright light, give colour vision). The image is formed on the retina (real, inverted, diminished).
  • Optic nerve: Transmits electrical signals from the retina to the brain, which interprets the image.
  • Blind spot: The point where the optic nerve leaves the eye; no photoreceptors here, so no vision at this point.

Power of Accommodation

  • The ability of the eye lens to adjust its focal length by changing its curvature (through ciliary muscle action) is called the power of accommodation.
  • For near objects: ciliary muscles contract → lens becomes thicker → focal length decreases → image focuses on retina.
  • For far objects: ciliary muscles relax → lens becomes thinner → focal length increases → image focuses on retina.
  • Near point (least distance of distinct vision): 25 cm for a normal young adult eye.
  • Far point: Infinity for a normal eye.

Myopia (Short-sightedness / Near-sightedness)

  • Defect: Can see nearby objects clearly, but distant objects appear blurred.
  • Cause: Eyeball is too long, or the eye lens is too converging (thick). Image of distant objects forms in front of the retina.
  • Far point: Closer than infinity (e.g., 1.2 m, 80 cm, etc.).
  • Correction: A concave (diverging) lens of suitable focal length diverges the incoming rays so that the image shifts back onto the retina.
  • Ray diagram description: A distant object at infinity sends parallel rays. Without correction, these converge in front of the retina. A concave lens placed in front of the eye diverges the rays before they enter the eye. The eye lens then converges them exactly onto the retina.

Hypermetropia (Long-sightedness / Far-sightedness)

  • Defect: Can see distant objects clearly, but nearby objects appear blurred.
  • Cause: Eyeball is too short, or the eye lens is too thin (weak converging power). Image of nearby objects forms behind the retina.
  • Near point: Beyond 25 cm (e.g., 1 m).
  • Correction: A convex (converging) lens of suitable focal length converges the incoming rays more so that the image shifts forward onto the retina.
  • Ray diagram description: An object held at 25 cm sends diverging rays. Without correction, these focus behind the retina. A convex lens placed in front of the eye converges the rays more strongly, so the eye lens can bring them to focus exactly on the retina.

Presbyopia

  • Defect: Gradual loss of accommodation with ageing (typically after 40 years). Both near and distant vision may become unclear.
  • Cause: Ciliary muscles weaken and the eye lens loses flexibility over time.
  • Not the same as hypermetropia — presbyopia affects accommodation (ability to change focus), while hypermetropia is a structural defect of the eyeball.
  • Correction: Bifocal lenses — upper portion is concave (for distance), lower portion is convex (for reading).

Dispersion of Light

  • Dispersion is the splitting of white light into its constituent colours (VIBGYOR) on passing through a prism.
  • VIBGYOR: Violet, Indigo, Blue, Green, Yellow, Orange, Red.
  • Different colours travel at different speeds in glass → different refractive indices → different amounts of bending.
  • Violet deviates the most (shortest wavelength, highest refractive index in glass).
  • Red deviates the least (longest wavelength, lowest refractive index in glass).
  • The angular separation between the deviated red and violet rays is called the angular dispersion.

Atmospheric Refraction

  • The atmosphere has layers of air with varying densities and refractive indices (hot air is less dense, cold air is denser).
  • Light from distant objects (stars, Sun) bends as it passes through these layers.
  • Twinkling of stars: The apparent position of a star keeps shifting slightly because the refractive index of air layers changes continuously due to air currents and temperature variations. The amount of starlight entering the eye flickers, so the star appears to twinkle.
  • Apparent position of stars: Stars appear slightly higher than their actual position because light bends downward (towards denser medium) as it enters the atmosphere.
  • Advance sunrise and delayed sunset: The Sun is visible about 2 minutes before actual sunrise and 2 minutes after actual sunset because atmospheric refraction bends sunlight around the horizon, making the Sun appear higher than its geometric position.

Tyndall Effect

  • The scattering of a beam of light by colloidal particles (particles whose size is comparable to the wavelength of light) is called the Tyndall effect.
  • Examples: a beam of sunlight becoming visible in a dusty room, light passing through fog, blue colour of the sky.
  • The Tyndall effect is observed when the particle size is between 1 nm and 1000 nm (colloidal range).

