The Human Eye

The human eye is a remarkable sense organ that allows us to perceive the visual world. It functions much like a camera, with a lens system that forms an image on a screen called the retina.

Structure of the human eye:

• **Cornea:** A thin, transparent, bulging membrane on the front surface of the eyeball. Most of the refraction of light entering the eye occurs at the outer surface of the cornea.
• **Iris:** A dark, muscular diaphragm located behind the cornea. It controls the size of the pupil.
• **Pupil:** The opening in the center of the iris. It regulates and controls the amount of light entering the eye. In bright light, the iris constricts the pupil; in dim light, it expands the pupil.
• **Crystalline lens (Eye lens):** A fibrous, jelly-like, transparent structure behind the iris. It is a biconvex lens. It provides the finer adjustment of focal length needed to focus light from objects at different distances onto the retina.
• **Ciliary muscles:** Muscles attached to the eye lens. They can change the curvature (and thus focal length) of the eye lens.
• **Retina:** A delicate, light-sensitive screen at the back of the eyeball. It contains a large number of light-sensitive cells (rods and cones). The eye lens forms a real, inverted image of the object on the retina.
• **Optic nerves:** Nerves that transmit electrical signals generated by the light-sensitive cells on the retina to the brain.

When light falls on the retina, the light-sensitive cells get activated and generate electrical signals. These signals are sent to the brain via the optic nerves. The brain interprets these signals, processes the information, and enables us to see objects upright and in their actual form.

The eyeball is approximately spherical, with a diameter of about 2.3 cm.

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Power Of Accommodation

The human eye lens is unique because its **focal length can be adjusted** to focus light from objects at different distances onto the retina. This ability is called **power of accommodation** and is achieved by the action of the ciliary muscles.

• When looking at **distant objects**, the ciliary muscles are relaxed. This causes the eye lens to become thinner, increasing its focal length. Distant objects are then focused clearly on the retina.
• When looking at **nearby objects**, the ciliary muscles contract. This increases the curvature of the eye lens, making it thicker and decreasing its focal length. Nearby objects are then focused clearly on the retina.

The focal length of the eye lens cannot be decreased beyond a certain limit. The minimum distance at which objects can be seen most distinctly without strain is called the **least distance of distinct vision** or the **near point** of the eye. For a young adult with normal vision, the near point is about **25 cm**.

The farthest point upto which the eye can see objects clearly is called the **far point** of the eye. For a normal eye, the far point is at **infinity**. A normal eye can comfortably see objects located anywhere between 25 cm and infinity.

With ageing, the crystalline lens can become cloudy and opaque, a condition called **cataract**, causing partial or complete vision loss. Cataract surgery can restore vision.

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Defects Of Vision And Their Correction

Sometimes, the eye's ability to focus light correctly is impaired, leading to refractive defects of vision. These defects cause blurred vision because the image is not formed sharply on the retina. Common refractive defects can often be corrected using suitable spherical lenses (in spectacles or contact lenses).

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Myopia (Near-Sightedness)

**Myopia**, or near-sightedness, is a defect where a person can see nearby objects clearly but has difficulty seeing distant objects distinctly. In a myopic eye, the image of a distant object is formed **in front of the retina** instead of directly on it.

Causes of myopia:

• Excessive curvature of the eye lens (lens is too converging).
• Elongation of the eyeball (image falls short of the retina).

Correction of myopia: Myopia is corrected by using a **concave lens** (diverging lens) of suitable power. The concave lens diverges the incoming distant light rays slightly before they enter the eye, so that the eye lens can then focus them correctly onto the retina.

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Hypermetropia (Far-Sightedness)

**Hypermetropia**, or far-sightedness, is a defect where a person can see distant objects clearly but has difficulty seeing nearby objects distinctly. The near point of a hypermetropic eye is farther away than the normal 25 cm. When looking at nearby objects, the image is formed **behind the retina**.

Causes of hypermetropia:

• The focal length of the eye lens is too long (lens is not converging enough).
• The eyeball has become too short (retina is too close to the lens).

