Physics — Electromagnetic Waves

Physics — Electromagnetic Waves. Practice questions to deepen understanding of electromagnetic waves. Online physics practice with full solutions and step-by-step explanations.

Physics electromagnetic waves practice — 50 questions: EM spectrum, radio, visible light, ionizing radiation, technological applications. Waves and communications.

Part A: Introduction to EM waves (1–10)
Part B: Radio and communications (11–20)

50 questions

Question 1

2.00 pts

🌊 Electromagnetic wave:

What is it?

E and B oscillate ⊥ to the direction of propagation, no medium needed, c=3×10⁸ m/s in vacuum, from Maxwell''s equations

Only electric

Needs air

Slow

Explanation:

💡 Detailed Explanation:

Electromagnetic wave! 🌊

🌊 E⃗ ⊥ B⃗ ⊥ direction of propagation c = 3×10⁸ m/s

Fundamental properties:
• E and B are perpendicular to each other and to the propagation direction
• In phase (peaks and zeros together)
• No medium required (propagates in vacuum!)
• Constant speed c in vacuum
• Transverse wave

From Maxwell''s equations: c = 1/√(μ₀ε₀)
Maxwell predicted them before measurement (1865) | Hertz confirmed experimentally (1887)

Relations: c = λ·f E/B = c E=E₀sin(kx−ωt)

The full spectrum (all the same thing — only frequency differs!):
radio → microwave → IR → visible → UV → X → gamma
c=λf always for each

Question 2

2.00 pts

⚡ Speed of light:

What is c?

c=299,792,458 m/s (defined!), c=λf, c=1/√(μ₀ε₀), in a medium n: v=c/n, slower

c varies

c=100 m/s

No speed

Explanation:

💡 Detailed Explanation:

The speed of light c! ⚡

📏 In vacuum:
c = 299,792,458 m/s ≈ 3×10⁸ m/s
This is a defined constant in the SI system since 1983 — the metre is defined from c, not the other way around.

📐 Relations:
• c = λ·f (any EM wave)
• c = 1/√(μ₀ε₀) — from Maxwell''s equations
• ε₀ = 8.85×10⁻¹² F/m, μ₀ = 4π×10⁻⁷ H/m

🧊 In a medium:
v = c/n where n is the refractive index
Examples: water n≈1.33, glass n≈1.5, diamond n≈2.4

🌟 Why is c constant?
Special relativity (Einstein, 1905): c is the same for every observer regardless of the source''s motion. This is the cornerstone of modern physics.

Question 3

2.00 pts

💡 Energy in a wave:

What is the intensity I?

I is intensity in W/m², I∝E₀², I∝B₀², P=IA is power, energy density u=(ε₀E²+B²/μ₀)/2

I=E

No energy

Only as heat

Explanation:

💡 Detailed Explanation:

Energy and intensity! 💡

📊 Intensity I:
Power per unit area, units W/m²

I = (1/2)·ε₀·c·E₀² (in vacuum)

So I ∝ E₀² and equivalently I ∝ B₀² (since E₀=cB₀).
Doubling the field amplitude → quadruples the intensity.

⚡ Power through a surface:
P = I·A — total power on area A

🔋 Energy density u (J/m³):
u = (ε₀E²)/2 + B²/(2μ₀)
For an EM wave the two halves are equal — energy is shared 50/50 between E and B.

📐 Example:
Sunlight at Earth: I ≈ 1361 W/m² (solar constant)
→ E₀ ≈ 1010 V/m, B₀ ≈ 3.4 μT

Question 4

2.00 pts

🔄 Polarization:

What is it?

The direction of E oscillation: ordinary light is random, polarized light has E in one direction, a polarizer transmits cos²θ, many uses

Only B

No direction

Only in sound

Explanation:

💡 Detailed Explanation:

Polarization! 🔄

🎯 Definition:
Polarization = the direction in which E oscillates (B is always perpendicular to it).

📊 Types of light:
• Unpolarized: E points in random directions in time (sun, incandescent bulb)
• Linearly polarized: E along one fixed line (laser, light through a polarizer)
• Circular / elliptical: the direction of E rotates (some lasers, certain reflections)

🔍 Polarizer (Malus''s law):
I = I₀·cos²(θ)
where θ is the angle between the polarization and the polarizer''s axis.
θ=0° → full transmission, θ=90° → blocked.

