The Human Eye and the Colourful World - Study Notes

10.1 The Human Eye

The eye is one of the most valuable and sensitive sense organs and enables us to see objects and colours around us.
On closing the eyes, we can identify objects by smell, taste, sound, or touch, but not colours—making sight the most significant sense.
The eye can be compared to a camera:
- Its lens system forms an image on a light-sensitive screen called the retina.
- Light enters through the cornea, which forms a transparent bulge on the front surface of the eyeball.
The eyeball is approximately spherical with a diameter of about 2.3 cm.
Refraction: Most bending of light (refraction) occurs at the outer surface of the cornea; the crystalline lens changes focal length for focusing on objects at different distances (fine adjustment).
Iris: Behind the cornea, the iris is a dark muscular diaphragm that controls pupil size. The pupil regulates the amount of light entering the eye.
The eye lens forms an inverted real image on the retina. The retina contains many light-sensitive cells which, when illuminated, generate electrical signals.
These signals are transmitted to the brain via the optic nerves, and the brain processes them to perceive objects as they are.

10.1.1 Power of Accommodation

The eye lens is fibrous and jelly-like; its curvature can be altered by the ciliary muscles.
Change in curvature changes the focal length of the lens:
- When the ciliary muscles are relaxed, the lens becomes thinner and its focal length increases, enabling clear vision of distant objects.
- When looking at near objects, the ciliary muscles contract, increasing lens curvature, making the lens thicker, so the focal length decreases and near objects are focused clearly.
The ability of the eye to adjust focal length for different distances is called accommodation.
There is a minimum focal length beyond which the lens cannot decrease its focal length; reading very close to the eye may blur the image or cause strain.
For comfortable, distinct vision, a near object is typically held at about 25 cm from the eye. The minimum distance for clear vision without strain is the near point of the eye.
- Near point (for a young adult with normal vision): N \,\approx \,25\ \text{cm}
The farthest distance up to which the eye can see clearly is the far point: for a normal eye, this is infinity; hence a normal eye can see clearly from 25 cm to infinity.
Cataract: The crystalline lens can become milky and cloudy with age, causing partial or complete loss of vision. Cataract can be treated with cataract surgery.

10.2 Defects of Vision and Their Correction

The eye can lose accommodation with age or due to refractive defects, causing blurred vision.
Three common refractive defects:
- (i) Myopia (nearsightedness)
- (ii) Hypermetropia (farsightedness)
- (iii) Presbyopia
These defects can be corrected using spherical lenses. Summary:
- Myopia: image of distant objects forms in front of the retina. Corrected with a concave lens.
- Hypermetropia: light from nearby objects is focussed behind the retina. Corrected with a convex lens.
- Presbyopia: reduced accommodation with age; near point recedes. Corrected with glasses; often bi-focal lenses.
Bi-focal lenses: a common type combines both concave and convex lenses:
- Upper portion: concave lens for distant vision.
- Lower portion: convex lens for near vision.
Modern corrections include contact lenses and surgical interventions.

(a) Myopia (near-sightedness)

A myopic person can see nearby objects clearly but distant objects appear blurred.
Far point is nearer than infinity; the image of a distant object forms in front of the retina.
Causes:
- Excessive curvature of the eye lens, or
- Elongation of the eyeball.
Correction: a concave lens of suitable power. (Fig. 10.2)

(b) Hypermetropia (far-sightedness)

A hypermetropic person can see distant objects clearly but has difficulty with nearby objects.
Near point is farther away than the normal near point (25 cm).
Causes:
- Focal length of the eye lens is too long, or
- Eyeball is too small.
Correction: a convex lens of appropriate power.
Eye-glasses with converging lenses provide the extra focusing power needed to form the image on the retina (Fig. 10.3).

With ageing, the eye’s accommodation power decreases and the near point recedes.
People find it difficult to see nearby objects clearly without corrective glasses.
Correction: reading glasses or bi-focal lenses; often, bi-focals combine both near and distance correction as described above.
Bi-focals are a common solution; modern options also include contact lenses and surgical interventions.

10.3 Refraction Through a Prism

A triangular prism has two triangular bases and three rectangular lateral surfaces. The angle between its two lateral faces is called the angle of the prism.
Refraction through a prism causes dispersion (splitting) of white light into its component colours.
Activity 10.1 (summary): Refraction through a triangular glass prism
- Trace the outline of the prism on white paper.
- Draw a line PE inclined to a refracting surface AB.
- Place pins P and Q on PE and observe the images of these pins through the opposite face AC.
- Place pins R and S so that lines PR, QS and their images are aligned.
- Remove the prism; join E and F and extend; draw perpendiculars to the surfaces at E and F; mark angles of incidence i, refraction r, and emergence e as shown in the schematic Fig. 10.4.
The line PE meets the boundary of the prism at E. The lines joining the boundary points form a crossed geometry used to study refraction inside the prism.
This activity helps illustrate Snell’s law in a prism context and reveals the emergence direction differs from the incident direction due to the prism geometry.

Note: Eye donation information is included in this section as part of ethical and social context related to vision.

10.4 Dispersion of White Light by a Glass Prism

Dispersion: white light splits into its constituent colours when passed through a prism.
The prism splits white light into a spectrum of colours: Violet, Indigo, Blue, Green, Yellow, Orange, Red (sequence remembered by VIBGYOR).
Spectrum: the band of colours produced by dispersion.
Why colours appear: different colours bend by different amounts when passing through the prism; red bends least, violet bends most.
Newton's experiment: using a second identical prism in an inverted arrangement reconstituted white light, proving sunlight is made of seven colours.
White light is often characterized by its spectrum; a rainbow is a natural spectrum seen in the sky after rain.
Rainbow formation mechanism: dispersion of sunlight by tiny water droplets, internal reflection inside droplets, and refraction on exit.
Figures referenced: Fig. 10.5 (dispersion), Fig. 10.6 (recombination), Fig. 10.7 (rainbow in sky), Fig. 10.8 (rainbow formation with droplets).

