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Light & EM Waves

Optics, refraction, and the electromagnetic spectrum

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Light Travels in Straight Lines

Speed of light in vacuum: c = 3 × 10⁸ m/s (constant, fastest speed known)

Nature of light: Transverse electromagnetic wave

Can travel through vacuum (unlike sound)

Can be reflected, refracted, diffracted (wave behavior)

Speed in other media: Slower than in vacuum

Glass: ≈ 2 × 10⁸ m/s | Water: ≈ 2.25 × 10⁸ m/s

Reflection: Laws & Plane Mirrors

Law of reflection: Angle of incidence = angle of reflection

Both angles measured from the normal (perpendicular to surface)

Plane mirror images:

✓ Virtual (behind mirror)

✓ Same size as object

✓ Same distance from mirror as object

✓ Laterally inverted (left-right reversed)

Refraction: Light Bends at Boundaries

Refraction: Light changes direction when entering a medium with different optical density

Why does it happen? Light speed changes in different media

Faster medium → bends away from normal

Slower medium (denser) → bends toward normal

Real example: Straw in water appears bent. Light from straw refracts at water surface.

Snell's Law: n₁ sin i = n₂ sin r

n₁ sin θ₁ = n₂ sin θ₂

where: n = refractive index, θ = angle from normal

Refractive index (n): How much the medium slows light

Vacuum: n = 1 | Air: n ≈ 1 | Water: n ≈ 1.33 | Glass: n ≈ 1.5

Alternative form: n = c / v (refractive index = speed in vacuum / speed in medium)

Snell's Law: Worked Example

Question:
Light enters glass (n=1.5) from air (n=1) at angle of incidence 40°. Find angle of refraction.

Solution:

n₁ sin θ₁ = n₂ sin θ₂

1 × sin 40° = 1.5 × sin θ₂

0.643 = 1.5 × sin θ₂

sin θ₂ = 0.429

θ₂ ≈ 25.4°

Light bends toward normal (25° < 40°) because glass is optically denser

Critical Angle & Total Internal Reflection (TIR)

Critical angle (θc): Angle of incidence where refracted ray grazes surface (angle of refraction = 90°)

sin θc = n₂ / n₁

where: n₁ = denser medium, n₂ = less dense medium

Total Internal Reflection (TIR):

If angle of incidence > critical angle → light reflects (no refraction!)

For glass-to-air (n=1.5 to 1): θc ≈ 41.8°. Any angle > 41.8° = total reflection

Critical Angle: Worked Example

Question: Find critical angle for glass-to-air boundary (n_glass = 1.5, n_air = 1)

Solution:

sin θc = n₂ / n₁ = 1 / 1.5

sin θc = 0.667

θc ≈ 41.8°

Meaning: If light hits glass-air interface at angle > 41.8°, it reflects completely (bounces back into glass, no light escapes)

Optical Fibres: Using TIR

Principle: Light enters fiber at shallow angle → undergoes TIR at walls → bounces down fiber without loss

Advantages:

✓ Fast (light speed)

✓ High bandwidth (carries lots of data)

✓ Secure (hard to tap into)

✓ Immune to electromagnetic interference

Applications: Internet fiber, phone lines, medical endoscopes

Converging (Convex) Lens

Shape: Thicker in center, thinner at edges

Effect: Brings parallel rays to a point (focal point F)

Key terms:

Focal length (f): Distance from lens to focal point

Focal point: Where rays converge

Power of lens: P = 1/f (in dioptres, D), if f in metres
Stronger lens (shorter focal length) = higher power

Diverging (Concave) Lens

Shape: Thinner in center, thicker at edges

Effect: Spreads out parallel rays (as if from virtual focal point behind lens)

Focal point: Virtual (behind lens), light rays never actually converge

Sign convention:
Converging lens: f is positive
Diverging lens: f is negative

Ray Diagrams: Real vs Virtual Images

Real images:

• Rays actually converge

• Can be projected on screen

• Inverted (upside-down)

• Formed by converging lens (object beyond 2F)

Virtual images:

• Rays appear to come from point (don't actually converge)

• Cannot be projected

• Upright (same way as object)

• Formed by diverging lens or converging lens when object is between lens and F

Magnifying Glass: Virtual Image

How it works: Object placed between lens and focal point → produces enlarged virtual image on same side

Why virtual? Light rays appear to come from behind the lens (haven't actually converged)

Why magnified? Converging lens makes light rays spread out less → brain interprets larger angle → appears larger

Magnification: M = image distance / object distance (upright & virtual)

Eye Correction: Short-sightedness (Myopia)

The problem: Eyeball too long OR lens too powerful → images form in front of retina → distant objects blurry

The correction: Diverging lens (concave, negative power)

Why diverging works: Spreads light rays outward → focal point pushed back onto retina → image sharp

Contact lens/glasses: Negative diopter power (e.g., -2.00D)

Eye Correction: Long-sightedness (Hyperopia)

The problem: Eyeball too short OR lens too weak → images form behind retina → close objects blurry

The correction: Converging lens (convex, positive power)

Why converging works: Brings light rays together → focal point moved forward onto retina → image sharp

Contact lens/glasses: Positive diopter power (e.g., +2.00D)

IGCSE exam tip: Short-sighted = diverging (minus). Long-sighted = converging (plus). Think: "spread rays out if eyeball is too long"

