Chapter 11: Human Eye and the Colourful World
NCERT Solutions
Detailed NCERT Solutions for Human Eye and the Colourful World.
Complete answers for vision defects and dispersion for Class 10.
How to Use This Exercise Widget
Each question block contains a "Show Answer" button. Click it to reveal the detailed answer. These solutions cover human eye structure, vision defects, prism refraction, dispersion, atmospheric refraction, and light scattering.
Question 1
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
Explanation:
Accommodation is the ability of the eye lens to adjust its focal length to focus on objects at varying distances.
How it works:
• Ciliary muscles control the curvature of the eye lens
• For distant objects: Ciliary muscles relax → lens becomes thin → focal length increases
• For near objects: Ciliary muscles contract → lens becomes thick → focal length decreases
Comparison with other options:
• Presbyopia: Age-related loss of accommodation (not the ability itself)
• Near-sightedness (Myopia): Defect where distant objects appear blurred
• Far-sightedness (Hypermetropia): Defect where nearby objects appear blurred
Key concept: Accommodation allows us to see clearly from 25 cm (near point) to infinity (far point).
Explanation:
Accommodation is the ability of the eye lens to adjust its focal length to focus on objects at varying distances.
How it works:
• Ciliary muscles control the curvature of the eye lens
• For distant objects: Ciliary muscles relax → lens becomes thin → focal length increases
• For near objects: Ciliary muscles contract → lens becomes thick → focal length decreases
Comparison with other options:
• Presbyopia: Age-related loss of accommodation (not the ability itself)
• Near-sightedness (Myopia): Defect where distant objects appear blurred
• Far-sightedness (Hypermetropia): Defect where nearby objects appear blurred
Key concept: Accommodation allows us to see clearly from 25 cm (near point) to infinity (far point).
Question 2
The human eye forms the image of an object at its:
(a) cornea.
(b) iris.
(c) pupil.
(d) retina.
Answer: (d) retina
Explanation:
The retina is the light-sensitive screen at the back of the eyeball where images are formed.
Image formation process:
1. Light enters through cornea → refracted
2. Passes through pupil (controlled by iris)
3. Further refracted by eye lens
4. Forms inverted, real image on retina
Role of other parts:
• Cornea: Initial refraction of light (major bending occurs here)
• Iris: Controls pupil size to regulate light entering
• Pupil: Opening through which light enters
• Eye lens: Fine adjustment of focus (accommodation)
Retina function:
• Contains photoreceptor cells (rods and cones)
• Converts light energy to electrical signals
• Signals sent to brain via optic nerve for processing
Explanation:
The retina is the light-sensitive screen at the back of the eyeball where images are formed.
Image formation process:
1. Light enters through cornea → refracted
2. Passes through pupil (controlled by iris)
3. Further refracted by eye lens
4. Forms inverted, real image on retina
Role of other parts:
• Cornea: Initial refraction of light (major bending occurs here)
• Iris: Controls pupil size to regulate light entering
• Pupil: Opening through which light enters
• Eye lens: Fine adjustment of focus (accommodation)
Retina function:
• Contains photoreceptor cells (rods and cones)
• Converts light energy to electrical signals
• Signals sent to brain via optic nerve for processing
Question 3
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
Explanation:
The least distance of distinct vision (also called near point) is the minimum distance at which an object can be seen clearly without strain.
For different age groups:
• Young adult with normal vision: 25 cm
• Children: Can be as close as 10 cm
• Elderly (presbyopia): Increases to 1-2 m or more
Why 25 cm is significant:
• Closer than this causes eye strain
• Image becomes blurred due to limit of accommodation
• Standard reading distance is about 25-30 cm
Related terms:
• Far point: Farthest distance of clear vision (infinity for normal eye)
• Range of vision: 25 cm to infinity for normal eye
Practical test: Bring a book close to your eyes until text blurs - that's approximately your near point.
Explanation:
The least distance of distinct vision (also called near point) is the minimum distance at which an object can be seen clearly without strain.
For different age groups:
• Young adult with normal vision: 25 cm
• Children: Can be as close as 10 cm
• Elderly (presbyopia): Increases to 1-2 m or more
Why 25 cm is significant:
• Closer than this causes eye strain
• Image becomes blurred due to limit of accommodation
• Standard reading distance is about 25-30 cm
Related terms:
• Far point: Farthest distance of clear vision (infinity for normal eye)
• Range of vision: 25 cm to infinity for normal eye
Practical test: Bring a book close to your eyes until text blurs - that's approximately your near point.
