The Human Eye and the Colourful World

Introduction

• The human eye, a vital sense organ, uses light to enable vision, perceiving the world’s colors and beauty.
• Building on refraction and lens properties from Chapter 9, this chapter explores the eye’s lens function, vision defect corrections, and optical phenomena like rainbows, light dispersion, and the sky’s blue color.
• Understanding the eye’s optics and natural light phenomena reveals the interplay of physics in vision and the environment.

10.1 The Human Eye

• The eye functions like a camera, forming images on the retina, a light-sensitive screen (Fig. 10.1).
• Structure:
  • Cornea: Transparent front membrane; primary refraction site.
  • Eyeball: ~2.3 cm diameter, nearly spherical.
  • Iris: Dark muscular diaphragm controlling pupil size, regulating light entry.
  • Pupil: Opening that adjusts light intake.
  • Crystalline Lens: Fine-tunes focal length for focusing.
  • Retina: Contains light-sensitive cells; forms inverted real image, converts light to electrical signals.
  • Optic Nerve: Transmits signals to brain for interpretation.
• The eye’s components work together to process light, enabling clear vision of objects and colors.

10.1.1 Power of Accommodation

• Accommodation: Ability of the eye lens to adjust focal length via ciliary muscles.
• Mechanism:
  • Relaxed ciliary muscles: Lens thins, focal length increases (distant objects clear).
  • Contracted ciliary muscles: Lens thickens, focal length decreases (near objects clear).
• Limits:
  • Near Point: Minimum distance for clear vision (~25 cm for young adults).
  • Far Point: Maximum distance for clear vision (infinity for normal eyes).
  • Objects closer than 25 cm appear blurred due to accommodation limits.
• Cataract: Cloudy lens in old age, causing partial/complete vision loss; treatable via surgery.
• Accommodation enables versatile focusing, but has physical constraints affecting close-up vision.

10.2 Defects of Vision and Their Correction

• Refractive defects arise when accommodation fails, causing blurred vision.
• Common Defects:
  1. Myopia (Near-sightedness)
  2. Hypermetropia (Far-sightedness)
  3. Presbyopia

(a) Myopia

• Description: Clear near vision, blurred distant vision; far point closer than infinity (e.g., a few meters).
• Cause: Image forms in front of retina due to excessive lens curvature or elongated eyeball (Fig. 10.2b).
• Correction: Concave lens shifts image to retina (Fig. 10.2c).
• Myopia limits distant vision, correctable with diverging lenses.

(b) Hypermetropia

• Description: Clear distant vision, blurred near vision; near point beyond 25 cm.
• Cause: Image forms behind retina due to long focal length or small eyeball (Fig. 10.3b).
• Correction: Convex lens adds focusing power to place image on retina (Fig. 10.3c).
• Hypermetropia affects near tasks like reading, correctable with converging lenses.

(c) Presbyopia

• Description: Age-related loss of accommodation; difficulty seeing near objects.
• Cause: Weakened ciliary muscles, reduced lens flexibility; near point recedes.
• Correction:
  • Convex lenses for near vision.
  • Bi-focal lenses for combined myopia/hypermetropia: upper concave (distance), lower convex (near).
• Alternatives: Contact lenses, surgical interventions.
• Presbyopia is common in aging, manageable with specialized lenses.

10.3 Refraction of Light Through a Prism

• Prism: Triangular glass with two refracting surfaces and an angle of prism between them.
• Activity 10.1:
  • Trace light path through prism (Fig. 10.4): Incident ray (PE) bends toward normal at first surface (AB, air to glass), away from normal at second surface (AC, glass to air).
  • Emergent ray (FS) deviates from incident ray; angle of deviation (∠D) measured.
• Key Difference from Glass Slab: Prism’s non-parallel surfaces cause net deviation, unlike slab’s parallel emergent ray.
• Prism refraction highlights angular bending due to its geometry.

10.4 Dispersion of White Light by a Glass Prism

• Dispersion: Splitting of white light into component colors (spectrum).
• Activity 10.2:
  • Pass sunlight through prism; observe spectrum (VIBGYOR: Violet, Indigo, Blue, Green, Yellow, Orange, Red) on screen (Fig. 10.5).
  • Colors appear because each wavelength bends differently: violet bends most, red least.
• Newton’s Experiments:
  • Single prism splits light; second prism cannot split colors further.
  • Inverted second prism recombines spectrum into white light, proving sunlight comprises seven colors (Fig. 10.6).
• Rainbow Formation:
  • Natural spectrum from sunlight dispersed by water droplets acting as prisms (Fig. 10.7).
  • Process: Refraction, dispersion, internal reflection, and refraction again in droplets (Fig. 10.8).
  • Visible opposite Sun, e.g., after rain, near waterfalls, or fountains.
• Dispersion explains vibrant natural phenomena like rainbows, driven by wavelength-dependent refraction.

10.5 Atmospheric Refraction

• Definition: Refraction of light by Earth’s atmosphere due to varying refractive index with altitude.
• Examples:
  • Flickering of objects above hot surfaces (e.g., radiator) due to density changes in air.
• Twinkling of Stars:
  • Starlight refracts continuously in atmosphere’s changing refractive index, bending toward normal (Fig. 10.9).
  • Apparent position shifts slightly, causing flickering (brighter/fainter) as light path varies.
  • Stars as point sources amplify effect.
• Why Planets Don’t Twinkle:
  • Planets are closer, appearing as extended sources (many point sources).
  • Light variations from individual points average out, canceling twinkling.
• Advance Sunrise/Delayed Sunset:
  • Atmospheric refraction makes Sun visible ~2 minutes before actual sunrise, after actual sunset (Fig. 10.10).
  • Sun appears higher than actual position; also causes apparent flattening of Sun’s disc at horizon.
• Atmospheric refraction creates dynamic visual effects, altering celestial appearances.

