The Human Eye and the Colourful World Comprehensive Study Notes

Anatomy and Function of the Human Eye

The human eye is a highly sensitive and valuable sense organ that acts similarly to a camera, allowing humans to perceive the world and its various colours. Unlike identification of objects through smell, taste, sound, or touch, the identification of colours is only possible through sight. The eye functions by using a lens system to form an inverted real image on a light-sensitive screen known as the retina. Light enters the eye through a thin membrane called the cornea, which forms a transparent bulge on the front surface of the eyeball. The eyeball itself is approximately spherical in shape, possessing a diameter of about $2.3\,cm$. Most of the refraction for incoming light rays occurs at the outer surface of the cornea. Behind the cornea lies the iris, a dark muscular diaphragm responsible for controlling the size of the pupil. The pupil, in turn, regulates and controls the amount of light that enters the eye. The crystalline lens is located behind the pupil and provides the finer adjustment of focal length necessary to focus objects at different distances onto the retina. The retina is a delicate membrane containing an enormous number of light-sensitive cells that activate upon illumination to generate electrical signals. These signals are transmitted to the brain via the optic nerves, where the brain interprets and processes the information so that objects are perceived in their true orientation and form.

Power of Accommodation and Adjusting Vision

The eye lens is composed of a fibrous, jelly-like material, and its curvature can be modified by the ciliary muscles. This modification of curvature changes the focal length of the lens, a process known as accommodation. When ciliary muscles are in a relaxed state, the eye lens becomes thin, and its focal length increases, which enables the eye to see distant objects clearly. Conversely, when looking at nearby objects, the ciliary muscles contract, which increases the curvature and thickness of the eye lens, thereby decreasing its focal length. This allows for the clear visualization of nearby objects. However, there is a minimum limit to how much the focal length can decrease. To see an object comfortably and distinctly without strain, it must be held at the least distance of distinct vision, also known as the near point of the eye. For a young adult with normal vision, the near point is approximately $25\,cm$. The farthest point up to which the eye can see objects clearly is the far point, which is at infinity for a normal eye. A normal eye can thus see objects clearly between $25\,cm$ and infinity. In some older individuals, the crystalline lens may become milky and cloudy, a condition known as a cataract. This condition leads to partial or complete loss of vision but can often be restored through cataract surgery.

Primary Refractive Defects of Vision and Their Correction

Vision can become blurred when the eye gradually loses its power of accommodation due to refractive defects. There are three common refractive defects: myopia, hypermetropia, and presbyopia. Myopia, or near-sightedness, allows a person to see nearby objects clearly while distant objects appear blurred. In a myopic eye, the far point is closer than infinity, and the image of a distant object is formed in front of the retina rather than on it. This defect arises from excessive curvature of the eye lens or elongation of the eyeball and is corrected using a concave lens of suitable power. Hypermetropia, or far-sightedness, allows a person to see distant objects clearly while nearby objects are blurred. The near point for a hypermetropic person is farther than the normal $25\,cm$, and light rays from a close object are focused at a point behind the retina. This occurs because the focal length of the eye lens is too long or the eyeball has become too small. It is corrected using a convex (converging) lens of appropriate power. Presbyopia is a defect associated with ageing, where the near point recedes due to the gradual weakening of ciliary muscles and diminishing flexibility of the eye lens. Some individuals may suffer from both myopia and hypermetropia, requiring bi-focal lenses. In a bi-focal lens, the upper portion is a concave lens for distant vision, and the lower part is a convex lens for near vision. Modern corrections also include contact lenses or surgical interventions.

Ethics and Procedures of Eye Donation

Human eyes can be donated after death to restore sight to the blind, particularly those suffering from corneal blindness. In the developing world, approximately $35$ million people are blind, and about $4.5$ million of these cases involve corneal blindness that could be cured through transplantation. Notably, $60\%$ of those with corneal blindness are children under the age of $12$. Eye donors can be of any age or sex. Individuals who use spectacles, have had cataract surgery, or suffer from conditions like diabetes, hypertension, and asthma can still donate their eyes, provided they do not have communicable diseases. Eyes must be removed within $4$ to $6$ hours after death, and the process, which takes only $10$ to $15$ minutes, can be performed at a home or hospital without causing disfigurement. However, those who died from or were infected with AIDS, Hepatitis B or C, rabies, acute leukaemia, tetanus, cholera, meningitis, or encephalitis are ineligible for donation. Donated eyes are evaluated by eye banks; those unsuitable for transplant are used for medical research and education. One pair of donated eyes can provide vision for up to four people suffering from corneal blindness.

