The Human Eye and Colourful World

• How the human eye forms images, and the role of the cornea, iris, pupil, lens, and retina
• What "power of accommodation" means and why the eye lens changes shape
• The common eye defects (myopia, hypermetropia, presbyopia) and how spectacle lenses correct them
• How a glass prism splits white light into its component colours (dispersion)
• Why the atmosphere makes stars twinkle and the sun appear flattened at the horizon
• Why the sky is blue, sunsets are red, and how scattering explains everyday colours

1. Structure of the human eye. Light enters through the transparent cornea, which does most of the refraction. The iris is the coloured, muscular diaphragm behind the cornea that controls the size of the pupil (the opening through which light passes), regulating how much light enters the eye. Behind the pupil is the crystalline lens, a transparent, flexible, convex structure held in place by ciliary muscles. The lens fine-tunes the focus so that a sharp, inverted, real image forms on the retina, a light-sensitive screen at the back of the eye containing rod and cone cells. The optic nerve carries these signals to the brain, which processes the inverted image the right way up.

2. Power of accommodation. The eye lens changes its curvature (and hence focal length) using the ciliary muscles: the muscles contract to make the lens more curved (shorter focal length) for viewing near objects, and relax to flatten the lens (longer focal length) for distant objects. This ability to adjust focal length is called the power of accommodation. It is not unlimited — objects closer than the near point (25 cm for a normal young adult) cannot be focused sharply, and the far point of a normal eye is infinity.

3. Myopia (near-sightedness). A myopic eye can see nearby objects clearly but not distant ones; its far point is nearer than infinity. Cause: the eyeball is too elongated, or the eye lens is too strongly curved, so images of distant objects form in front of the retina. Correction: a concave (diverging) lens of suitable negative power diverges incoming rays slightly before they reach the eye, pushing the image back onto the retina.

4. Hypermetropia (far-sightedness). A hypermetropic eye can see distant objects clearly but not nearby ones; its near point is farther than 25 cm. Cause: the eyeball is too short, or the eye lens is too flat, so images of nearby objects form behind the retina. Correction: a convex (converging) lens of suitable positive power converges the rays before they enter the eye, bringing the image forward onto the retina.

5. Presbyopia. With age, the ciliary muscles weaken and the lens loses flexibility, so the power of accommodation decreases and the near point recedes. Presbyopia often accompanies myopia in older people, requiring bifocal lenses — the upper part (concave) for distance vision and the lower part (convex) for near vision.

6. Refraction through a prism and dispersion. A prism has two inclined refracting surfaces. When light passes through, it bends towards the base at both surfaces, and the net bending is called the angle of deviation. White light is a mixture of seven colours (VIBGYOR). Since the refractive index of glass is slightly different for each colour (highest for violet, lowest for red, because refractive index depends on wavelength), each colour bends by a different amount. Violet, with the shortest wavelength, bends the most; red, with the longest wavelength, bends the least. This splitting of white light into its constituent colours is called dispersion. A rainbow is a natural example: dispersion, refraction, and internal reflection of sunlight inside suspended raindrops produce the coloured arc, seen when the sun is behind the observer and rain is in front.

7. Atmospheric refraction. The refractive index of air increases as we go from the outer layers of the atmosphere towards the Earth's surface (air becomes denser and hotter/cooler in shifting layers), so light from a star does not travel in a straight line — it bends gradually as it passes through layers of changing refractive index, and the layers themselves shift due to convective air currents. This causes the apparent position of a star to fluctuate slightly, and since stars are point sources, this produces the twinkling effect. Planets do not twinkle (or twinkle much less) because they are much closer and are effectively extended sources — light from many points averages out the fluctuation. Atmospheric refraction also makes the sun visible about 2 minutes before actual sunrise and after actual sunset, and causes the sun's disc to look flattened (oval) near the horizon.

8. Scattering of light. When light interacts with particles much smaller than its wavelength (like air molecules), it scatters — this is called Rayleigh scattering, and shorter wavelengths (blue, violet) scatter much more strongly than longer wavelengths (red). The sky appears blue because blue light is scattered in all directions far more than red light by the gas molecules in the atmosphere (our eyes are also more sensitive to blue than violet). At sunrise and sunset, sunlight travels through a much greater thickness of atmosphere to reach us; most of the blue is scattered away along this long path, leaving mostly red and orange light to reach our eyes directly — hence the reddish sun and sky. Clouds appear white because water droplets in clouds are much larger than air molecules and scatter all wavelengths almost equally. The Tyndall effect is the scattering of a beam of light by suspended colloidal particles, making the light path visible (e.g., a beam of sunlight through dust in a room, or headlight beams in fog).

Problem. A person cannot read a book comfortably unless it is held at least 1 m away from the eye (i.e., their near point has receded to 1 m). Find the power of the corrective lens needed so the person can read a book held at the normal near point of 25 cm.

Solution. This is hypermetropia. The lens must form a virtual image of an object placed at 25 cm at the person's actual near point (1 m), so the eye can then focus it.

• Object distance: u = −25 cm = −0.25 m
• Image distance: v = −1 m (virtual image, same side as object)

Using the lens formula: 1/f = 1/v − 1/u 1/f = (−1/1) − (−1/0.25) = −1 + 4 = 3 m⁻¹ f = 1/3 m ≈ 0.33 m

Power, P = 1/f (in metres) = +3 D

A convex lens of power +3 dioptres is required.

• Mixing up myopia and hypermetropia: myopia = distant objects blurry, far point too near, corrected by concave lens; hypermetropia = near objects blurry, near point too far, corrected by convex lens.
• Confusing dispersion (splitting of white light into colours by a prism, due to different refractive indices for different wavelengths) with scattering (redirection of light by particles, responsible for the blue sky and red sunsets) — they are different phenomena that both involve colour, but different physics.
• Thinking violet bends the least in a prism — it actually bends the most because glass has the highest refractive index for violet light.
• Believing the retina forms an upright image — the image on the retina is real, inverted, and diminished; the brain interprets it as upright.
• Forgetting that power of a lens is measured in dioptres (D) and P = 1/f(in metres), with sign convention: convex/converging lens has positive power, concave/diverging lens has negative power.

• Why does a person with myopia see nearby objects clearly but not distant ones, and which type of lens corrects this?
• Explain, using scattering of light, why the sky looks blue during the day but the setting sun looks red.

Open the Practice tab for graded questions on The Human Eye and Colourful World.