The Human Eye and the Colourful World – Comprehensive Study Notes

10.1 THE HUMAN EYE

The eye is a valuable and sensitive sense organ; enables us to see the world and colours.
Eye ~ camera: lens system forms an image on the retina (light-sensitive screen).
Light enters through the cornea, the transparent bulge on the eye’s front surface.
Eyeball is approximately spherical with diameter ~2.3 cm.
Refraction: most bending of light occurs at the cornea surface; crystalline lens provides fine adjustment of focal length for different object distances.
Iris lies behind the cornea; it is a dark muscular diaphragm that controls the size of the pupil.
Pupil regulates the amount of light entering the eye.
The eye lens forms an inverted real image on the retina.
Retina contains light-sensitive cells that generate electrical signals when illuminated.
Signals travel via the optic nerves to the brain; brain processes signals to form the visual perception.

10.1.1 POWER OF ACCOMMODATION

Eye lens is a fibrous, jelly-like material; its curvature can be changed by ciliary muscles.
Change in curvature → change in focal length; accommodates for objects at different distances.
When ciliary muscles relax: lens becomes thinner; focal length increases; enables clear distant vision.
When looking at nearby objects: ciliary muscles contract; lens becomes thicker; focal length decreases; enables clear near vision.
Accommodation: the ability of the eye lens to adjust focal length.
Focal length has a minimum limit; cannot decrease beyond a point.
Common experience: holding a page very close causes blur and eye strain; comfortable near reading distance ~25 cm.
NEAR POINT (least distance of distinct vision, N): the minimum distance at which an object can be seen distinctly without strain; for a young adult with normal vision, N ≈ 25 cm.
FAR POINT: the farthest distance at which the eye can see clearly; for a normal eye, far point is infinity.
A normal eye can clearly see objects between 25 cm and infinity.
CATARACT: milky/cloudy lens in old age; can cause partial/complete loss of vision; cataract surgery can restore vision.

10.2 DEFECTS OF VISION AND THEIR CORRECTION

Visual defects arise when accommodation power decreases or refractive power is inappropriate for retina focusing.
Three common refractive defects (corrected by spherical lenses):
(i) MYOPIA (nearsightedness): distant objects blurred; far point is finite; image of distant object forms in front of retina.
(ii) HYPERMETROPIA (farsightedness): near objects blurred; near point is farther than normal; light focuses behind retina.
(iii) PRESBYOPIA: loss of accommodation with age; near point recedes; difficulty reading at normal near distances.
Corrective lenses:
- Myopia: concave lens of suitable power; P < 0, moves image onto retina.
- Hypermetropia: convex lens of suitable power; P > 0, helps focus on retina.
- Presbyopia: bifocal lenses (upper concave for distance, lower convex for near).
Bi-focal lenses: combinations of concave and convex lenses; common for people with both myopia and hypermetropia.
Modern corrections: contact lenses and surgical interventions are also common.

(a) MYOPIA

Also called near-sightedness.
Far point nearer than infinity; can see clearly up to a few metres.
Image of distant objects forms in front of retina (Fig. 10.2 (b)).
Causes: excessive curvature of the eye lens or elongation of the eyeball.
Correction: concave lens of suitable power (Fig. 10.2 (c)).

(b) HYPERMETROPIA

Also called far-sightedness.
Near point farther from the normal near point (25 cm).
Light rays from near objects are focused behind the retina (Fig. 10.3 (b)).
Causes: focal length of eye lens is too long or eyeball is too small.
Correction: convex lens of appropriate power (Fig. 10.3 (c)); converges light to retina.
Eye-glasses with converging lenses provide the additional focusing power to form image on retina.

Accommodation power decreases with age; near point recedes.
Difficulty seeing nearby objects clearly without corrective glasses.

Think it over – Eye donation and related ethical/practical aspects

About 35 million people in the developing world are blind; many can be cured.
About 4.5 million people with corneal blindness can be cured via corneal transplantation from donated eyes; ~60% of these are children below 12.
Eye donors can be of any age and sex; wearing spectacles or having undergone cataract surgery does not disqualify donation.
People with diabetes, hypertension, asthma, or who do not have communicable diseases can donate eyes.
Eye removal should occur within 4–6 hours after death; the eye bank team can remove eyes at home or in hospital; the procedure takes 10–15 minutes and does not disfigure the body.
Donors with AIDS, Hepatitis B or C, rabies, acute leukemia, tetanus, cholera, meningitis, or encephalitis cannot donate eyes.
An eye bank collects, evaluates, and distributes donated eyes; unsuitable eyes are used for research and education; donor and recipient identities remain confidential.
One pair of eyes can give vision to up to four corneal blind people.

