Architecture of Light

NODE 01

What is Light?

• Wave: Electromagnetic radiation.
• Ray: Straight-line approximation for large systems.
• The ray model is the main tool of this realm.

NODE 02

Sources of Light

☀️💡

• Natural (Sun, fire) vs Artificial (Lasers, LEDs).
• Luminous objects (emit) vs Illuminated objects (reflect).

NODE 03

Transp & Opaque

• Transparent: Transmits clearly.
• Translucent: Transmits but scatters.
• Opaque: Does not transmit visible light.

NODE 04

Rectilinear Prop

• Light travels in straight lines in homogeneous media.
• Establishes the geometry of optics.

NODE 05

Shadows

• Umbra (dark) and Penumbra (partial).
• Depends on point vs extended source.
• Eclipses.

NODE 06

Pinhole Camera

• Object → tiny aperture → inverted image.
• First true image-forming system.

NODE 07

Laws of Reflection

• Angle of incidence = Angle of reflection.
• Incident, Reflected, Normal all in same plane.

NODE 08

Plane Mirror

• Virtual, upright, same size.
• Image distance = Object distance.
• Laterally inverted.

NODE 09

Lateral Inversion

F↔F

• Mirror reverses coordinate direction perpendicular to surface.
• Produces apparent left-right reversal.

NODE 10

Multiple Reflection

• Number of images depends on angle and symmetry.
• Periscopes, Kaleidoscopes.

NODE 11

Spherical Mirrors

• Concave (Converging) & Convex (Diverging).
• Pole, Centre/Radius of curvature, Principal axis/focus.

NODE 12

Mirror Focus

• Paraxial approximation: f = R/2.
• Focal length is half the radius of curvature.

NODE 13

Principal Rays

• Parallel → through focus.
• Through focus → parallel.
• Through C → returns along itself.

NODE 14

Image Formation

• Construct images for objects at various positions.
• Record Position, Size, Orientation, Real/Virtual.

NODE 15

Mirror Formula

• 1/f = 1/v + 1/u.
• Standard Cartesian sign convention applies.

NODE 16

Magnification

• m = hᵢ/hₒ = -v/u.
• Sign indicates upright vs inverted.

NODE 17

Convex Mirror

• Always Virtual, Upright, Diminished.
• Vehicle side mirrors, security (wide field of view).

NODE 18

Concave Apps

🪞🔦🔭

• Shaving mirrors, searchlights, headlamps.
• Solar furnaces, telescope mirrors.

NODE 19

Refraction

• Change in speed alters propagation direction.
• Incident, refracted, normal.

NODE 20

Refractive Index (n)

n = c/v(VACUUM / MEDIUM)

• Optical density shorthand.
• Speed of light in vacuum vs medium.

NODE 21

Snell's Law

• The central law of refraction.
• n₁ sin i = n₂ sin r.

NODE 22

Why Light Bends

v ↓f ≈ const

∴ λ ↓RAY BENDS

• Speed drops, frequency stays tied to source.
• Therefore wavelength drops → ray changes direction.

NODE 23

Apparent Depth

• Objects underwater appear closer to surface.
• Real depth vs Apparent depth.

NODE 24

Parallel Slab

• Emergent ray is parallel to incident ray.
• Lateral displacement depends on thickness and angle.

NODE 25

Total Int Reflection

• Travels Denser → Rarer medium.
• Incidence angle > Critical angle.
• 100% reflection.

NODE 26

Critical Angle

sin C = n₂/n₁(n₁ > n₂)

• Threshold of TIR (refraction angle = 90°).
• For denser medium to air: sin C = 1/n.

NODE 27

Apps of TIR

🌐💎🔭

• Optical fibres, prisms, endoscopes.
• Binoculars, periscopes. Technologically vital.

NODE 28

Prisms

• Refracts and deviates light.
• Refraction at two surfaces. Prism angle.

NODE 29

Dispersion

• Different wavelengths refract by different amounts.
• White light separates into spectral colours.

NODE 30

Angular Dispersion

RED = LESS BENDBLUE = MORE BEND

• Different λ experience different refractive indices.
• Different λ → different deviation.

