Human Eye and Colourful World
The paper tests the structure and accommodation of the eye, correction of defects with lens power, dispersion through a prism, and scattering of light in the atmosphere.
Structure and working
The cornea and the crystalline lens focus light onto the retina, where rods detect dim light and cones detect colour. The optic nerve carries signals to the brain. The iris controls pupil size, and the ciliary muscles change the lens curvature - this is accommodation. For a normal eye the near point is about 25 cm and the far point infinity.
Defects and correction
- Myopia (short sight): the image forms in front of the retina, the far point is finite, and a concave lens of negative power corrects it.
- Hypermetropia (long sight): the image forms behind the retina, the near point is beyond 25 cm, and a convex lens corrects it.
- Presbyopia is the age-related loss of accommodation, corrected by bifocal lenses.
- Power P = 1/f with f in metres; the unit is the dioptre (D).
Dispersion and scattering
White light splits in a prism because each colour has a different refractive index, violet most and red least. A rainbow is refraction, dispersion and total internal reflection inside water droplets, with red on the outer edge and violet inside. Rayleigh scattering makes the sky blue because short wavelengths scatter most; at sunrise and sunset light travels a longer path, blue is scattered away and red reaches the eye. Danger signals are red because red scatters least and is seen far off in fog. Above the atmosphere the sky appears black.
Worked example
A myopic student has a far point of 80 cm. The correcting lens must image an object at infinity at 80 cm, so f = −80 cm = −0.8 m, and P = 1/(−0.8) = −1.25 D.
Traps
Do not reverse the corrections for myopia and hypermetropia; a concave lens has negative power; power must use focal length in metres, not centimetres.