Activity 10.1 – Refraction through a triangular glass prism

Procedure:
- Fix a sheet of white paper on a drawing board with drawing pins; place a glass prism on it so it rests on its triangular base; trace the outline of the prism.
- Draw a straight line PE inclined to AB (one refracting surface).
- Fix pins at P and Q on PE; look for images of P and Q through the other face AC.
- Place two more pins R and S such that R and S and the images of P and Q lie on a straight line.
- Remove pins and prism; line PE meets boundary at E; extend to meet boundary at F; join E and F.
- Draw perpendiculars to refracting surfaces AB and AC at E and F; mark angles of incidence ∠i, refraction ∠r, and emergence ∠e as shown in Fig. 10.4.
Key concepts: angle of incidence, angle of refraction, angle of emergence, angle of deviation (∠D).

Activity 10.2 – Dispersion and spectrum of white light

Setup: thick cardboard with a narrow slit; sunlight through slit forms a narrow beam; direct it onto a glass prism so the refracted light emerges on a screen.
Observation: a beautiful band of colours appears; the spectrum sequence is Violet, Indigo, Blue, Green, Yellow, Orange, Red (VIBGYOR).
Note: White light is dispersed into seven colours; spectrum is visible because different colours bend by different amounts in the prism.
Newton’s experiment: a second identical prism inverted with respect to the first recombines the spectrum back into white light.
A rainbow is a natural spectrum formed by dispersion of sunlight in water droplets; droplets act as tiny prisms; sunlight is refracted, internally reflected, and refracted again to form colors seen by the observer.
Other notes: red light bends least, violet bends most.

10.5 ATMOSPHERIC REFRACTION

Twinkling of stars is due to atmospheric refraction by a medium with a gradually changing refractive index.
Starlight bends toward the normal entering Earth’s atmosphere; apparent position shifts as atmospheric conditions change; stars appear to twinkle because they are point sources.
Planets do not twinkle because they are extended sources; light from many point sources averages out fluctuations.
The Sun appears to rise earlier and set later due to atmospheric refraction; apparent sunrise is about 2 minutes before actual sunrise; apparent sunset is about 2 minutes after actual sunset; apparent solar disk is flattened at sunrise and sunset due to refraction.

10.6 SCATTERING OF LIGHT

Interplay of light with particles leads to several phenomena; the Tyndall effect arises when light travels through heterogeneous media with fine particles (smoke, dust, mist).
Tyndall effect: a beam becomes visible because particles scatter light; more scattering for smaller particles (blue) and less for larger particles (towards white).
Why is the sky blue?
- Air molecules and small particles scatter shorter wavelengths (blue) more than longer wavelengths (red).
- Red light has wavelength ~1.8 times that of blue; thus blue light is scattered more and enters our eyes, making the sky appear blue.
- In the absence of atmosphere, the sky would appear dark; at high altitude, scattering is reduced, so sky looks dark.

What you have learnt

Accommodation: eye’s ability to focus on near and far objects by adjusting focal length.
Near point: the smallest distance for clear vision without strain; ~25 cm for a normal young adult.
Common refractive defects and corrections: myopia (concave lens), hypermetropia (convex lens), presbyopia (aging-related reduction in accommodation).
Dispersion: splitting of white light into colours by a prism; spectrum sequence: VIBGYOR; dispersion leads to colours.
Scattering: explains blue sky and related phenomena.
Atmospheric refraction effects: twinkling stars, sunrise/sunset displacement, apparent solar disc shape.

EXERCISES

The human eye can focus on 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.

The human eye forms the image of an object at the

(a) cornea.
(b) iris.
(c) pupil.
(d) retina.

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.

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.

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?

Show using $P = \frac{1}{f}$, with f in metres and P in dioptres.

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?
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 near point of normal eye is 25 cm.
Why is a normal eye not able to see clearly objects placed closer than 25 cm?
What happens to the image distance in the eye when we increase the distance of an object from the eye?
Why do stars twinkle?
Explain why the planets do not twinkle.
Why does the sky appear dark instead of blue to an astronaut?

Notes: All numerical references and formulas appear as LaTeX when relevant, e.g., near point $d_{\text{near}} \approx 25\ \text{cm}$, focal lengths and powers related to dioptres $P = \dfrac{1}{f}$, and computed lens powers for exercise 5: for distant vision $P = -5.5\ \text{D}$ giving $f = -\dfrac{1}{5.5} \text{ m} \approx -0.1818\ \text{m} (-18.18\ \text{cm})$; for near vision $P = +1.5\ \text{D}$ giving $f = \dfrac{1}{1.5} \text{ m} \approx 0.666\ \text{m} (66.7\ \text{cm}).