Summary and Quick Revision

The Human Eye

  • The eye works like a camera; the retina is the light-sensitive screen where a real, inverted image forms.
  • Light path: cornea → pupil (iris controls it) → crystalline lens → retina → optic nerve → brain.
  • Most refraction happens at the cornea; the lens gives fine focal-length adjustment. Eyeball diameter ≈ 2.3 cm.

Accommodation, near and far point

  • Accommodation = ability of the eye lens to change focal length (via ciliary muscles).
  • Relaxed muscles → thin lens → long f → distant objects. Contracted muscles → thick lens → short f → near objects.
  • Near point (least distance of distinct vision) ≈ 25 cm; far point = infinity for a normal eye.
  • Cataract: cloudy lens; corrected by surgery.

Defects of Vision

Defect Sees clearly Image forms Correcting lens
Myopia (near-sighted) near, not far in front of retina Concave (−P)
Hypermetropia (far-sighted) far, not near behind retina Convex (+P)
Presbyopia (age) loses accommodation near point recedes often bi-focal
  • Myopia causes: lens too curved or eyeball too long. Hypermetropia causes: focal length too long or eyeball too short.
  • Bi-focal lens: upper concave (distant vision), lower convex (near vision).
  • Lens formula 1v−1u=1f\dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{f}; Power P=1fP = \dfrac{1}{f} (f in m, unit dioptre, D).

Prism, Dispersion and Rainbow

  • Prism angles: angle of prism ∠A\angle A, incidence ∠i\angle i, refraction ∠r\angle r, emergence ∠e\angle e, deviation ∠D\angle D. Light bends towards the base.
  • Dispersion: splitting of white light into VIBGYOR. Violet bends most, red least. The band of colours is the spectrum.
  • Newton: a second inverted prism recombines the colours into white light.
  • Rainbow: refraction + dispersion → internal reflection → refraction in water droplets; seen opposite the Sun.

Atmospheric Refraction

  • Caused by the atmosphere's gradually changing refractive index.
  • Twinkling of stars: stars are point sources; refraction makes their light fluctuate. Star appears higher near the horizon.
  • Planets don't twinkle: extended sources; fluctuations average out.
  • Advance sunrise / delayed sunset: Sun seen about 2 minutes early and late; Sun's disc looks flattened.

Scattering of Light

  • Tyndall effect: scattering by fine colloidal particles makes a light beam's path visible.
  • Blue sky: air molecules (smaller than the wavelength of light) scatter shorter (blue) wavelengths more. Red wavelength ≈ 1.8× blue.
  • No atmosphere → no scattering → dark sky (astronauts, high altitude).
  • Red danger signals and reddish Sun at sunrise/sunset: red is scattered the least and travels farthest.

One-line formula recall

  • P=1/fP = 1/f (dioptre); myopia lens power negative, hypermetropia lens power positive.
  • Myopia correction: 1f=1−(far point)\dfrac{1}{f} = \dfrac{1}{-(\text{far point})}.
  • Hypermetropia correction: 1f=1−(actual near pt)−1−(25 cm)\dfrac{1}{f} = \dfrac{1}{-(\text{actual near pt})} - \dfrac{1}{-(25\,\text{cm})}.