Why the Sky is Blue

  • Gas molecules in the atmosphere are very small — they scatter shorter wavelengths (blue, violet) much more strongly than longer wavelengths (Rayleigh scattering, intensity proportional to 1/lambda^4).
  • When we look away from the Sun, we see the blue light scattered in all directions by these molecules.

Why Sunsets and Sunrises are Red

  • At sunrise and sunset, sunlight travels a much longer path through the atmosphere (along the horizon) compared to when the Sun is overhead.
  • Most of the blue light is scattered away in this long path. Only the longer wavelengths (red, orange) — which are scattered the least — reach the observer's eye directly.
  • Hence, the Sun appears reddish at sunrise and sunset.

Why Clouds are White

  • Clouds contain water droplets and ice crystals that are much larger than the wavelength of visible light.
  • These large particles scatter all wavelengths equally (Mie scattering), so the scattered light remains white.

Intext Questions

Page 190

Q1. What is meant by the power of accommodation of the eye?
Answer

The power of accommodation is the ability of the eye lens to adjust its focal length by changing its curvature, so that objects at different distances can be focused clearly on the retina.

  • When viewing nearby objects: the ciliary muscles contract, the lens becomes more convex (thicker), its focal length decreases, and the image falls on the retina.
  • When viewing distant objects: the ciliary muscles relax, the lens becomes less convex (thinner), its focal length increases, and the image falls on the retina.

For a normal eye, accommodation allows clear vision from the near point (25 cm) to the far point (infinity).

Q2. A person with a myopic eye cannot see objects beyond 1.2 m distinctly. What should be the type and power of the corrective lens used to restore proper vision?
Given
  • Far point of the myopic person = 1.2 m
  • The corrective lens must form a virtual image of distant objects at the far point (1.2 m from the eye).
  • Object distance, u = –infinity (distant object)
  • Image distance, v = –1.2 m (virtual image at far point, same side as object)

Type of lens: Concave (diverging) lens — because a myopic eye needs diverging rays to shift the image back to the retina.

Formula1/f = 1/v – 1/u
Substitution1/f = 1/(–1.2) – 1/(–infinity) = –1/1.2 – 0 = –0.833
Calculationf = 1/(–0.833) = –1.2 m P = 1/f = 1/(–1.2) = –0.83 D
AnswerA concave lens of power –0.83 D (focal length –1.2 m) is required.
Q3. What is the far point and near point of the human eye with normal vision?
Answer
  • Near point: The closest distance at which the eye can focus clearly on an object. For a normal young adult, the near point is 25 cm from the eye. This is also called the least distance of distinct vision.
  • Far point: The farthest distance at which the eye can focus clearly. For a normal eye, the far point is at infinity — a person with normal vision can see distant stars clearly.

Page 197

Q1. A student has difficulty reading the blackboard while sitting in the last row. What could be the defect the child has? How can it be corrected?
Answer

The student can see the blackboard clearly from the front rows but not from the last row — this means distant objects appear blurred while nearby objects are clear. This is myopia (short-sightedness).

Cause: The eyeball may be too long, or the eye lens may be too converging, causing the image of distant objects to form in front of the retina instead of on it.

Correction: A concave (diverging) lens of appropriate power should be worn. The concave lens diverges the incoming light rays before they enter the eye, shifting the image back onto the retina.

Ray diagram description: Parallel rays from the distant blackboard enter the eye. Without correction, they converge in front of the retina. The concave lens diverges these rays; the eye lens then converges them exactly onto the retina, producing a clear image.

Chapter-End Exercise

Q1. The human eye can focus objects at different distances by adjusting the focal length of the eye lens. This is due to: (a) Presbyopia (b) Accommodation (c) Near-sightedness (d) Far-sightedness

Answer(b) Accommodation

The ciliary muscles adjust the curvature of the eye lens, changing its focal length so that objects at various distances can be focused on the retina. This process is called accommodation. Presbyopia is a defect, near-sightedness is myopia, and far-sightedness is hypermetropia — none of these describe the focusing mechanism itself.

Q2. The human eye forms the image of an object at its: (a) Cornea (b) Iris (c) Pupil (d) Retina

Answer(d) Retina

The eye lens focuses light onto the retina, which acts as the light-sensitive screen. The retina contains photoreceptor cells (rods and cones) that convert light into electrical signals sent to the brain via the optic nerve. The cornea refracts light, the iris controls pupil size, and the pupil is the opening — none of these form the image.