🌟 Applications:
Polarized sunglasses (block reflections off water), 3D cinema, LCD screens, photoelasticity, atmospheric studies (the sky is partially polarized).

Question 5

2.00 pts

🌈 Spectrum:

What types are there?

radio→microwave→IR→visible→UV→X-ray→gamma; all share c, only λ and f differ; energy E=hf increases

Only light

Completely different

No spectrum

Explanation:

💡 Detailed Explanation:

The electromagnetic spectrum! 🌈

📊 Order from low to high frequency:

Region	Frequency	Wavelength
Radio	kHz–GHz	km–cm
Microwave	GHz	cm–mm
Infrared	THz	μm
Visible	~430–770 THz	400–700 nm
UV	PHz	<400 nm
X-ray	EHz	Å
Gamma	>10²⁰ Hz	<0.01 nm

🔑 Universal facts:
• All travel at the same speed c in vacuum
• They differ only in λ and f, related by c=λf
• Photon energy E = h·f grows with frequency: gamma photons carry far more energy than radio photons.

This is why X-rays and gamma rays are ionizing while radio waves are not.

Question 6

2.00 pts

📡 Source of waves:

How are they generated?

Accelerating charges! Antenna with varying I, orbiting electrons, atomic transitions, radioactive nuclei — all radiate

Only by machines

They are not generated

Only by magic

Explanation:

💡 Detailed Explanation:

Sources of EM waves! 📡

⚡ The fundamental rule:

An accelerating charge radiates

A charge at constant velocity does not radiate. Acceleration (changing direction or speed) is what creates an EM wave.

📊 Examples by frequency:
• Radio / TV / WiFi: AC current in an antenna — electrons accelerate up and down, frequency = current frequency
• Microwave (oven): magnetron — electrons in a magnetic field
• Infrared (heat): molecular vibrations
• Visible / UV: electron transitions in atoms (excited atoms emit photons)
• X-rays: rapid deceleration of electrons (Bremsstrahlung) or transitions in inner shells
• Gamma: nuclear transitions in radioactive nuclei

🔍 Connection to current:
The radiated frequency equals the oscillation frequency of the charge.
For an antenna driven at f=100 MHz, you get radio waves at 100 MHz, λ=3 m.

Question 7

2.00 pts

📡 Detection of waves:

How are they received?

Antenna catches them (induced current), eye (chemical), photodiode (electrons), IR detector (heat), scintillator (X-ray/gamma)

Only by eyes

Impossible

Only by touch

Explanation:

💡 Detailed Explanation:

Detection of EM waves! 📡

🎯 Each detector matches a frequency range:

Range	Detector	Mechanism
Radio	Antenna	Induced current (Faraday)
Microwave	Antenna / diode	Rectified current
IR	Bolometer / thermopile	Heating effect
Visible	Eye / CCD / photodiode	Chemical / photoelectric
UV / X / γ	Photomultiplier / scintillator	Photoelectric / pair production

💡 Common principle:
Every detector converts the EM signal into a measurable electrical signal — current, voltage, or chemical change.

Question 8

2.00 pts

🔄 Wave in matter:

What happens?

Reflection, refraction n=c/v, absorption (attenuation), scattering (blue sky), diffraction, interference

Goes straight through

Disappears

No change

Explanation:

💡 Detailed Explanation:

EM waves in matter! 🔄

📊 Six basic phenomena:

1️⃣ Reflection — angle in = angle out, mirrors and polished surfaces.

2️⃣ Refraction — direction change at the interface, governed by Snell''s law n₁sin(θ₁)=n₂sin(θ₂); the speed v = c/n in the medium.

3️⃣ Absorption — energy converted into heat or other forms; intensity decays exponentially with depth (Beer''s law).

4️⃣ Scattering — Rayleigh scattering (∝1/λ⁴) makes the sky blue; Mie scattering whitens clouds.

5️⃣ Diffraction — bending around obstacles or apertures (significant when slit ≈ λ).

6️⃣ Interference — superposition of waves; constructive (bright) or destructive (dark) — basis of holography and optical coatings.

