Human Eye and Colourful World — Notes

The Human Eye

The human eye is a complex biological organ that functions like a camera, capturing light and converting it into electrical signals that the brain interprets as vision.

The eyeball is roughly spherical with a diameter of about 2.3 cm. Light enters the eye through the cornea, a transparent outer layer at the front. Most of the refraction (bending of light) occurs here.

Behind the cornea is the iris, a dark, muscular diaphragm that acts like the aperture of a camera. The iris controls the size of the pupil, the opening in the center, regulating the amount of light that enters the eye.

The eye lens, a transparent, fibrous, jelly-like structure, is located behind the iris. Its primary role is to make fine adjustments to the focal length to ensure objects at various distances are focused precisely on the retina.

The retina is a light-sensitive membrane lining the back of the eye. It contains millions of light-sensitive cells (rods and cones). When light illuminates these cells, they generate electrical signals.

These signals are transmitted to the brain via the optic nerves. The brain processes these signals, allowing us to perceive the world as it is.

The eye lens forms a real and inverted image of an object on the retina.

Power of Accommodation

The eye lens is made of a fibrous, jelly-like material. Its shape, and therefore its focal length, can be adjusted by the action of the ciliary muscles. This ability of the eye to adjust its focal length to focus on objects at different distances is called the power of accommodation.

• Distant Objects: When viewing distant objects, the ciliary muscles are relaxed. This makes the eye lens thinner, increasing its focal length. A longer focal length allows the eye to focus light from distant objects onto the retina.
• Nearby Objects: When viewing nearby objects, the ciliary muscles contract. This increases the curvature of the eye lens, making it thicker. A shorter focal length allows the eye to focus light from nearby objects onto the retina.

The eye lens has a limit to how much it can change its focal length.

The least distance of distinct vision, also known as the near point, is the minimum distance at which an object can be seen clearly and distinctly without any strain. For a young adult with normal vision, this is approximately 25 cm.

The far point is the farthest distance at which an eye can see objects clearly. For a normal eye, the far point is at infinity.

A normal eye can see objects clearly at distances ranging from 25 cm to infinity.

In old age, the crystalline lens can become opaque and cloudy, a condition called cataract. This can lead to partial or complete loss of vision but can often be corrected with surgery.

Remember

The power of accommodation is the eye's ability to change the focal length of the lens by altering its curvature using ciliary muscles, enabling clear vision of both near and far objects.

Exam-smart

A question might present a scenario where someone is struggling to read a book held very close. This implies their near point has shifted, and you would need to identify this as a potential issue with accommodation or the eye's ability to decrease its focal length. You might also be asked to explain how the ciliary muscles and lens shape change for near vs. far vision.

Defects of Vision and Their Correction

The human eye's ability to adjust its focal length to see objects at different distances clearly is called accommodation. However, sometimes this ability diminishes, leading to blurred vision. These visual impairments are often due to refractive defects where light is not focused precisely on the retina. The three main refractive defects are:

1. Myopia (Near-sightedness): Difficulty seeing distant objects clearly.
2. Hypermetropia (Far-sightedness): Difficulty seeing near objects clearly.
3. Presbyopia: Age-related loss of accommodation, making near vision difficult.

These defects can be corrected using lenses that alter the path of light to ensure it focuses correctly on the retina.

Myopia

Myopia, also known as near-sightedness, is a refractive defect where a person can see nearby objects clearly but distant objects appear blurred.

• Cause: In a myopic eye, the image of distant objects is formed in front of the retina, not on it. This can happen due to:
• Excessive curvature of the eye lens: The lens becomes too curved, increasing its refractive power.
• Elongation of the eyeball: The distance between the lens and the retina becomes too long.
• Correction: Myopia is corrected by using a concave lens. A concave lens diverges the incoming light rays before they enter the eye, effectively shifting the focal point back onto the retina.
• Far Point: The far point of a myopic eye is closer than infinity. This means the person can only see objects clearly up to a certain distance, which is less than infinity.

Hypermetropia

Hypermetropia, also known as far-sightedness, is a refractive defect where a person can see distant objects clearly but nearby objects appear blurred.

• Cause: In a hypermetropic eye, the image of nearby objects is focused behind the retina. This occurs because:
• The focal length of the eye lens is too long: The lens has too little refractive power.
• The eyeball has become too short: The distance between the lens and the retina is insufficient.
• Correction: Hypermetropia is corrected by using a convex lens. A convex lens converges the light rays, increasing the overall refractive power of the eye and bringing the focal point onto the retina.
• Near Point: The near point of a hypermetropic eye is farther away than the normal near point (25 cm). This requires the person to hold reading material further away from their eyes.