Q3. The least distance of distinct vision for a young adult with normal vision is about: (a) 25 m (b) 2.5 cm (c) 25 cm (d) 2.5 m

Answer(c) 25 cm

The near point (least distance of distinct vision) for a normal young adult is approximately 25 cm. Objects closer than this distance cannot be focused clearly because the eye lens cannot become thick enough to bend the light sufficiently.

Q4. The change in focal length of an eye lens is caused by the action of the: (a) Pupil (b) Retina (c) Cornea (d) Ciliary muscles

Answer(d) Ciliary muscles

The ciliary muscles contract and relax to change the curvature of the eye lens. When they contract, the lens becomes thicker and focal length decreases; when they relax, the lens becomes thinner and focal length increases. The pupil only controls light amount, the retina receives the image, and the cornea does not change shape for focusing.

Q5. A person needs a lens of power –5.5 dioptres for correcting his distant vision; for correcting his near vision he needs a lens of power +1.5 dioptre. What is the focal length of the lens required for correcting (i) distant vision, and (ii) near vision?
Answer

(i) Distant vision:

Given
  • Power of lens for distant vision, P = –5.5 D
Formulaf = 1/P
Substitutionf = 1/(–5.5)
Calculationf = –1/5.5 = –0.1818 m
Answerf = –0.182 m (or –18.2 cm). The negative sign indicates a concave lens, which corrects myopia by diverging light.

(ii) Near vision:

Given
  • Power of lens for near vision, P = +1.5 D
Formulaf = 1/P
Substitutionf = 1/(+1.5)
Calculationf = 1/1.5 = 0.6667 m
Answerf = +0.667 m (or +66.7 cm). The positive sign indicates a convex lens, which corrects hypermetropia by converging light.
Q6. The far point of a myopic person is 80 cm in front of the eye. What is the nature and power of the lens required to correct the problem?
Given
  • Far point of myopic person = 80 cm = 0.80 m (in front of the eye)
  • Object is at infinity: u = –infinity
  • Image must form at the far point: v = –0.80 m (virtual image, same side as object)

Type of lens: Concave lens (myopia is corrected by a diverging lens)

Formula1/f = 1/v – 1/u
Substitution1/f = 1/(–0.80) – 1/(–infinity) = –1/0.80 – 0 = –1.25
Calculationf = 1/(–1.25) = –0.80 m P = 1/f = –1.25 D
AnswerA concave lens of power –1.25 D (focal length –0.80 m) is required to correct this myopic defect.

Ray diagram description: Parallel rays from a distant object enter the concave lens. The lens diverges the rays. To the observer's eye, these diverging rays appear to come from a point 80 cm in front of the eye (the far point). The eye lens then converges these diverging rays onto the retina, forming a clear image.

Q7. Make a diagram to show how hypermetropia is corrected. The near point of a hypermetropic eye is 1 m. What is the power of the lens required to correct this defect? Assume that the near point of the normal eye is 25 cm.
Given
  • Near point of the hypermetropic eye = 1 m
  • Near point of a normal eye = 25 cm = 0.25 m
  • The convex lens must form a virtual image of an object at 25 cm at the person's near point (1 m from the eye).
  • Object distance, u = –25 cm = –0.25 m (object at normal near point)
  • Image distance, v = –1 m = –1.0 m (virtual image at the person's near point; negative because it is on the same side as the object)

Type of lens: Convex (converging) lens — hypermetropia is corrected by a converging lens.

Formula1/f = 1/v – 1/u
Substitution1/f = 1/(–1.0) – 1/(–0.25) 1/f = –1 + 4 1/f = 3
Calculationf = 1/3 = 0.333 m = +33.3 cm P = 1/f = 1/0.333 = +3.0 D
AnswerA convex lens of power +3.0 D (focal length +33.3 cm) is required.

Ray diagram description of hypermetropia correction: 1. Without correction: An object held at 25 cm sends diverging rays. The weak eye lens cannot bend them enough. The rays converge to a point behind the retina — the image is blurred. 2. With convex lens: The convex lens placed in front of the eye pre-converges the rays. The combined action of the convex lens and the eye lens brings the rays to focus exactly on the retina. The virtual image formed by the convex lens acts as the object for the eye, located at the person's near point (1 m). Since the eye can see objects up to 1 m clearly, the image on the retina is sharp.