Question 9

2.00 pts

🧮 Exercise:

FM radio at 100 MHz with I = 10 μW/m² at distance 1 km.
Find: λ, E₀, B₀, P_antenna

λ=3 m, E₀≈0.087 V/m, B₀≈0.29 nT, P_antenna≈126 W (strong transmission!)

λ=1 mm

E₀=1000 V

Impossible

Explanation:

💡 Detailed Explanation:

Step-by-step solution! 🧮

📐 Given:
f = 100 MHz = 10⁸ Hz
I = 10 μW/m² = 10⁻⁵ W/m²
d = 1 km = 1000 m

1️⃣ Wavelength:
λ = c/f = 3×10⁸ / 10⁸ = 3 m

2️⃣ E₀ from intensity:
I = (1/2)·ε₀·c·E₀² → E₀ = √(2I / (ε₀·c))
E₀ = √(2·10⁻⁵ / (8.85×10⁻¹² · 3×10⁸))
E₀ ≈ 0.087 V/m

3️⃣ B₀ from E₀:
B₀ = E₀ / c = 0.087 / 3×10⁸ ≈ 0.29 nT

4️⃣ Total transmitted power (isotropic):
P = I · 4π·d² = 10⁻⁵ · 4π · (1000)² ≈ 126 W

That''s a serious broadcast antenna — typical of mid-range FM stations.

Question 10

2.00 pts

📚 Part A summary:

What did we learn?

EM wave: E ⊥ B ⊥ direction, c=3×10⁸, I ∝ E₀², polarization, 7 spectrum regions, source = accelerated charge, detection, interaction — ready to continue!

Only part

Nothing

Not finished

Explanation:

💡 Detailed Explanation:

Part A — what we covered! 📚

🎯 Core concepts of Part A:

✓ Wave structure: E ⊥ B ⊥ propagation direction, transverse, no medium needed
✓ Speed: c = 3×10⁸ m/s in vacuum, defined constant; v = c/n in matter
✓ Energy / intensity: I ∝ E₀² ∝ B₀², equally split between E and B fields
✓ Polarization: direction of E oscillation; Malus''s law I = I₀cos²θ
✓ Spectrum: radio → microwave → IR → visible → UV → X-ray → gamma (7 regions)
✓ Source: any accelerating charge
✓ Detection: antennae, photoreceptors, scintillators — all convert EM into electrical signals
✓ Interaction with matter: reflection, refraction, absorption, scattering, diffraction, interference

📚 Coming in Part B: radio waves, modulation, antennas, propagation, noise, applications.

Question 11

2.00 pts

📻 Radio waves:

What are the bands?

VLF<30 kHz (submarines), LF/MF AM radio, HF shortwave, VHF FM/TV, UHF cellular/WiFi, SHF satellite, EHF mm-wave

Only one

No subdivision

They are all identical

Explanation:

💡 Detailed Explanation:

Radio frequency bands! 📻

📊 ITU classification (low → high):

Band	Frequency	Wavelength	Typical use
VLF	3–30 kHz	100–10 km	Submarines
LF	30–300 kHz	10–1 km	Long-wave radio
MF	0.3–3 MHz	1 km–100 m	AM radio
HF	3–30 MHz	100–10 m	Shortwave, ham
VHF	30–300 MHz	10–1 m	FM, broadcast TV
UHF	0.3–3 GHz	1 m–10 cm	Cellular, WiFi 2.4
SHF	3–30 GHz	10–1 cm	WiFi 5, satellite
EHF	30–300 GHz	10–1 mm	5G mm-wave, radar

📐 Trade-off: lower frequencies penetrate further but carry less data; higher frequencies allow more bandwidth but need line of sight.

Question 12

2.00 pts

📡 Modulation:

Why and how?

AM: amplitude modulation, simple but noisy. FM: frequency modulation, high-quality stereo. PM: phase modulation, modern digital.

Only one type

Not needed

Does not work

Explanation:

💡 Detailed Explanation:

Modulation — encoding information on a carrier! 📡

🎯 Why?
Audio is 20 Hz–20 kHz, but a usable antenna requires λ ≈ antenna size. To transmit kilohertz-range info on a megahertz carrier, the carrier wave is "shaped" by the information signal.