Correction of hypermetropia: Hypermetropia is corrected by using a **convex lens** (converging lens) of appropriate power. The convex lens provides the additional converging power needed to focus the light rays from nearby objects correctly onto the retina.

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Presbyopia

**Presbyopia** is a defect related to ageing. The power of accommodation of the eye decreases with age, primarily due to the gradual weakening of the ciliary muscles and decreased flexibility of the eye lens. This makes it difficult to see nearby objects comfortably and distinctly; the near point recedes.

Presbyopia can be corrected by using **convex lenses**. Sometimes, a person may suffer from both myopia and hypermetropia (e.g., difficulty seeing both far and near objects). In such cases, they often require **bi-focal lenses**, which combine both concave and convex lenses (upper part typically concave for distant vision, lower part typically convex for near vision).

Refractive defects can also be corrected using contact lenses or surgical procedures.

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Refraction Of Light Through A Prism

Unlike a rectangular glass slab with parallel refracting surfaces, a glass prism has two inclined refracting surfaces. When light passes through a prism, it undergoes refraction at both surfaces, but the emergent ray is not parallel to the incident ray.

Consider a triangular glass prism. A ray of light incident on one refracting surface enters the prism and bends towards the normal (as it goes from air to glass). Inside the prism, it travels in a straight line. When it exits the prism from the second refracting surface (glass to air), it bends away from the normal. The peculiar geometry of the prism causes the emergent ray to bend at an angle to the direction of the incident ray. This angle is called the **angle of deviation** ($\angle D$).

In the diagram (Fig 10.4 in textbook): PE is the incident ray, EF is the refracted ray, FS is the emergent ray. $\angle i$ is the angle of incidence, $\angle r$ is the angle of refraction, $\angle e$ is the angle of emergence, $\angle A$ is the angle of the prism, and $\angle D$ is the angle of deviation (the angle between the direction of the incident ray and the direction of the emergent ray).

Dispersion Of White Light By A Glass Prism

A fascinating phenomenon occurs when white light (like sunlight) passes through a glass prism – it splits into its component colours. This splitting of white light into its constituent colours is called **dispersion**.

When a narrow beam of white light is incident on a glass prism, the light is refracted upon entering the prism. Inside the prism, the different colours that make up white light travel at slightly different speeds. This causes them to bend at slightly different angles relative to the incident direction.

The extent of bending is different for each colour: **Violet light bends the most**, while **Red light bends the least**. This differential bending causes the colours to separate. Upon emerging from the prism, the colours are separated, forming a band of distinct colours called a **spectrum**.

The sequence of colours in the spectrum of white light is commonly remembered by the acronym **VIBGYOR**: Violet, Indigo, Blue, Green, Yellow, Orange, Red.

Isaac Newton demonstrated that white light is composed of these seven colours. He showed that a second identical prism placed inverted relative to the first can recombine the dispersed spectrum back into white light, confirming that the prism does not create the colours but merely separates existing ones.

A **rainbow** is a natural spectrum formed by the dispersion of sunlight by tiny water droplets (from rain or mist) in the atmosphere. These water droplets act like small prisms. Sunlight enters the droplet, is refracted and dispersed, undergoes internal reflection at the back surface, and is refracted again upon emerging. The different colours emerge at slightly different angles, reaching an observer's eye to create the visible rainbow arc, always in the direction opposite to the Sun.

Atmospheric Refraction

**Atmospheric refraction** is the refraction (bending) of light as it passes through the Earth's atmosphere. The atmosphere is a layer of air whose density and refractive index change with altitude (denser and higher refractive index near the surface, less dense and lower refractive index higher up). Light from celestial objects undergoes continuous refraction as it passes through these layers with varying optical densities before reaching our eyes. This phenomenon leads to several optical effects.

Observing objects through rising hot air (e.g., above a fire) shows wavering due to local atmospheric refraction caused by variations in air density and refractive index.