Q8. Why is a normal eye not able to see clearly the objects placed closer than 25 cm?
Answer

The eye lens has a limit on how much it can increase its curvature (i.e., how short its focal length can become). When an object is placed closer than 25 cm:

1. The ciliary muscles must contract maximally to make the lens as thick as possible (minimum focal length). 2. Even at maximum curvature, the lens cannot bend the light rays enough to focus them on the retina. 3. The rays converge to a point behind the retina, so the image on the retina is blurred.

The distance of 25 cm is the near point (least distance of distinct vision). Any object closer than this requires greater converging power than the eye lens can provide. This is a physical limitation of the eye — the ciliary muscles and the lens material have a maximum range of adjustment.

Q9. What happens to the image distance in the eye when we increase the distance of an object from the eye?
Answer

The image distance in the eye does not change. The distance between the eye lens and the retina is fixed (the eyeball does not change size).

When the object moves farther away:

  • The ciliary muscles relax, making the eye lens thinner (less convex).
  • The focal length of the eye lens increases.
  • The eye adjusts the focal length so that the image always falls exactly on the retina.

This is the essence of accommodation — the eye changes its focal length (not the image distance) to keep the image on the retina regardless of object distance.

Q10. Why do stars twinkle?
Answer

Stars twinkle due to atmospheric refraction.

The Earth's atmosphere is not uniform — it consists of layers of air with different densities and refractive indices. These variations are caused by:

  • Temperature differences (hot air rises, cold air sinks)
  • Wind and convection currents that constantly mix the layers

As starlight passes through these turbulent layers: 1. The path of the light ray bends continuously as it moves through layers of changing refractive index. 2. The apparent position of the star shifts slightly and fluctuates rapidly. 3. The amount of starlight entering the eye fluctuates, causing the star's brightness to vary — this is perceived as twinkling.

Stars are effectively point sources of light (they are very far away), so even a small shift in apparent position causes a noticeable change in brightness. This is purely an atmospheric effect — stars do not twinkle when observed from space.

Q11. Explain why the planets do not twinkle.
Answer

Planets do not twinkle because they are extended sources of light (not point sources like stars).

  • Planets are much closer to Earth than stars. As a result, they appear as small discs (collections of many point sources) rather than single points.
  • While atmospheric refraction causes each individual point on the planet's disc to twinkle, the fluctuations at different points are random and independent.
  • When the total light from the entire disc reaches the eye, these random fluctuations average out (cancel each other).
  • The net brightness of the planet remains essentially constant, so the planet appears steady and does not twinkle.

In summary: twinkling averages to zero for extended sources but not for point sources.

Q12. Why does the Sun appear reddish early in the morning?
Answer

At sunrise (and similarly at sunset), the Sun appears reddish due to Rayleigh scattering of light by atmospheric particles.

1. At sunrise, the Sun is near the horizon. Sunlight must travel a much longer distance through the Earth's atmosphere compared to when the Sun is overhead. 2. During this long path, most of the shorter wavelengths (blue, violet, indigo) are scattered away by atmospheric molecules and dust particles. Scattering intensity is proportional to 1/lambda^4, so shorter wavelengths scatter much more. 3. The longer wavelengths (red, orange) are scattered the least and therefore travel relatively straight to the observer's eye. 4. As a result, the light that reaches the eye directly from the Sun at sunrise/sunset is predominantly red and orange, making the Sun appear reddish.

The same explanation applies to the red appearance of the Sun at sunset.

Q13. Why does the sky appear dark instead of blue to an astronaut?
Answer

The sky appears blue on Earth because of scattering of sunlight by atmospheric particles (gas molecules, dust). This is Rayleigh scattering — shorter wavelengths scatter in all directions, making the sky appear blue when we look away from the Sun.

An astronaut in space (or at very high altitudes) is above the Earth's atmosphere. In outer space:

  • There are no gas molecules or dust particles to scatter sunlight.
  • Without scattering, there is no diffuse light coming from any direction except directly from the Sun and stars.
  • Therefore, the sky appears dark (black) — the astronaut sees only the blackness of space with the Sun and stars as bright points.

Common Mistakes to Avoid

1. Confusing myopia and hypermetropia corrections: Myopia is corrected with a concave lens (not convex), and hypermetropia is corrected with a convex lens (not concave). A helpful mnemonic: "Myopia = Minus power = concave."