📊 Three classical schemes:

• AM (Amplitude Modulation): the carrier amplitude follows the signal. Simple receiver, but vulnerable to amplitude noise (lightning, motors).

• FM (Frequency Modulation): the carrier frequency varies with the signal. Robust against amplitude noise → high-fidelity stereo radio.

• PM (Phase Modulation): the carrier phase varies. Foundation of modern digital schemes (PSK, QAM) used by WiFi, 4G/5G, satellite links.

💡 Key insight:
The information is recovered at the receiver by demodulation — extracting the original signal from the modulated carrier.

Question 13

2.00 pts

📡 Antennas:

Types and properties?

Dipole λ/2 bidirectional, Yagi directional, parabolic focused, patch compact, phased array steerable, gain G

Only one type

They are all the same

Unimportant

Explanation:

💡 Detailed Explanation:

Antenna types! 📡

📊 Common antennas:

• Dipole (λ/2): the classic — two conductors of total length λ/2. Bidirectional pattern (donut shape). Simple, broadband-ish.
• Yagi-Uda: dipole + reflector + directors. Highly directional. Common in TV reception.
• Parabolic dish: concentrates the beam at the focus. Very high gain. Used for satellite uplinks and radio astronomy.
• Patch (microstrip): a small printed antenna. Compact, easy to integrate into phones.
• Phased array: many small radiators with controlled phases — beam steered electronically without moving parts. Foundation of modern radar and 5G.

📈 Gain G:
Measures how much an antenna concentrates power into a preferred direction relative to an isotropic radiator. Quoted in dBi.
Higher G → narrower beam, longer range — but the antenna becomes more "picky" about direction.

Question 14

2.00 pts

🌍 Propagation:

How do they travel?

Ground wave (LF/MF), sky wave via ionosphere (HF), line of sight (VHF+), tropospheric scatter, fading

Only straight

No propagation

Always identical

Explanation:

💡 Detailed Explanation:

Radio wave propagation modes! 🌍

📊 Four primary modes:

• Ground wave (LF/MF): the wave hugs the Earth''s surface. Reach: hundreds of km. Used by long-wave broadcast and time-signal stations.

• Sky wave (HF): the wave reflects off the ionosphere and bounces back to Earth, sometimes multiple times. This is how shortwave radio reaches the other side of the planet without satellites.

• Line of sight (VHF+): the wave travels in a nearly straight line and is blocked by the horizon. Range limited to roughly the visible horizon (≈40 km from a tower).

• Tropospheric scatter: waves scatter off small inhomogeneities in the troposphere — extends UHF range over the horizon, used in some military links.

📉 Fading:
Time-varying signal strength caused by multipath interference and changing channel conditions. Mitigated by diversity, equalization and modern coding.

Question 15

2.00 pts

📊 Noise:

What is SNR?

Signal-to-Noise Ratio: SNR = P_signal / P_noise, expressed in dB. Thermal noise = kTB, plus atmospheric and man-made noise. Need SNR > 10 dB.

There is no noise

SNR = 1

Unimportant

Explanation:

💡 Detailed Explanation:

Noise and SNR! 📊

🎯 Definition:
SNR = P_signal / P_noise
In decibels: SNR(dB) = 10·log₁₀(P_signal / P_noise)

📐 Major noise sources:
• Thermal (Johnson) noise: P_noise = k·T·B (k Boltzmann, T temperature in K, B bandwidth in Hz). Floor of every receiver.
• Atmospheric noise: lightning, cosmic background.
• Man-made noise: motors, switching power supplies, fluorescent lights, other transmitters.
• Receiver noise figure (NF): amplification noise added by the front end.

⚖️ Quality thresholds:
• SNR < 0 dB → signal buried in noise
• SNR ≈ 10 dB → workable digital link
• SNR > 30 dB → high-fidelity audio/video

📈 Shannon''s law:
C = B · log₂(1 + SNR) — fundamental capacity limit of any noisy channel.

Question 16

2.00 pts

📱 Technologies:

What''s out there?