Dispersion: Rainbows & Prisms

Dispersion: Different wavelengths refract by different amounts

Why? Refractive index depends on wavelength. Red (longer λ) refracts less; violet (shorter λ) refracts more

Order (ROYGBIV):
Red → Orange → Yellow → Green → Blue → Indigo → Violet

Monochromatic light: Single wavelength (no dispersion)

White light: All wavelengths mixed (fully disperses in prism)

The Electromagnetic Spectrum

All EM waves travel at c = 3 × 10⁸ m/s in vacuum

Order by wavelength (longest to shortest):

1. Radio waves (km → mm) — lowest frequency

2. Microwaves (mm → μm)

3. Infrared (μm)

4. Visible light (0.4–0.7 μm) — only thing we see!

5. Ultraviolet (nm)

6. X-rays (pm)

7. Gamma rays (fm) — highest frequency

Radio & Microwaves: Uses (IGCSE Syllabus)

Radio waves: λ ≈ km to mm

✓ Broadcasting (TV, FM/AM radio)

✓ Telecommunications (phone signals)

✓ Satellite communication

Microwaves: λ ≈ mm to μm

✓ Cooking (microwave oven — heats water molecules)

✓ Mobile phone signals

✓ Radar (detect objects)

✓ Satellite communication (dish antennas)

Danger: Microwave energy can heat body tissues (keep distance from sources)

Infrared, Visible, Ultraviolet: Uses & Dangers

Infrared (IR): λ ≈ μm

✓ Heating (heaters, lamps, thermal cameras)

✓ Remote controls

⚠ Danger: Intense IR causes skin burns

Visible light: 0.4–0.7 μm

✓ Vision (only EM wave humans see)

✓ Photosynthesis (plants)

Ultraviolet (UV): λ ≈ nm

✓ Sterilization (kills bacteria)

✓ Fluorescent materials (glow under UV)

⚠ Danger: Damages skin (causes sunburn, skin cancer)

X-rays & Gamma Rays: Uses & Dangers

X-rays: λ ≈ pm

✓ Medical imaging (X-ray photos of bones)

✓ Airport security scanning

⚠ Danger: Ionizing radiation damages cells → cancer, mutations

Gamma rays: λ ≈ fm (shortest wavelength)

✓ Cancer treatment (targets tumor cells)

✓ Sterilization (medical equipment)

⚠ Danger: Highly penetrating, extremely ionizing → severe cell damage

As wavelength decreases (frequency increases) → radiation becomes more ionizing & dangerous

EM Spectrum: Complete Summary

Type	Use/Detection	Main Danger
Radio	Broadcasting, comms	None (low energy)
Microwave	Cooking, phones	Tissue heating
Infrared	Heating, cameras	Skin burns
Visible	Vision	None (except intense light)
UV	Sterilization	Skin damage, cancer
X-ray	Medical imaging	Cell damage, cancer
Gamma	Treatment, sterilization	Severe cell damage

Digital vs Analogue Signals (IGCSE 3.3)

Analogue signal: Continuous range of values

Example: Traditional vinyl record (groove varies smoothly)

Digital signal: Discrete values (0 and 1)

Example: CD (pits and lands = 0 and 1)

Transmission: Both can be carried by EM waves (radio, microwaves, fiber optics)

Benefits of Digital Signals (IGCSE 3.3)

✓ Noise immunity: Small noise won't corrupt 0/1 (unlike analogue where any noise degrades signal)

✓ Easier to amplify: Just need to regenerate 0s and 1s

✓ Compression: Can compress digital data (reduce file size)

✓ Error correction: Can detect & correct errors in digital transmission

✓ Encryption: Digital signals can be encrypted for security

This is why modern communication (internet, mobile, TV) is digital, not analogue!

Satellite Communication

How it works:
Ground station → radio/microwave signal → satellite → reflected back to ground station

Frequency bands used:
Radio waves & microwaves (can penetrate atmosphere)

Visible light & UV would be absorbed by atmosphere (don't work for satellites)

Applications:

• TV broadcasting

• Telephone signals

• GPS positioning

• Weather monitoring

Exam Tips: Light & EM Waves

✓ Snell's Law: n₁ sin θ₁ = n₂ sin θ₂. Watch your angles (from normal)!

⚠ Critical angle: sin θc = n_less / n_more. For glass-to-air ≈ 41.8°.

✓ Eye correction: Short-sighted = diverging (minus). Long-sighted = converging (plus).

⚠ EM spectrum order: Radio → Microwave → IR → Visible → UV → X-ray → Gamma.

✓ Digital benefits: Noise immunity, compression, error correction, encryption — know all four!

Key Takeaways

✅ Light: transverse EM wave, c = 3×10⁸ m/s in vacuum

✅ Reflection: law of reflection (i = r from normal)

✅ Refraction: Snell's law (n₁ sin θ₁ = n₂ sin θ₂)

✅ Critical angle: sin θc = n₂/n₁ → TIR (optical fibres)

✅ Lenses: converging (focal point F), diverging (virtual F)

✅ Eye correction: diverging for myopia, converging for hyperopia

✅ EM spectrum: 7 types, different uses, ionizing dangers increase toward gamma

✅ Digital > analogue: noise immunity, compression, error correction, encryption

Master optics & EM spectrum — ace Topic 3! 💡