2. Wrong sign convention in corrective lens calculations: For myopia correction, the image distance v is negative (virtual image at far point). For hypermetropia correction, both u and v are negative. Always use the sign convention: distances measured against the direction of incident light are negative.

3. Forgetting that presbyopia is different from hypermetropia: Presbyopia is an age-related loss of accommodation (the lens and ciliary muscles lose flexibility). Hypermetropia is a structural defect (short eyeball or weak lens). Presbyopia affects both near and far vision and requires bifocal lenses, not just a convex lens.

4. Mixing up Tyndall effect and Rayleigh scattering: The Tyndall effect is scattering by colloidal particles (size comparable to wavelength of light, e.g., dust in air, milk in water). Rayleigh scattering is scattering by gas molecules (much smaller than wavelength). The blue sky is explained by Rayleigh scattering, not the Tyndall effect (though the Tyndall effect can produce similar observations in colloidal mixtures).

5. Confusing dispersion with scattering: Dispersion is the splitting of white light into constituent colours by a prism (due to different refractive indices for different wavelengths). Scattering is the redistribution of light in different directions by particles. Dispersion needs a medium with varying refractive index (like a prism); scattering needs particles.

6. Wrong explanation for twinkling: Stars twinkle due to atmospheric refraction (changing refractive index of air layers), NOT due to the Tyndall effect. The Tyndall effect involves scattering by colloidal particles, which is a different phenomenon.

7. Forgetting that the near point is 25 cm (not 25 m or 2.5 cm): The least distance of distinct vision for a normal young adult is 25 cm. A common exam trap is giving 25 m or 2.5 cm as options.

8. Confusing which colour deviates most in a prism: In a prism, violet light deviates the most (shortest wavelength, highest refractive index in glass) and red light deviates the least (longest wavelength, lowest refractive index). Students often reverse this. In scattering, the situation is different — blue is scattered most, but in a prism, violet is deviated most.

9. Writing "image distance changes" for Q9: When object distance increases, the image distance in the eye does NOT change — the retina is fixed. The focal length changes. Many students incorrectly write that the image moves closer to or farther from the lens.

10. Forgetting units or signs in numerical answers: Power must always be stated in dioptres (D) and focal length in metres (m). Always include the sign (+ for convex, – for concave) and the unit in your final answer.

Exam Checklist

Before your exam, verify you can tick off each item:

  • [ ] I can label all parts of the human eye (cornea, iris, pupil, lens, retina, optic nerve, blind spot) and state their functions.
  • [ ] I can define power of accommodation and state the near point (25 cm) and far point (infinity) of a normal eye.
  • [ ] I can explain the cause, correction, and describe the ray diagram for myopia (concave lens, image in front of retina).
  • [ ] I can explain the cause, correction, and describe the ray diagram for hypermetropia (convex lens, image behind retina).
  • [ ] I can distinguish presbyopia from hypermetropia and explain bifocal lens correction.
  • [ ] I can solve numerical problems on corrective lenses using the lens formula with correct sign convention (Given, Formula, Substitution, Calculation, Answer).
  • [ ] I can explain dispersion and state which colour deviates most (violet) and least (red) in a prism.
  • [ ] I can explain why stars twinkle (atmospheric refraction) and why planets do not (extended sources, averaging out).
  • [ ] I can explain why the sky is blue (Rayleigh scattering), why sunrise/sunset are red, and why the sky is dark for astronauts (no atmosphere to scatter light).
  • [ ] I can distinguish between dispersion, scattering, and the Tyndall effect.

Internal Links

  • [Chapter 11 Guide — The Human Eye and the Colourful World](/school/cbse/class/10/science/cbse-human-eye-and-colourful-world)
  • [All Class 10 Science Solutions](/school/cbse/class/10/science/solutions)
  • [Class 10 Science Subject Guide](/school/cbse/class/10/science)

Frequently Asked Questions

The power of accommodation is the ability of the eye lens to change its focal length by adjusting its curvature so that both near and distant objects can be focused on the retina. Ciliary muscles contract to make the lens thicker (shorter focal length) for near objects and relax to make the lens thinner (longer focal length) for far objects. For a normal eye, this range is from the near point (25 cm) to the far point (infinity).