10.6 Scattering of Light

• Scattering: Light’s interaction with particles, making light paths visible.
• Examples: Blue sky, deep sea color, red sunrise/sunset.

10.6.1 Tyndall Effect

• Definition: Scattering of light by colloidal particles (e.g., smoke, dust, water droplets) makes beam visible.
• Observations:
  • Sunlight through smoke-filled room or forest canopy (mist droplets scatter light).
• Color Dependence:
  • Small particles scatter short wavelengths (blue); larger particles scatter longer wavelengths (red) or white light.
• Tyndall effect highlights particle-light interactions in everyday settings.

10.6.2 Why is the Sky Blue?

• Explanation:
  • Atmospheric molecules/particles, smaller than visible light wavelengths, scatter short wavelengths (blue) more than red (red wavelength ~1.8× blue).
  • Scattered blue light reaches eyes from all directions.
• No Atmosphere: Sky would appear dark (e.g., to astronauts at high altitudes where scattering is minimal).
• Red Danger Signals: Red scatters least in fog/smoke, ensuring visibility at distance.
• Scattering explains the sky’s color and practical choices like red signals.

Eye Donation

• Importance:
  • 35 million blind in developing world; 4.5 million with corneal blindness (60% children <12) can be cured via corneal transplantation.
  • One donor’s eyes can restore vision for up to four people.
• Eligibility:
  • Any age/sex; spectacle users, cataract patients, diabetics, hypertensives, asthma patients eligible if free of communicable diseases.
  • Ineligible: Those with AIDS, Hepatitis B/C, rabies, acute leukemia, tetanus, cholera, meningitis, encephalitis.
• Process:
  • Remove eyes within 4-6 hours post-death; contact eye bank.
  • Removal: 10-15 minutes, no disfigurement, done at home/hospital.
  • Eye banks evaluate/distribute eyes; unsuitable eyes used for research/education.
  • Donor/recipient identities confidential.
• Eye donation is a powerful act of giving, restoring sight to the blind.

Key Questions and Answers

1. Power of Accommodation:
   • Eye lens adjusts focal length to focus on near/distant objects via ciliary muscles.
2. Myopia (Far Point 1.2 m):
   • Concave lens to extend far point to infinity.
3. Normal Eye Points:
   • Near point: 25 cm; Far point: infinity.
4. Difficulty Reading Blackboard:
   • Likely myopia; correct with concave lens.
5. Lens Powers (-5.5 D, +1.5 D):
   • Distant vision: f = \(\frac{1}{-5.5} = -0.182 \, \text{m} = -18.2 \, \text{cm}\) (concave).
   • Near vision: f = \(\frac{1}{1.5} = 0.667 \, \text{m} = 66.7 \, \text{cm}\) (convex).
6. Myopia (Far Point 80 cm):
   • Concave lens; image at infinity should form at 80 cm.
   • u = ∞, v = -80 cm; \(\frac{1}{f} = \frac{1}{-80} - \frac{1}{\infty} = -\frac{1}{80}\); f = -80 cm.
   • P = \(\frac{1}{-0.8} = -1.25 \, \text{D}\).
7. Hypermetropia Correction (Near Point 1 m):
   • Convex lens to shift near point to 25 cm.
   • u = -25 cm, v = -100 cm; \(\frac{1}{f} = \frac{1}{-100} - \frac{1}{-25} = \frac{3}{100}\); f = 33.33 cm.
   • P = \(\frac{1}{0.3333} = +3.0 \, \text{D}\).
   • Diagram: Object at 25 cm, convex lens forms virtual image at 100 cm (Fig. 10.3c).
8. Objects Closer than 25 cm:
   • Eye lens cannot decrease focal length enough; image forms behind retina, causing blur.
9. Image Distance with Object Distance:
   • Eye adjusts focal length to keep image on retina; image distance remains constant (retina’s position fixed).
10. Stars Twinkle:
    • Atmospheric refraction shifts star’s apparent position due to varying refractive index; light from point source flickers.
11. Planets Don’t Twinkle:
    • Extended sources; light variations from multiple points average out, stabilizing image.
12. Dark Sky for Astronauts:
    • High altitudes lack atmosphere; no scattering of blue light, sky appears dark.

Exercises

1. Eye Focusing Mechanism:
   • (b) Accommodation.
2. Image Formation:
   • (d) Retina.
3. Least Distance of Distinct Vision:
   • (c) 25 cm.
4. Focal Length Change:
   • (c) Ciliary muscles.
5. Lens Focal Lengths:
   • (i) Distant: f = -18.2 cm (concave).
   • (ii) Near: f = 66.7 cm (convex).
6. Myopia Correction:
   • Concave lens, P = -1.25 D.
7. Hypermetropia Correction:
   • Convex lens, P = +3.0 D; diagram as in Fig. 10.3c.
8. Close Object Blur:
   • Lens cannot focus closer than 25 cm due to accommodation limit.
9. Image Distance:
   • Remains constant on retina; eye adjusts lens curvature.
10. Star Twinkling:
    • Atmospheric refraction causes fluctuating apparent position of point source.
11. Planet Stability:
    • Extended source; light variations cancel out.
12. Dark Sky:
    • No atmosphere, no scattering, sky appears dark.