Olympiad Notes: Human Eye and Colourful World

Table of Contents
1. Human Eye
2. Eye Defects and Corrections
3. Refraction through a Prism
4. Rainbow Formation
5. Atmospheric Refraction
6. Scattering of Light
7. Tyndall Effect
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Human Eye

The human eye is a naturally occurring optical instrument that enables vision by forming images of objects on a light-sensitive surface and converting them into electrical signals for the brain. Humans normally have a pair of eyes placed in the eye sockets of the skull which protect and support them.

Structure of the Eye

The eye is approximately spherical with a slight anterior bulge. Its wall is made up of three main concentric layers and contains fluids and optical elements that enable image formation.

Layers of the Eye

• Sclera: The tough, white outer coat which protects the internal structures and maintains the shape of the eyeball.
• Choroid: The middle, vascular layer rich in blood vessels that supplies oxygen and nutrients to the retina and reduces internal reflection of light inside the eye.
• Retina: The innermost, light-sensitive layer that acts as the screen where images are formed. It contains photoreceptor cells (rods and cones) and neural layers that begin processing visual information.

Main Optical Parts and Supporting Structures

• Cornea: The transparent, dome-shaped front window of the eye that admits and refracts light entering the eye.
• Iris: The coloured muscular diaphragm that surrounds the pupil and controls its diameter, regulating the amount of light entering the eye.
• Pupil: The central aperture in the iris through which light passes. It appears black because most incident light is absorbed by the tissues inside the eye.
• Lens: A transparent, flexible, biconvex structure that further refracts light to help form a clear image on the retina. It is a converging (convex) lens.
• Ciliary muscles and suspensory ligaments: The ciliary muscles change the tension on the suspensory ligaments to alter the curvature (and therefore focal length) of the lens during accommodation.
• Retinal special points: The yellow spot (fovea) is a small region of the retina where visual acuity is highest. The blind spot (optic disc) is where the optic nerve leaves the eye; no photoreceptor cells are present there.
• Optic nerve: The bundle of nerve fibres that transmits visual information from the retina to the brain.

Aqueous and Vitreous Humours

Aqueous humour

The aqueous humour is a clear, watery fluid. Aqueous humour fills the space between cornea and lens (anterior chamber and posterior chamber separately divided by iris).

• Function: It maintains intraocular pressure, nourishes the cornea and lens (which are avascular), and helps keep the anterior tissues moist and healthy.

Vitreous humour

The vitreous humour is a transparent, gelatinous substance that fills the large space between the lens and the retina (the vitreous chamber).

• Function: It helps maintain the shape of the eyeball, supports the retina, and transmits light to the retina.

Adjustment of Pupil Size

• In bright light: The iris constricts the pupil (miosis) to reduce the amount of light entering the eye and improve image sharpness.
• In dim light: The iris dilates the pupil (mydriasis) to allow more light into the eye and improve visibility.

Accommodation of the Eye

Accommodation is the process by which the eye changes the focal length of the lens to form clear images of objects at different distances on the retina.

• For distant objects: The ciliary muscles relax, the suspensory ligaments become taut, the lens becomes thinner (flatter), and the focal length increases so that the image forms on the retina.
• For near objects: The ciliary muscles contract, suspensory ligaments relax, the lens becomes thicker (more convex), and the focal length decreases so that the image forms on the retina.

Eye Defects and Corrections

Myopia (Short-sightedness)

• Definition: Distant objects appear blurred while nearby objects can be seen clearly.
• Cause: The eyeball is often too long or the cornea/lens system is too powerful, so parallel rays from distant objects are focused in front of the retina.
• Correction: Use of a concave (diverging) lens in spectacles to diverge incoming light rays so that they are focused on the retina.

Hypermetropia / Hyperopia (Long-sightedness)

• Definition: Near objects appear blurred while distant objects are relatively clear.
• Cause: The eyeball is too short or the lens system is too weak, so light from nearby objects is focused behind the retina.
• Correction: Use of a convex (converging) lens in spectacles to increase the converging power so that images form on the retina.

Presbyopia

• Definition: An age-related gradual loss of the eye's ability to accommodate (focus) on near objects due to reduced elasticity of the lens and weakening of ciliary muscles.
• Effect: Difficulty in seeing nearby objects; reading text at normal close distances becomes harder with age.
• Correction: Bifocal lenses or other multifocal lens designs provide different powers for near and distant vision.

Refraction through a Prism

• Prism: A transparent optical element with two plane refracting surfaces that meet along a line called the refracting edge; a triangular prism has a triangular cross-section perpendicular to the refracting edge.
• Refracting surfaces: The two plane faces where refraction occurs.
• Angle of the prism: The angle between the two refracting surfaces; it influences the deviation of a light ray passing through the prism.
• Principal section: The cross-section of the prism perpendicular to the refracting edge, used for two-dimensional ray diagrams.
• Difference from a glass slab: In a glass slab with parallel faces, an emergent ray remains parallel to the incident ray (only laterally displaced). In a prism, the two faces are not parallel so the emergent ray is deviated and not parallel to the incident ray.