Refraction of Light Through a Triangular Glass Prism

A triangular glass prism consists of two triangular bases and three rectangular lateral surfaces inclined toward each other. The angle between the two lateral faces is defined as the angle of the prism ($\angle A$). In a rectangular glass slab, the emergent ray is parallel to the incident ray but laterally displaced. In a prism, however, the peculiar shape causes the emergent ray to bend at an angle relative to the direction of the incident ray. This specific angle is known as the angle of deviation ($\angle D$). When a light ray enters the prism, it moves from air to glass at the first surface, bending toward the normal. Upon exiting the glass into air at the second surface, it bends away from the normal. The specific path involves the incident ray ($PE$), the refracted ray ($EF$), and the emergent ray ($FS$). The angle of incidence is denoted as $\angle i$, the angle of refraction as $\angle r$, and the angle of emergence as $\angle e$.

Dispersion of White Light and Rainbow Formation

Dispersion is the phenomenon where white light splits into its component colours when passing through a glass prism. This occurs because different colours of light bend through different angles relative to the incident ray; red light bends the least, while violet light bends the most. This creates a band of distinct colours called a spectrum, remembered by the acronym VIBGYOR: Violet, Indigo, Blue, Green, Yellow, Orange, and Red. Isaac Newton was the first to use a prism to obtain the spectrum of sunlight. He demonstrated that sunlight is composed of seven colours by using a second, identical, inverted prism to recombine the spectrum back into white light. A rainbow is a natural application of this phenomenon, appearing in the sky opposite the Sun after rain. Tiny water droplets in the atmosphere act as small prisms; they refract and disperse incident sunlight, then reflect it internally, and finally refract it again as it exits the droplet. This combination of dispersion and internal reflection allows the various colours to reach the observer's eye.

Atmospheric Refraction and Its Natural Effects

Atmospheric refraction is the refraction of light by the Earth's atmosphere, which occurs because the atmosphere consists of layers with gradually changing refractive indices. Hotter air is less dense and has a lower refractive index than cooler air. This causes several optical phenomena. The flickering or wavering of objects seen through hot air is a local effect of this refraction. On a larger scale, the twinkling of stars is caused by the continuous refraction of starlight as it enters the atmosphere. Because stars are distant point-sized sources, the path of light varies slightly due to non-stationary atmospheric conditions, causing the star to appear to flicker in brightness and change position slightly. Planets do not twinkle because they are much closer and act as extended sources; the variations from individual points within the planet average out to zero. Atmospheric refraction also causes the Sun to be visible about $2\,minutes$ before the actual sunrise and $2\,minutes$ after the actual sunset, resulting from the bending of light over the horizon. It also causes the Sun’s disc to appear flattened at sunrise and sunset.

Scattering of Light and the Tyndall Effect

The Earth's atmosphere is a heterogeneous mixture containing smoke, water droplets, dust, and air molecules. When light strikes these fine particles, it is reflected diffusely, making the path of the beam visible—a phenomenon known as the Tyndall effect. This can be seen when sunlight enters a smoke-filled room or passes through a forest canopy. The colour of the scattered light depends on the size of the scattering particles. Molecules of air and other fine particles are smaller than the wavelength of visible light and are more effective at scattering shorter wavelengths (blue) than longer wavelengths (red). Red light has a wavelength approximately $1.8\,times$ greater than blue light. Consequently, sunlight passing through the atmosphere has its blue component scattered most strongly, which is why the clear sky appears blue. At very high altitudes, such as for those in space or high-flying aircraft, the sky appears dark because scattering is not prominent. Red is used for 'danger' signal lights because it is the colour least scattered by fog or smoke, allowing it to be seen from a distance.

Questions & Discussion

1. What is meant by power of accommodation of the eye? Response: The ability of the eye lens to adjust its focal length to focus on both near and distant objects is called accommodation.

2. A person with a myopic eye cannot see objects beyond $1.2\,m$ distinctly. What should be the type of the corrective lens used to restore proper vision? Response: A concave lens of suitable power should be used to correct myopia.

3. What is the far point and near point of the human eye with normal vision? Response: For a normal eye, the near point is about $25\,cm$ and the far point is at infinity.

4. A student has difficulty reading the blackboard while sitting in the last row. What could be the defect the child is suffering from? How can it be corrected? Response: The student is suffering from myopia (near-sightedness). This can be corrected by using a concave lens of suitable power.