The human eye is a remarkable optical instrument that allows us to see the world. It works on the principle of refraction of light through a natural lens. This chapter also explores defects of vision, dispersion of white light, and atmospheric optical phenomena.
Structure of the Human Eye
- Cornea: Transparent front part of the eye; responsible for most of the eye's refraction.
- Iris: Coloured muscular diaphragm that controls the amount of light entering through the pupil.
- Pupil: The opening in the iris; dilates in dim light and contracts in bright light.
- Crystalline lens: A flexible convex lens behind the iris; fine-tunes focus.
- Ciliary muscles: Control the curvature (and hence focal length) of the crystalline lens.
- Retina: Light-sensitive inner layer containing rods (for dim light) and cones (for colour and bright light).
- Optic nerve: Transmits electrical signals from the retina to the brain.
- Least distance of distinct vision: ~25 cm for a normal adult eye.
- Far point: The farthest point at which the eye can see clearly — infinity for a normal eye.
Accommodation
Accommodation is the ability of the eye to adjust its focal length by changing the curvature of the lens to focus on objects at different distances. Ciliary muscles contract to increase lens curvature (shorter focal length) for near objects and relax for distant objects.
Defects of Vision
Myopia (short-sightedness): Can see near objects clearly but not distant ones. The image forms in front of the retina. Cause: elongated eyeball or excessive curvature of the lens. Correction: concave (diverging) lens.
Hypermetropia (long-sightedness or far-sightedness): Can see distant objects clearly but not near ones. Image forms behind the retina. Cause: shortened eyeball or weak lens. Correction: convex (converging) lens.
Presbyopia: Age-related loss of accommodation; the lens becomes less flexible. Both near and far vision affected. Correction: bifocal lenses.
Cataract: The crystalline lens becomes cloudy (opaque), causing blurred vision. Corrected by surgical removal and replacement of the lens.
Refraction of Light Through a Prism
A glass prism splits (disperses) white light into its component colours: VIBGYOR (Violet, Indigo, Blue, Green, Yellow, Orange, Red). This is called dispersion. Violet light bends the most and red bends the least because different wavelengths travel at slightly different speeds in glass.
The angle of deviation (d) is the angle between the emergent ray and the original incident ray. d = (i1 + i2) - A, where A is the prism angle.
Atmospheric Refraction and Dispersion
Rainbow: Formed by dispersion and total internal reflection of sunlight in water droplets. Always seen opposite to the sun. Primary rainbow has red on the outside and violet on the inside.
Atmospheric refraction: The bending of light as it passes through layers of atmosphere with different densities. Causes the Sun to appear about 2 minutes before it actually rises (advance sunrise) and after it sets.
Twinkling of stars: Due to atmospheric refraction — the constantly changing atmospheric layers refract starlight variably, causing apparent brightness to fluctuate (twinkle). Planets do not twinkle because they appear as extended sources.
Scattering of light (Tyndall effect): Particles scatter shorter wavelengths more than longer ones. Blue sky: the atmosphere scatters blue light (shorter wavelength) more than red, making the sky appear blue. Red sky at sunrise/sunset: Light travels through a thicker atmosphere; most blue is scattered away, leaving red and orange to reach our eyes.
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A myopic person cannot see objects beyond 2 m. What power of lens is needed? For myopia correction, the lens must form a virtual image of a distant object (at infinity) at the person's far point (2 m). Using the lens formula: u = -infinity, v = -2 m. 1/f = 1/v - 1/u = 1/(-2) - 0 = -0.5. P = 1/f = -0.5 D = -0.5 dioptre. A concave lens of power -0.5 D is needed.
A hypermetropic person has a near point of 1 m. What lens corrects it to 25 cm? The lens must form a virtual image of an object at 25 cm at the person's near point (1 m). u = -0.25 m, v = -1.0 m (virtual image on same side). 1/f = 1/(-1) - 1/(-0.25) = -1 + 4 = 3. P = +3 D. A convex lens of +3 D.
Explain why the sky is blue. When sunlight enters the atmosphere, fine particles and gas molecules scatter light. Blue light (shorter wavelength, ~450 nm) is scattered much more than red light (~700 nm). This scattered blue light reaches our eyes from all directions, making the sky appear blue.
Why does the sun appear red at sunrise and sunset? At these times, sunlight must pass through a much greater thickness of the atmosphere. Most of the blue and violet wavelengths are scattered away en route, and predominantly red and orange light (longer wavelengths, scattered least) reaches our eyes.
White light passes through a prism. The angle of the prism is 60 degrees and the angles of incidence and emergence are each 45 degrees. Find the angle of deviation. d = (i1 + i2) - A = (45 + 45) - 60 = 30 degrees.
Why do stars twinkle but planets do not? Stars are point sources of light; their light passes through varying atmospheric layers causing random refraction and hence twinkling. Planets are extended sources (discs); the average of random refractions across the disc cancels out, so planets appear steady.
A person can read text clearly at 15 cm but cannot see things beyond 80 cm. Identify the defect and suggest the corrective lens. The person can focus on near objects (near point normal at ~15 cm) but cannot see beyond 80 cm — this is myopia. A concave lens forming a virtual image of distant objects at 80 cm is needed. f = -80 cm, P = 1/(-0.80) = -1.25 D.
Key Formulas
Key formulas
Common mistakes
Students often mix up myopia and hypermetropia. Remember: MyoPia = My eye can see near (short-sighted, corrected by concave/minus lens). Hypermetropia = can see far (long-sighted, corrected by convex/plus lens). Also, twinkling is due to atmospheric refraction, not diffraction or dispersion.
Summary
The human eye uses accommodation to focus at different distances. Myopia, hypermetropia, and presbyopia are common vision defects corrected by appropriate lenses. Dispersion of white light through a prism produces VIBGYOR. Atmospheric optical phenomena such as the blue sky, red sunset, twinkling stars, and rainbows are all explained by scattering and refraction of light.