Dispersion of White Light by a Glass Prism

• When white light enters a prism, it splits into a band of colours because different colours bend at different angles.; this is called dispersion.
• The separated band of colours is called the spectrum; the typical order from least to most refracted is Red → Orange → Yellow → Green → Blue → Indigo → Violet (remembered as VIBGYOR when listed from most to least refracted).
• Cause: The refractive index of glass varies with wavelength (dispersion of refractive index); shorter wavelengths (violet) experience a larger refractive index and therefore are deviated more than longer wavelengths (red).

V I B G Y O R

• The angle of deviation is approximately inversely related to wavelength; red light (longest visible wavelength) is least deviated, and violet (shortest) is most deviated.

Recombination of White Light

Isaac Newton showed that white sunlight is composed of many colours. He passed sunlight through a prism to produce a spectrum, then used a second inverted prism to recombine these colours back into white light. This experiment demonstrated that dispersion separates existing colours rather than creating new ones.

Rainbow Formation

A rainbow is a natural spectrum of light appearing in the sky as an arc, formed by the dispersion and internal reflection of sunlight in spherical water droplets present in the atmosphere.

Process of Rainbow Formation

1. Refraction on entry: Sunlight entering a raindrop refracts and splits into its component colours because different wavelengths are bent by different amounts when passing from air into water.
2. Internal reflection: The refracted rays reflect from the inner surface of the raindrop.
3. Refraction on exit: As the rays leave the raindrop, they refract again and emerge at different angles; red emerges at about 42° and violet at about 40° relative to the direction opposite the Sun, producing a circular arc of colours.

Atmospheric Refraction

Atmospheric refraction is the bending of light rays when they pass through layers of the atmosphere of varying density. This leads to several observable phenomena.

Twinkling of Stars

• Light from a star passes through many turbulent layers of the atmosphere with changing temperature and density; each layer refracts the light slightly differently.
• These rapid changes in the direction and intensity of incoming starlight cause the apparent position and brightness to fluctuate, so stars appear to twinkle.
• Planets generally do not twinkle appreciably because they are nearer and appear as tiny discs; light from different parts of the disc averages out the rapid fluctuations. 

Sun's Apparent Shape and Colour During Sunrise and Sunset

• At sunrise and sunset sunlight traverses a greater thickness of atmosphere, so more scattering occurs. Shorter wavelengths (blue/violet) are scattered out and the transmitted light is richer in red/orange/yellow, making the Sun appear reddened.
• Atmospheric refraction causes the apparent position of the Sun to be slightly higher than its true geometric position when near the horizon. This produces an optical advance of sunrise and a delay of sunset (the Sun appears about two minutes earlier and remains visible for about two minutes longer than it would without refraction).

Advanced sunrise and delayed sunset

• The sun appears about two minutes earlier than the actual sunrise, and it remains visible for about two minutes after the actual sunset.
• When the sun is below the horizon, the rays have to pass from rarer to denser medium.
• The time difference between the actual sunset and the apparent sunset is approximately 2 minutes.
• So, rays bend towards the normal. As a result, the sun appears higher than its actual position.

Scattering of Light

Scattering is the process by which light is forced to deviate from a straight trajectory because of irregularities or particles in the medium through which it passes. The nature of scattering depends on the size of the particles relative to the wavelength of light.

• When light hits dust, smoke, or gas particles in the atmosphere, it gets deflected in many directions.

• Very small particles scatter shorter wavelengths(blue) more. Larger particles scatter all wavelengths nearly equally. 

• Scattering is responsible for many natural phenomena, like the blue color of the sky and the reddish appearance of the sun during sunrise and sunset.

Applications and Observed Effects

1. The Sky Appears Blue

• When white sunlight enters the Earth's atmosphere, it interacts with gas molecules and small particles. Shorter wavelengths like violet, indigo, and blue scatter more than longer wavelengths. Among them, blue light dominates as our eyes are more sensitive to it (violet is mostly absorbed).As a result, we see the sky as blue.

2. The Sun Appears Yellow

• As sunlight passes through the atmosphere, blue and violet light are mostly scattered away. The remaining light reaching our eyes has relatively more red ,orange,yellow, which appears yellow. This mix gives the sun a yellowish appearance, especially during midday when it is overhead.

3. Sun appears reddish at sunrise and sunset:

• Sunlight travels a longer path through the atmosphere near the horizon, removing much of the shorter wavelengths and leaving red/orange light.

4. The Sky Appears Dark to an Astronaut

• In outer space, there is no atmosphere and thus no particles to scatter sunlight.Since there is no scattering, the sky looks black or dark to astronauts, even when the sun is shining.

Tyndall Effect

 The scattering of light by colloidal solution particles is called the Tyndall effect. It makes the path of a light beam visible when it passes through such a mixture.

• Examples: Sunlight forming visible rays in mist or fog; a beam of light visible in a dusty room; milk dispersed in water showing a visible beam.
• Conditions: The mixture must be a colloid or contain fine suspended particles. The particle size should be large enough to scatter light but small enough to remain suspended.