ποΈ The Human Eye β Structure
- Cornea: Transparent front membrane; provides ~β
of focusing power.
- Iris: Coloured muscular diaphragm; controls pupil size.
- Pupil: Opening in iris; regulates light entry (dilates/constricts).
- Crystalline Lens: Biconvex, flexible; adjusted by ciliary muscles.
- Retina: Light-sensitive screen; rods (dim light) + cones (colour: R/G/B).
- Optic Nerve: Transmits electrical signals from retina to brain.
- Blind Spot: No receptors at optic nerve exit point.
Key: Eye = biological camera. Cornea+Lens = camera lens. Retina = film/sensor. Image: real, inverted, diminished.
π Power of Accommodation
- Ability of eye lens to change focal length to focus at different distances.
- Near point (D): 25 cm β least distance of distinct vision.
- Far point: β (infinity) for normal eye.
- Range of vision: 25 cm to β.
Mechanism
| Viewing | Ciliary Muscles | Lens | Focal Length |
|---|
| Distant object | Relaxed | Thin (flat) | Maximum |
| Near object | Contracted | Thick (curved) | Minimum |
Remember: Contract β Curved β Close objects. Relax β flat β faR objects.
π Defects of Vision & Corrections
| Defect | Can't See | Image Forms | Cause | Correction | Lens Sign |
|---|
Myopia
(Near-sighted) | Far objects | In front of retina | Elongated eyeball or excessive curvature | Concave lens | βve power |
Hypermetropia
(Far-sighted) | Near objects | Behind retina | Short eyeball or weak curvature | Convex lens | +ve power |
Presbyopia
(Age-related) | Near objects | Behind retina | Ciliary muscles weaken; lens loses flexibility | Bifocal lens | +ve (lower) |
Mnemonics: Myopia = Minus lens. Hypermetropia = High (+ve) lens. Presbyopia = Progressive/Bifocal.
Key Formulas
P = 1/f (in metres) Far point (myopia) = |f of concave lens|
1/f = 1/v β 1/u (for calculating power of corrective lens)
πΊ Refraction Through a Prism
- Prism: Triangular glass body with angle of prism A.
- Incident ray bends towards base on entering and again on exiting.
- Angle of deviation (Ξ΄): Angle between incident ray and emergent ray.
- Ξ΄ depends on: angle of prism, refractive index, angle of incidence.
Key relationship: A = rβ + rβ and Ξ΄ = (iβ + iβ) β A
π Dispersion of Light
- Dispersion: Splitting of white light into 7 colours by a prism.
- Spectrum: VIBGYOR β Violet, Indigo, Blue, Green, Yellow, Orange, Red.
- Cause: Different Ξ» β different refractive indices in glass.
- Violet: Ξ» β 380 nm, ΞΌ highest β bends MOST.
- Red: Ξ» β 700 nm, ΞΌ lowest β bends LEAST.
Newton's Experiment
- 1st prism: White β VIBGYOR (dispersion).
- 2nd inverted prism: VIBGYOR β White (recombination).
- Proves: White = mixture of 7 colours; prism only separates, doesn't create.
π Rainbow Formation
- Formed in water droplets after rain (or near fountains/waterfalls).
- Steps in each droplet:
- 1. Refraction (entering) β 2. Dispersion β 3. Total Internal Reflection β 4. Refraction (exiting)
- Conditions: Sun behind observer, rain in front.
| Rainbow | Angle | Reflections | Colour Order (outsideβinside) | Brightness |
|---|
| Primary | 42Β° | 1 TIR | Red β Violet | Brighter |
| Secondary | 51Β° | 2 TIRs | Violet β Red (reversed) | Fainter |
π« Scattering of Light
Rayleigh Scattering Law
Intensity of scattered light β 1/Ξ»β΄
- By particles much smaller than wavelength (air molecules: Nβ, Oβ).
- Shorter wavelength β scatters MUCH more. Blue scatters ~5.5Γ more than red.
Tyndall Effect
- Scattering by colloidal particles (size ~ wavelength).
- Can scatter all colours depending on particle size.
- Examples: dusty room beam, forest mist, blue smoke from incense.
| Phenomenon | Cause | Key Reasoning |
|---|
| Blue sky | Rayleigh scattering | Blue (short Ξ») scatters most β reaches eyes from all directions |
| White clouds | Mie scattering | Large water droplets scatter all Ξ» equally β white |
| Red sunset/sunrise | Rayleigh scattering | Long path β blue scattered away β only red/orange remains |
| Red danger signals | Least scattering | Red (longest Ξ») β least scattered β travels farthest |
| Black sky on Moon | No atmosphere | No molecules β no scattering β sky is black |
β Atmospheric Refraction
- Atmosphere has layers of varying density (denser near surface).
- Light continuously bends towards denser layers (towards ground).
Effects
| Phenomenon | Explanation |
|---|
| Twinkling of stars | Point source + varying refractive index β apparent position shifts β intensity fluctuates |
| Planets don't twinkle | Extended source β individual fluctuations average out |
| Advanced sunrise (+2 min) | Refraction makes Sun appear above actual position |
| Delayed sunset (+2 min) | Sun visible after crossing below horizon |
| Flattened Sun at horizon | Bottom edge refracted more than top β vertical compression |
Total extra daylight due to atmospheric refraction β 4 minutes/day (2 min sunrise + 2 min sunset).
π Wavelength & Colour Data
| Colour | Wavelength (nm) | Frequency | ΞΌ in glass | Deviation |
|---|
| Violet | 380β450 | Highest | Highest | Maximum |
| Indigo | 450β490 | β | β | β |
| Blue | 490β520 | | | |
| Green | 520β565 | | | |
| Yellow | 565β590 | | | |
| Orange | 590β625 | β | β | β |
| Red | 625β700 | Lowest | Lowest | Minimum |
Remember: Ξ» increases VβR. Frequency increases RβV. Speed in glass increases VβR. All colours have same speed in vacuum (c = 3Γ10βΈ m/s).
π§ Exam Quick-Fire Facts
- Persistence of vision: ~1/16 second. Movies use 24+ fps to exploit this.
- Colour of an object: Determined by wavelength it reflects. Red rose reflects red, absorbs rest.
- At noon: Sun overhead β short path β white/yellow Sun.
- On Moon: No atmosphere β black sky + no twinkling + no refraction effects.
- Deep sea: Appears blue-green (water absorbs red wavelengths).
- Stars twinkle, planets don't = point source vs extended source.
- Human eye focal length β 2.5 cm (approx).
- Eye can distinguish about 10 million colours.
π Important Numericals Pattern
Type 1: Power of Corrective Lens
P = 1/f (f in metres)
- Myopia: Far point given β f = β(far point) β P = 1/f
- Hypermetropia: Near point given β use lens formula with v = β(near point), u = β25 cm
Type 2: Combination of Lenses
P = Pβ + Pβ + Pβ ...
Example
A person's far point is 80 cm. Find the power of corrective lens.
f = β80 cm = β0.8 m (concave lens for myopia)
P = 1/(β0.8) = β1.25 D
π Key Differences
| Feature | Rayleigh Scattering | Tyndall Effect |
|---|
| Particle size | βͺ Ξ» (molecules) | β Ξ» (colloidal) |
| Dependence | Strong (β 1/Ξ»β΄) | Weaker Ξ» dependence |
| Example | Blue sky | Dusty room beam |
| Feature | Primary Rainbow | Secondary Rainbow |
|---|
| Internal reflections | 1 | 2 |
| Angle | 42Β° | 51Β° |
| Intensity | Brighter | Fainter |
| Order (outsideβin) | Red β Violet | Violet β Red |