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Twinkling Of Stars

The **twinkling of stars** is a phenomenon caused by atmospheric refraction. Stars are very distant and appear as point sources of light. As starlight enters the Earth's atmosphere, it undergoes continuous refraction through layers of air with varying refractive indices (due to changes in temperature and density). The path of starlight is slightly bent towards the normal as it enters denser lower layers. This causes the apparent position of the star to appear slightly higher than its actual position when viewed near the horizon.

Because the atmospheric conditions (density, temperature, refractive index) are constantly fluctuating and turbulent, the path of starlight varies slightly over time. This causes the amount of starlight entering the eye to flicker – sometimes appearing brighter, sometimes fainter. This flickering effect is what we perceive as twinkling.

**Planets do not twinkle**. Planets are much closer to Earth than stars and appear as extended sources of light (like small discs), not point sources. A planet can be considered as a collection of many point sources. The light from individual point sources of a planet might fluctuate, but the total variation in the amount of light received from all the point sources averages out to zero, cancelling the twinkling effect.

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Advance Sunrise And Delayed Sunset

Atmospheric refraction also causes the Sun to be visible to us about 2 minutes before the actual sunrise and about 2 minutes after the actual sunset. When the Sun is slightly below the horizon, sunlight coming from it enters the Earth's atmosphere and undergoes refraction, bending towards the normal. This bending causes the light rays to appear to come from a point above the horizon, making the Sun visible earlier in the morning and later in the evening.

By 'actual sunrise' and 'actual sunset', we mean the moment the Sun actually crosses the horizon. Atmospheric refraction causes the **apparent sunrise** to occur earlier and the **apparent sunset** to occur later, resulting in a difference of about 2 minutes for each. The apparent flattening of the Sun's disc at sunrise and sunset is also attributed to atmospheric refraction.

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Scattering Of Light

**Scattering of light** occurs when light rays interact with particles in a medium and are redirected in various directions. The colour of the scattered light depends on the size of the scattering particles and the wavelength of the incident light.

The Earth's atmosphere contains a mixture of minute particles including molecules of air, dust, smoke, and tiny water droplets.

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Tyndall Effect

The **Tyndall effect** is the phenomenon of scattering of light by colloidal particles. When a beam of light passes through a colloidal solution (or a medium containing fine particles), the path of the light beam becomes visible because the particles scatter the light. This is seen when sunlight enters a dusty or smoke-filled room through a small hole, making the beam visible.

The colour of scattered light depends on particle size:

• Very fine particles (like air molecules) scatter mainly **blue light** (shorter wavelengths).
• Particles of larger size scatter light of **longer wavelengths** (towards red).
• If particles are large enough, they scatter all wavelengths equally, and the scattered light appears **white**.

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Why Is The Colour Of The Clear Sky Blue?

The clear sky appears blue due to the scattering of sunlight by the molecules of air and other very fine particles in the atmosphere. These particles are much smaller than the wavelength of visible light.

According to the principle of scattering (Rayleigh scattering), the amount of scattering is inversely proportional to the fourth power of the wavelength ($\propto 1/\lambda^4$). Shorter wavelengths (like blue light at the violet-blue end of the spectrum) are scattered much more strongly than longer wavelengths (like red light). Red light has a wavelength about 1.8 times greater than blue light, so blue light is scattered much more effectively.

When sunlight enters the atmosphere, the blue component is scattered in all directions by the air molecules. This scattered blue light reaches our eyes from all parts of the sky, making the sky appear blue. The longer wavelengths (like red and orange) are scattered less and travel relatively straight towards the observer, giving the Sun its reddish appearance at sunrise and sunset when light travels through a larger portion of the atmosphere.

If there were no atmosphere, there would be no scattering, and the sky would appear dark, as seen by astronauts at high altitudes where the atmosphere is very thin.

Danger signals are red because red light is scattered the least by fog or smoke (longer wavelength), making it visible from a greater distance in its original colour.

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Page No. 164

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