10.5 Atmospheric Refraction

Turbulent air above hot surfaces causes apparent wavering or flickering of objects—due to varying refractive index of air (atmospheric refraction).
Twinkling of stars: starlight refracted as it passes through a medium with changing refractive index in the atmosphere; stars appear to glitter because they are point sources.
Apparent star position shifts: stars appear higher near the horizon due to refraction.
Planets do not twinkle: they are extended sources, so the tiny fluctuations average out, producing a steady light.
Advanced sunrise/sunset effects: the Sun is visible about 2 minutes before actual sunrise and about 2 minutes after actual sunset due to atmospheric refraction; the Sun's disc appears flattened at the horizon during sunrise/sunset due to the same phenomenon.
Figure 10.9 depicts the apparent position of stars due to atmospheric refraction; Fig. 10.10 shows sunrise and sunset timing differences.

10.6 Scattering of Light

Scattering phenomena arise when light interacts with particles in the environment, giving rise to spectacular natural effects.

10.6.1 Tyndall Effect

The atmosphere contains a mixture of minute particles (smoke, dust, mist, dust, etc.). A beam of light becomes visible when it scatters off these particles.
This scattering makes the path of the beam visible in smoke-filled rooms or through canopies of dense forests.
The colour of the scattered light depends on particle size: very fine particles scatter blue light more than red; larger particles scatter longer wavelengths and may appear white.

10.6.2 Why is the Colour of the Clear Sky Blue?

Air molecules and fine particles are smaller than the wavelength of visible light.
Shorter wavelengths (blue end) scatter more strongly than longer wavelengths (red end) when sunlight passes through the atmosphere.
The scattered blue light entering our eyes makes the sky appear blue.
If there were no atmosphere, the sky would look dark; at high altitudes, scattering is reduced, so the sky appears darker.
The red colour of danger signal lights is due to them being least scattered by fog or smoke, allowing visibility at a distance.

What You Have Learnt

Accommodation: The eye’s ability to focus on near and distant objects by adjusting its focal length.
Near point: The smallest distance from the eye at which objects are seen clearly without strain (for a normal eye, about N \approx 25\ \text{cm}).
Refractive defects: myopia, hypermetropia, presbyopia; corrections via lenses; bi-focal lenses can correct both distant and near vision.
Dispersion: Splitting of white light into its component colours by a prism; spectrum: \text{VIBGYOR}; color order; Newton’s prism experiment and recombination.
Scattering and atmospheric optics: blue sky; rainbow formation; twinkling of stars and apparent sunrise/sunset effects due to atmospheric refraction.
Basic ideas of cataract and eye donation (ethical, social context).

Think it over

It is possible to donate eyes after death to help others see.
About 35 million people in the developing world are blind; around 4.5 million have corneal blindness and can be cured by corneal transplantation.
Eye donation facts:
- Donors can be of any age and sex; wearing spectacles or prior cataract surgery does not prevent donation.
- People with diabetes, hypertension, asthma, or those without communicable diseases can donate.
- Eye bank processes involve removal within 4–6 hours of death, a simple process lasting 10–15 minutes, and confidentiality of donor/recipient identities.
- Some donated eyes are unsuitable for transplantation and are used for research/education.
- One pair of donated eyes can give vision to up to four corneal blind people.

Questions?

1) What is meant by the power of accommodation of the eye?
2) A person with a myopic eye cannot see objects beyond 1.2 m distinctly. What should be the type of corrective lens used to restore proper vision?
3) What is the far point and near point of the human eye with normal vision?
4) A student has difficulty reading the blackboard from the last row. What could be the defect?
How can it be corrected?

10.6 EXERCISES (Multiple Choice Questions)

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 distant vision. For correcting near vision, he needs a lens of power +1.5 dioptres. What are the focal lengths for (i) distant vision correction and (ii) near vision correction?

(i) ( f = \frac{1}{-5.5}\ \text{m} \approx -0.1818\ \text{m} = -18.2\ \text{cm} )
(ii) ( f = \frac{1}{+1.5}\ \text{m} \approx 0.6667\ \text{m} = 66.7\ \text{cm} )

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: Diverging lens with power (P = -\frac{1}{0.80}\,\text{D} = -1.25\,\text{D})

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 the near point of the normal eye is 25 cm.

Required lens power ≈ +3.0 D (using P = 1/0.25 − 1/1.0 = 4 − 1 = 3 D).

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

Because the near point of a normal eye is about 25 cm; the eye cannot increase its accommodation further to form a focused image on the retina for closer objects.

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

The image distance (distance from lens to retina) remains essentially fixed on the retina; the eye changes focal length (accommodation) to keep the image in focus on the retina.

Why do stars twinkle?

Because atmospheric refraction changes due to the Earth's atmosphere (refractive index varies), causing the star’s light to bend differently and its apparent position and brightness to vary.

Explain why the planets do not twinkle.

Planets are relatively close and appear as extended sources; the sum of many tiny point sources averages out fluctuations, so planets do not appear to twinkle like stars.

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

In space (no atmosphere), there is no scattering of sunlight by atmospheric particles; hence the sky appears dark.