Question 4
The change in focal length of an eye lens is caused by the action of the:
(a) pupil.
(b) retina.
(c) ciliary muscles.
(d) iris.
Answer: (c) ciliary muscles
Explanation:
Ciliary muscles are responsible for changing the curvature and thus the focal length of the eye lens during accommodation.
Mechanism of accommodation:
Role of other structures:
• Pupil: Controls amount of light entering (diameter changes)
• Retina: Image formation and light detection
• Iris: Controls pupil size (contains muscles for dilation/constriction)
Clinical significance:
• Presbyopia: Weakening of ciliary muscles with age
• Accommodation spasm: Overworked ciliary muscles (eye strain)
• Accommodation range decreases from about 14 diopters in children to 1-2 diopters in elderly
Explanation:
Ciliary muscles are responsible for changing the curvature and thus the focal length of the eye lens during accommodation.
Mechanism of accommodation:
| Object Distance | Ciliary Muscles | Lens Curvature | Focal Length |
|---|---|---|---|
| Distant object | Relaxed | Thin (less curved) | Increases |
| Near object | Contract | Thick (more curved) | Decreases |
Role of other structures:
• Pupil: Controls amount of light entering (diameter changes)
• Retina: Image formation and light detection
• Iris: Controls pupil size (contains muscles for dilation/constriction)
Clinical significance:
• Presbyopia: Weakening of ciliary muscles with age
• Accommodation spasm: Overworked ciliary muscles (eye strain)
• Accommodation range decreases from about 14 diopters in children to 1-2 diopters in elderly
Question 5
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:
Formula: Power (P) = 1/f (where f is in meters)
Therefore: f = 1/P
(i) For distant vision:
P = -5.5 D
(ii) For near vision:
P = +1.5 D
Clinical diagnosis:
• Distant vision correction: -5.5 D → Myopia (nearsightedness)
• Near vision correction: +1.5 D → Presbyopia (age-related far-sightedness)
• This person needs bifocal lenses (concave upper part for distance, convex lower part for reading)
Calculation check:
• 1 diopter = 1/f(m) → f = 1/P in meters
• Negative power → diverging lens (concave)
• Positive power → converging lens (convex)
Formula: Power (P) = 1/f (where f is in meters)
Therefore: f = 1/P
(i) For distant vision:
P = -5.5 D
f = 1/P = 1/(-5.5) = -0.1818 m ≈ -0.18 m = -18 cm
Interpretation: Concave lens of focal length 18 cm(ii) For near vision:
P = +1.5 D
f = 1/P = 1/(+1.5) = +0.6667 m ≈ +0.67 m = +67 cm
Interpretation: Convex lens of focal length 67 cmClinical diagnosis:
• Distant vision correction: -5.5 D → Myopia (nearsightedness)
• Near vision correction: +1.5 D → Presbyopia (age-related far-sightedness)
• This person needs bifocal lenses (concave upper part for distance, convex lower part for reading)
Calculation check:
• 1 diopter = 1/f(m) → f = 1/P in meters
• Negative power → diverging lens (concave)
• Positive power → converging lens (convex)
Question 6
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?
Answer:
Given: Far point = 80 cm (instead of infinity for normal eye)
This means the person can see clearly only up to 80 cm.
Correction principle:
A concave lens should form a virtual image of distant object (at infinity) at the person's far point (80 cm).
Using lens formula: 1/f = 1/v - 1/u
Where:
• u = object distance = infinity (∞)
• v = image distance = -80 cm (virtual image, same side as object)
• Nature of lens: Concave (diverging) lens
• Power: -1.25 dioptres
Verification:
With this lens, parallel rays from infinity will appear to come from 80 cm, which is the person's far point.
Given: Far point = 80 cm (instead of infinity for normal eye)
This means the person can see clearly only up to 80 cm.
Correction principle:
A concave lens should form a virtual image of distant object (at infinity) at the person's far point (80 cm).
Using lens formula: 1/f = 1/v - 1/u
Where:
• u = object distance = infinity (∞)
• v = image distance = -80 cm (virtual image, same side as object)
1/f = 1/v - 1/u
1/f = 1/(-80) - 1/∞
1/f = -1/80 - 0
1/f = -1/80
f = -80 cm = -0.8 m
Power calculation:1/f = 1/(-80) - 1/∞
1/f = -1/80 - 0
1/f = -1/80
f = -80 cm = -0.8 m
P = 1/f (in meters)
P = 1/(-0.8) = -1.25 D
Result:P = 1/(-0.8) = -1.25 D
• Nature of lens: Concave (diverging) lens
• Power: -1.25 dioptres
Verification:
With this lens, parallel rays from infinity will appear to come from 80 cm, which is the person's far point.