Presbyopia

Presbyopia is an age-related condition where the eye's ability to accommodate for near vision decreases.

• Cause: It typically arises due to the gradual weakening of the ciliary muscles and the diminishing flexibility of the crystalline lens with age.
• Effect: People with presbyopia find it difficult to see nearby objects clearly and comfortably.
• Correction: Presbyopia is often corrected with convex lenses. If a person has both myopia and hypermetropia, they may need bifocal lenses, which have both concave and convex portions to address both defects. Modern corrections include contact lenses and surgical interventions.

Refraction of Light Through a Prism

A transparent prism, typically triangular, has two inclined refracting surfaces. When light enters a prism from one medium to another (e.g., air to glass), it refracts (bends).

• Angle of Prism (A): The angle between the two inclined refracting surfaces.
• Refraction:
• When light enters the prism from air (rarer to denser medium), it bends towards the normal.
• When light exits the prism into air (denser to rarer medium), it bends away from the normal.
• Angle of Deviation (D): The angle between the direction of the incident ray and the direction of the emergent ray. The shape of the prism causes the emergent ray to deviate from its original path.

Dispersion of White Light by a Glass Prism

When white light (like sunlight) passes through a prism, it splits into its constituent colours. This phenomenon is called dispersion.

• Spectrum: The band of colours produced is called the spectrum of white light. The colours in the spectrum of white light, in order, are Violet, Indigo, Blue, Green, Yellow, Orange, and Red (VIBGYOR).
• Cause: Different colours of light have different wavelengths and hence bend by different amounts when passing through the prism.
• Violet light bends the most.
• Red light bends the least.
• Newton's Experiment: Isaac Newton demonstrated this by passing sunlight through a prism and then passing the resulting spectrum through a second, inverted prism. The second prism recombined the colours to produce white light, proving that white light is composed of these colours.
• Rainbow: A rainbow is a natural spectrum caused by the dispersion of sunlight by tiny water droplets in the atmosphere, acting like small prisms. Sunlight undergoes refraction, internal reflection, and then refraction again as it passes through the raindrops.

Atmospheric Refraction

Atmospheric refraction is the bending of light rays as they pass through the Earth's atmosphere due to variations in air density and refractive index.

• Twinkling of Stars:
• Stars appear to twinkle because their light, travelling vast distances, undergoes continuous, slight variations in refraction as it passes through the Earth's atmosphere.
• The atmospheric conditions are not static, causing the apparent position and brightness of the star to fluctuate, leading to the twinkling effect.
• Planets do not twinkle because they are much closer to Earth and appear as extended sources rather than point sources. The light from different parts of a planet averages out the twinkling effect.
• Advance Sunrise and Delayed Sunset:
• The Sun appears to rise about 2 minutes earlier and set about 2 minutes later than its actual occurrence.
• This is because the atmosphere refracts sunlight, making the Sun visible even when it is slightly below the horizon.

Scattering of Light

Scattering of light is the phenomenon where light rays, upon striking small particles in the atmosphere, are deflected in various directions.

Tyndall Effect

The Tyndall effect is the scattering of light by particles in a colloid or a sufficiently fine suspension.

• Observation: When a beam of light passes through a medium containing suspended particles (like smoke, dust, or water droplets), the path of the light beam becomes visible.
• Cause: The particles in the medium scatter the incident light, making the beam visible. This is observed in smoke-filled rooms or through a forest canopy.
• Colour Dependence: The colour of the scattered light depends on the size of the scattering particles and the wavelength of the light.

Why is the colour of the clear Sky Blue?

The blue colour of the sky is a result of the scattering of sunlight by the tiny molecules and particles in the Earth's atmosphere.

• Rayleigh Scattering: The particles in the atmosphere (mainly air molecules) are much smaller than the wavelengths of visible light. These particles scatter shorter wavelengths (blue and violet light) much more effectively than longer wavelengths (red and orange light). This phenomenon is known as Rayleigh scattering.
• Observation: While violet light is scattered even more than blue light, our eyes are more sensitive to blue light, and some violet light is absorbed by the upper atmosphere. Therefore, the sky appears predominantly blue.
• Dark Sky at High Altitudes: At very high altitudes, where the atmosphere is thinner, scattering is less prominent, and the sky appears dark.
• Red Sunsets/Sunrises: At sunrise and sunset, sunlight travels through a greater thickness of the atmosphere. Most of the blue light is scattered away, leaving the longer wavelengths (red and orange) to reach our eyes, making the sun appear reddish.