NODE 31

Atmos Refraction

• Apparent star position, sunset timing, mirages.
• Atmosphere has continuously varying refractive index.

NODE 32

Lenses

• Convex (Converging) & Concave (Diverging).
• Optical centre, principal axis, focus, f.

NODE 33

Thin-Lens Approx

THINNESS NEGLECTED

• Lens thickness neglected relative to focal distance.
• Paraxial rays. Explains why school formulas work.

NODE 34

Princ Rays (Lens)

• Parallel → through focus.
• Through focus → parallel.
• Through center → undeviated.

NODE 35

Image Formation

• Varies by object position (Beyond 2F, At F, Inside F).
• Record Position, Size, Orientation, Real/Virtual.

NODE 36

Thin-Lens Formula

• 1/f = 1/v - 1/u.
• Requires standard Cartesian sign convention.

NODE 37

Lens Magnification

• m = hᵢ/hₒ = v/u.
• Use ray diagrams alongside calculation.

NODE 38

Concave Lens

• Diverges rays. Produces virtual, upright, diminished image.
• Myopia spectacles, beam expansion.

NODE 39

Power of a Lens

P = 1/f(f in metres)

• Unit: Dioptre (D).
• Positive (Convex) / Negative (Concave) power.

NODE 40

Combo of Lenses

• Thin lenses in contact: P_tot = P₁ + P₂ + ...
• 1/f = 1/f₁ + 1/f₂. Foundation for optical systems.

NODE 41

Lens-Maker Formula

1/f = (n-1)(1/R₁ - 1/R₂)

• Advanced. Thin lens in air.
• Connects material (n) + shape (R) → focal length.

NODE 42

Optical Center & Axis

• Review vocab: Principal axis, Focus, Focal plane.
• Essential for optical instruments.

NODE 43

Real vs Virtual

REAL:RAYS MEET

VIRT:EXTENSIONS MEET

• Real: can project on screen.
• Virtual: cannot project on screen (mirror, magnifying glass).

NODE 44

Image Size

• Diminished, Same size, Enlarged.
• Connected to object distance, f, magnification.

NODE 45

Refl + Refr Boundary

• Interface causes both reflection + transmission.
• Proportions depend on angle, material, polarization.

NODE 46

Fresnel Preview

• Some EM energy reflects even when transmission occurs.
• Electromagnetic explanation behind optical reflection.

NODE 47

Optical Fibre

• Core, cladding, total internal reflection.
• Internet, endoscopy, imaging. First complete application.

NODE 48

Human Vision

• Eye is an optical system (Cornea, Lens, Retina).
• Realm 23 will develop instruments in detail.

NODE 49

Atmos Optics

🌈☀️🌫️

• Mirage, Rainbow, Halo, Dispersion, Scattering.
• Connects R22 back to R21's EM wave world.

NODE 50

Exp Lab

i=r

n

TIR

f

• Verify reflection, determine refractive index.
• Investigate TIR, determine f for lens/mirror.

NODE 51

Ray Chamber

• Interactive constructions for mirrors, lenses, slabs, prisms.
• Most visual realm in the Universe.

NODE 52

Graph Chamber

• 1/f vs 1/u, sin i vs sin r, P vs 1/f.
• TIR transmission vs incidence angle.

NODE 53

Misconceptions

X

• "Light always straight" → Only in homogeneous medium.
• "Virtual = imaginary" → Real optical result.
• "Convex lens always real" → No, virtual inside f.

NODE 54

Solving Engine

• ID Medium → Ray or Wave? → Draw Normal/Rays.
• Reflection (i=r). Refraction (Snell). TIR (i>C).
• Lens/Mirror formula → Magnification → Classify.

NODE 55

Master Map

RAY → REFL → MIRRORREFR → SNELL → TIR → PRISMLENS → MAGNIFICATION → SYS

• The entire realm compressed.

NODE 56

Deep Synthesis

WAVES (R14)+EM (R21)= RAY OPTICS

• R14 (Waves) + R21 (EM) = R22 (Ray Optics).
• Same light acts as Ray for large-scale geometry.
• Wave model needed for interference/diffraction.