Question 7
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.
Answer:
Part 1: Diagram for hypermetropia correction
Part 2: Power calculation
Given:
• Normal near point = 25 cm = 0.25 m
• Hypermetropic near point = 1 m
• Need: Lens to form virtual image of object at 25 cm at the person's near point (1 m)
Using lens formula: 1/f = 1/v - 1/u
Where:
• u = object distance = -25 cm = -0.25 m (negative by convention)
• v = image distance = -1 m (virtual image, same side as object)
• Nature of lens: Convex (converging) lens
• Power: +3 dioptres
Explanation:
The convex lens of +3 D makes rays from an object at 25 cm appear to come from 1 m (the person's near point), allowing clear vision.
Part 1: Diagram for hypermetropia correction
[Students should draw:]
1. Hypermetropic eye with image formed behind retina
2. Convex lens placed in front of eye
3. Rays from near object (25 cm) converge more
4. Image now formed exactly on retina
5. Label: object, convex lens, corrected focal point on retina
1. Hypermetropic eye with image formed behind retina
2. Convex lens placed in front of eye
3. Rays from near object (25 cm) converge more
4. Image now formed exactly on retina
5. Label: object, convex lens, corrected focal point on retina
Part 2: Power calculation
Given:
• Normal near point = 25 cm = 0.25 m
• Hypermetropic near point = 1 m
• Need: Lens to form virtual image of object at 25 cm at the person's near point (1 m)
Using lens formula: 1/f = 1/v - 1/u
Where:
• u = object distance = -25 cm = -0.25 m (negative by convention)
• v = image distance = -1 m (virtual image, same side as object)
1/f = 1/v - 1/u
1/f = 1/(-1) - 1/(-0.25)
1/f = -1 + 4
1/f = 3
f = 1/3 m ≈ 0.33 m
Power calculation:1/f = 1/(-1) - 1/(-0.25)
1/f = -1 + 4
1/f = 3
f = 1/3 m ≈ 0.33 m
P = 1/f (in meters)
P = 1/(1/3) = +3 D
Result:P = 1/(1/3) = +3 D
• Nature of lens: Convex (converging) lens
• Power: +3 dioptres
Explanation:
The convex lens of +3 D makes rays from an object at 25 cm appear to come from 1 m (the person's near point), allowing clear vision.
Question 8
Why is a normal eye not able to see clearly the objects placed closer than 25 cm?
Answer:
Primary reason: Limit of accommodation of the eye lens.
Detailed explanation:
1. Ciliary muscles have a maximum contraction limit
2. Eye lens has a maximum curvature it can achieve
3. Focal length cannot be reduced below a certain minimum
What happens when object is closer than 25 cm:
• Ciliary muscles contract maximally
• Lens becomes as thick as possible
• But focal length is still too long to focus image on retina
• Image forms behind retina → blurred vision
The 25 cm significance:
• Least distance of distinct vision (near point)
• Minimum distance for comfortable, strain-free vision
• For young adults with normal vision: ~25 cm
• For children: Can be as close as 10 cm
• For elderly: Increases to 1-2 m (presbyopia)
Try this experiment:
Bring a book closer to your eyes until text becomes blurry. That's your near point. Any closer and your eye cannot adjust sufficiently.
Primary reason: Limit of accommodation of the eye lens.
Detailed explanation:
1. Ciliary muscles have a maximum contraction limit
2. Eye lens has a maximum curvature it can achieve
3. Focal length cannot be reduced below a certain minimum
What happens when object is closer than 25 cm:
• Ciliary muscles contract maximally
• Lens becomes as thick as possible
• But focal length is still too long to focus image on retina
• Image forms behind retina → blurred vision
The 25 cm significance:
• Least distance of distinct vision (near point)
• Minimum distance for comfortable, strain-free vision
• For young adults with normal vision: ~25 cm
• For children: Can be as close as 10 cm
• For elderly: Increases to 1-2 m (presbyopia)
Try this experiment:
Bring a book closer to your eyes until text becomes blurry. That's your near point. Any closer and your eye cannot adjust sufficiently.
Question 9
What happens to the image distance in the eye when we increase the distance of an object from the eye?
Answer:
The image distance remains constant (fixed at the retina).