Remember

The order of colours in the spectrum is VIBGYOR, where V is for Violet (least wavelength, most bending) and R is for Red (longest wavelength, least bending).

Exam-smart

Case studies often involve scenarios describing vision problems and asking to identify the defect (myopia, hypermetropia, presbyopia) and suggest the appropriate corrective lens (concave, convex, or bifocal) based on the description of what the person can or cannot see clearly. For example, a person unable to see distant hoardings clearly but able to read a newspaper comfortably suffers from myopia and needs a concave lens.

Hypermetropia

Hypermetropia, also known as far-sightedness, is a refractive defect of the human eye where the image of nearby objects is focused beyond the retina. This means that while distant objects may be seen clearly, near objects appear blurred.

How Hypermetropia Occurs

This condition arises because:

• The eyeball is too short.
• The eye lens has become too thin, or its power of accommodation is insufficient to increase its converging power adequately.

In a normal eye, the ciliary muscles contract to increase the curvature of the eye lens, thus increasing its power and decreasing its focal length, allowing us to see nearby objects clearly. In hypermetropia, this adjustment is either not enough, or the focal length of the eye lens becomes too long, causing light rays from nearby objects to converge behind the retina instead of on it.

Correction of Hypermetropia

Hypermetropia can be corrected by using a convex lens of appropriate power. A convex lens converges the light rays before they enter the eye. This increased convergence helps to focus the image of nearby objects precisely on the retina.

• Diagrammatic Representation: A diagram would typically show parallel rays from a distant object focusing on the retina. For a nearby object, the rays diverge more. In a hypermetropic eye, without correction, these rays would focus behind the retina. When a convex lens is placed in front of the eye, it bends the diverging rays inward, effectively shifting the focal point forward onto the retina.
• Calculating Lens Power: The power of the corrective lens ($P$) is determined by the near point of the defective eye and the near point of a normal eye. If the near point of the hypermetropic eye is $D_n$ (which is greater than 25 cm) and the near point of a normal eye is $D$ (taken as 25 cm or 0.25 m), the required focal length ($f$) of the convex lens is given by:

The power ($P$) in dioptres is then calculated as $P=\frac{1}{f(\text{in metres})}$.

Example Calculation (as in Exercise 7)

• Near point of hypermetropic eye ($D_n$) = 1 m = 100 cm
• Near point of normal eye ($D$) = 25 cm
• The object is placed at 25 cm, and the eye needs to form a clear image at 100 cm. The lens should create a virtual image of the object at 25 cm at the position where the hypermetropic eye can see it clearly (100 cm).
• Let the object distance be $u=-25$ cm (conventionally negative as it is on the left of the lens).
• The image should be formed at the near point of the hypermetropic eye, so $v=-100$ cm.
• Using the lens formula: $\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

So, $f=\frac{100}{3}$ cm.

• To calculate power, we need focal length in metres: $f=\frac{100}{3}\text{ cm}=\frac{1}{3}\text{ m}$.
• Power $P=\frac{1}{f(\text{in metres})}=\frac{1}{1\mathrm{/}3}=+3$ dioptres.

Presbyopia

Presbyopia is another refractive defect of vision that typically occurs with old age. It is characterized by the loss of the eye's power of accommodation. As people age, the flexibility of the eye lens decreases, and the ciliary muscles may also weaken. This makes it difficult for the eye to adjust its focal length to focus on nearby objects. Consequently, elderly individuals often find it challenging to read small print or perform close-up tasks.

Presbyopia can be corrected using bifocal lenses, which have two different powers: one for distant vision (usually a concave lens) and one for near vision (a convex lens).

Remember

Hypermetropia involves focusing behind the retina, requiring a convex lens to add converging power. Presbyopia is age-related loss of accommodation, also often corrected with convex lenses for near vision.

Exam-smart

A case study might describe a person who can see distant objects clearly but struggles with reading a book. You would need to identify this as hypermetropia and suggest a convex lens. For presbyopia, the clue would be the age of the person and difficulty with near tasks, often requiring bifocal lenses. The calculation of lens power from the near point is a common application.