Explanation:
In the human eye:
1. Retina position is fixed (image always forms here)
2. Eye adjusts focal length via accommodation
3. For different object distances, focal length changes, not image distance
How accommodation maintains constant image distance:
Mathematical perspective:
Using lens formula: 1/f = 1/v - 1/u
For eye: v = constant (retina distance ≈ 2.5 cm)
As u changes (object distance), f changes to keep v constant
Comparison with camera:
• Camera: Adjusts lens-to-film distance (v changes)
• Eye: Adjusts focal length (f changes), v fixed
Clinical significance:
This fixed image distance is why vision defects occur when eyeball shape changes (myopia: elongated, hypermetropia: shortened).
The image distance remains constant (fixed at the retina).
Explanation:
In the human eye:
1. Retina position is fixed (image always forms here)
2. Eye adjusts focal length via accommodation
3. For different object distances, focal length changes, not image distance
How accommodation maintains constant image distance:
| Object Distance | Ciliary Muscles | Lens Curvature | Focal Length | Image Distance |
|---|---|---|---|---|
| Increases (far) | Relax | Decreases | Increases | Constant (on retina) |
| Decreases (near) | Contract | Increases | Decreases |
Mathematical perspective:
Using lens formula: 1/f = 1/v - 1/u
For eye: v = constant (retina distance ≈ 2.5 cm)
As u changes (object distance), f changes to keep v constant
Comparison with camera:
• Camera: Adjusts lens-to-film distance (v changes)
• Eye: Adjusts focal length (f changes), v fixed
Clinical significance:
This fixed image distance is why vision defects occur when eyeball shape changes (myopia: elongated, hypermetropia: shortened).
Question 10
Why do stars twinkle?
Answer:
Stars twinkle due to atmospheric refraction of starlight.
Detailed explanation:
1. Atmospheric refraction: Starlight bends as it passes through different layers of atmosphere with varying refractive indices
2. Continuous refraction: Light undergoes multiple refractions before reaching our eyes
3. Changing path: Air turbulence causes continuous change in refraction path
4. Apparent position fluctuation: Star appears to change position slightly
5. Brightness variation: Amount of light reaching eye varies → twinkling effect
Why planets don't twinkle:
• Planets are closer → appear as extended sources (discs)
• Multiple point sources average out variations
• Refraction effects cancel out → no twinkling
Factors affecting twinkling:
• Altitude: Stars near horizon twinkle more (more atmosphere to pass through)
• Atmospheric conditions: More turbulence = more twinkling
• Weather: Clear nights show less twinkling than turbulent nights
Scientific term: Scintillation (astronomical term for twinkling)
Stars twinkle due to atmospheric refraction of starlight.
Detailed explanation:
1. Atmospheric refraction: Starlight bends as it passes through different layers of atmosphere with varying refractive indices
2. Continuous refraction: Light undergoes multiple refractions before reaching our eyes
3. Changing path: Air turbulence causes continuous change in refraction path
4. Apparent position fluctuation: Star appears to change position slightly
5. Brightness variation: Amount of light reaching eye varies → twinkling effect
Why planets don't twinkle:
• Planets are closer → appear as extended sources (discs)
• Multiple point sources average out variations
• Refraction effects cancel out → no twinkling
Factors affecting twinkling:
• Altitude: Stars near horizon twinkle more (more atmosphere to pass through)
• Atmospheric conditions: More turbulence = more twinkling
• Weather: Clear nights show less twinkling than turbulent nights
Scientific term: Scintillation (astronomical term for twinkling)
Question 11
Explain why the planets do not twinkle.
Answer:
Planets do not twinkle because they appear as extended sources (discs) rather than point sources.
Detailed explanation:
1. Extended source vs point source:
• Stars: Point sources (due to enormous distance)
• Planets: Extended sources (relatively closer, appear as discs)
2. Multiple light paths:
• Each point on planetary disc sends light through atmosphere
• Atmospheric refraction affects each point differently
• Variations average out → cancels twinkling effect
3. Mathematical reasoning:
• Total light = sum from all points on disc
• Refraction variations random and uncorrelated
• Statistical averaging → stable brightness
Comparison table:
Practical observation:
• Planets shine with steady light
• Stars flicker/twinkle noticeably
• This difference helps identify planets in night sky
Planets do not twinkle because they appear as extended sources (discs) rather than point sources.
Detailed explanation:
1. Extended source vs point source:
• Stars: Point sources (due to enormous distance)
• Planets: Extended sources (relatively closer, appear as discs)
2. Multiple light paths:
• Each point on planetary disc sends light through atmosphere
• Atmospheric refraction affects each point differently
• Variations average out → cancels twinkling effect
3. Mathematical reasoning:
• Total light = sum from all points on disc
• Refraction variations random and uncorrelated
• Statistical averaging → stable brightness
Comparison table:
| Feature | Stars | Planets |
|---|---|---|
| Distance | Light years away | Light minutes away |
| Appearance | Point source | Extended source (disc) |
| Atmospheric effect | Single path affected | Multiple paths average out |
| Twinkling | Yes (scintillates) | No (steady light) |
Practical observation:
• Planets shine with steady light
• Stars flicker/twinkle noticeably
• This difference helps identify planets in night sky
Question 12
Why does the Sun appear reddish early in the morning?
Answer:
The Sun appears reddish at sunrise due to scattering of light by atmospheric particles.
Physics behind the phenomenon:
1. Longer atmospheric path: At sunrise, sunlight travels through thicker atmosphere
2. Scattering: Air molecules and particles scatter shorter wavelengths (blue, violet) more
3. Selective removal: Blue light scattered away from our line of sight
4. Remaining light: Longer wavelengths (red, orange) reach our eyes directly
Why different colors scatter differently:
• Scattering ∝ 1/λ⁴ (Rayleigh scattering)
• Blue light (λ ≈ 450 nm) scatters ~10 times more than red light (λ ≈ 650 nm)
• At sunrise/sunset: More scattering → only red light survives the long path
Path length comparison:
• Noon: Sun overhead → shortest atmospheric path → less scattering → white appearance
• Sunrise/sunset: Sun near horizon → longest atmospheric path → maximum scattering → reddish appearance
Same phenomenon causes:
• Red sunset
• Blue sky during day (scattered blue light)
• Red danger signals (least scattered, visible from far)
The Sun appears reddish at sunrise due to scattering of light by atmospheric particles.
Physics behind the phenomenon:
1. Longer atmospheric path: At sunrise, sunlight travels through thicker atmosphere
2. Scattering: Air molecules and particles scatter shorter wavelengths (blue, violet) more
3. Selective removal: Blue light scattered away from our line of sight
4. Remaining light: Longer wavelengths (red, orange) reach our eyes directly
Why different colors scatter differently:
• Scattering ∝ 1/λ⁴ (Rayleigh scattering)
• Blue light (λ ≈ 450 nm) scatters ~10 times more than red light (λ ≈ 650 nm)
• At sunrise/sunset: More scattering → only red light survives the long path
Path length comparison:
• Noon: Sun overhead → shortest atmospheric path → less scattering → white appearance
• Sunrise/sunset: Sun near horizon → longest atmospheric path → maximum scattering → reddish appearance
Same phenomenon causes:
• Red sunset
• Blue sky during day (scattered blue light)
• Red danger signals (least scattered, visible from far)
Question 13
Why does the sky appear dark instead of blue to an astronaut?
Answer:
The sky appears dark to astronauts because there is no atmosphere in space to scatter sunlight.
Detailed explanation:
1. Scattering requires medium: Rayleigh scattering occurs due to air molecules and particles
2. Space vacuum: No atmosphere → no scattering particles
3. Direct sunlight: Light travels straight without scattering
4. No scattered blue light: No blue light reaches eyes from other directions
Comparison Earth vs Space:
Why we see blue sky on Earth:
• Air molecules scatter blue light (shorter λ) in all directions
• This scattered blue light reaches our eyes from all parts of sky
• Sun appears yellowish (blue component removed)
Astronaut's experience:
• Sun appears white (all wavelengths reach directly)
• Sky appears black/dark (no scattered light)
• Stars visible even when facing Sun
The sky appears dark to astronauts because there is no atmosphere in space to scatter sunlight.
Detailed explanation:
1. Scattering requires medium: Rayleigh scattering occurs due to air molecules and particles
2. Space vacuum: No atmosphere → no scattering particles
3. Direct sunlight: Light travels straight without scattering
4. No scattered blue light: No blue light reaches eyes from other directions
Comparison Earth vs Space:
| Aspect | Earth's Surface | Space (Astronaut's View) |
|---|---|---|
| Atmosphere | Present (scatters light) | Absent (vacuum) |
| Sunlight path | Scattered in all directions | Direct, straight path |
| Sky color | Blue (scattered blue light) | Black/dark (no scattering) |
| Stars visibility | Only at night (sunlight scattered) | Visible even during day |
Why we see blue sky on Earth:
• Air molecules scatter blue light (shorter λ) in all directions
• This scattered blue light reaches our eyes from all parts of sky
• Sun appears yellowish (blue component removed)
Astronaut's experience:
• Sun appears white (all wavelengths reach directly)
• Sky appears black/dark (no scattered light)
• Stars visible even when facing Sun