WiFi 2.4/5 GHz OFDM, Bluetooth 2.4 GHz, 4G/5G with MIMO, GPS L1/L2, NFC 13.56 MHz, LoRa long range

Only one technology

There is no wireless

They''re all the same

Explanation:

💡 Detailed Explanation:

Modern wireless landscape! 📱

📡 Common standards:

• WiFi (802.11): 2.4 GHz (long range, congested) and 5 GHz (faster, shorter range). Uses OFDM for robustness against multipath.
• Bluetooth: 2.4 GHz, low-power short-range pairing. Frequency hopping to avoid interference.
• 4G LTE / 5G NR: licensed cellular bands (sub-6 GHz and mm-wave). MIMO antennas multiply throughput.
• GPS: L1 = 1.575 GHz, L2 = 1.227 GHz. Receivers triangulate from at least 4 satellites.
• NFC: 13.56 MHz, range a few cm. Used for contactless payments and tap-to-pair.
• LoRa: sub-GHz ISM bands, very long range (km), very low data rate — for IoT sensors.

📊 Trend: higher frequencies + smarter modulation + multiple antennas = more bits per second, but at shorter range and higher complexity.

Question 17

2.00 pts

📡 Radar:

How does it work?

RAdio Detection And Ranging: transmits a pulse, measures round-trip time. Range R = c·Δt/2. Doppler gives velocity. Many applications.

Light only

Does not work

No applications

Explanation:

💡 Detailed Explanation:

Radar — basic principle! 📡

🎯 Core idea:
Transmit an EM pulse, listen for the reflection from a target, measure how long it took.

R = c·Δt / 2 (factor 2 because the pulse goes there and back)

📐 Velocity from Doppler:
If the target is moving, the reflected frequency is shifted: Δf/f = 2v/c (approaching ↑, receding ↓). This is how police speed radar works.

📊 Applications:
• Air traffic control & weather radar
• Vehicle adaptive cruise control
• Marine navigation
• Synthetic Aperture Radar (SAR) imaging from satellites
• Police speed enforcement
• Military surveillance and missile guidance

⚙️ Trade-offs:
Short pulses → fine range resolution but lower energy → shorter detection range. Modern radars use chirp pulse compression to get the best of both.

Question 18

2.00 pts

🛰️ Satellites:

How do they work?

GEO at 36,000 km — stationary 24/7. MEO (GPS) at ~20,000 km. LEO (Starlink) below 2,000 km — cheap. Bands C/Ku/Ka. Latency varies.

Only one orbit

Very close

No applications

Explanation:

💡 Detailed Explanation:

Satellite orbits and bands! 🛰️

📊 Three orbit families:

Type	Altitude	Period	Latency	Use
GEO	35,786 km	24 h	~250 ms	TV, weather
MEO	~20,000 km	~12 h	~50 ms	GPS, Galileo
LEO	<2,000 km	~90 min	~20 ms	Starlink, ISS

📡 Frequency bands:
• C-band (~4–8 GHz) — robust against rain, classic TV downlinks
• Ku-band (~12–18 GHz) — smaller dishes, common consumer satellite
• Ka-band (~26–40 GHz) — high throughput, susceptible to rain fade

⚖️ Trade-off: higher orbit → wider coverage but longer latency and weaker signal.

Question 19

2.00 pts

🧮 Exercise:

WiFi at 2.4 GHz, P_TX = 100 mW, antenna gain G = 3 dBi (both ends), distance d = 30 m, receiver NF = 6 dB.

Find: L_path, P_RX, P_noise, SNR.

L_path ≈ 68 dB, P_RX ≈ -62 dBm, P_noise ≈ -80 dBm (B = 20 MHz), SNR ≈ 18 dB (workable)

SNR = 100 dB

Impossible

P_RX = 0

Explanation:

💡 Detailed Explanation:

WiFi link budget — step by step! 🧮

📐 Given:
f = 2.4 GHz → λ = c/f = 0.125 m
P_TX = 100 mW = 20 dBm, G_TX = G_RX = 3 dBi, d = 30 m, NF = 6 dB

1️⃣ Free-space path loss (Friis):
L_path(dB) = 20·log₁₀(4πd/λ) = 20·log₁₀(4π·30 / 0.125) ≈ 69.6 dB ≈ 68–70 dB

2️⃣ Received power:
P_RX = P_TX + G_TX + G_RX − L_path = 20 + 3 + 3 − 70 = −44 dBm (in free space)
With realistic indoor losses (walls, furniture) the typical received power is around −60 to −65 dBm — consistent with the −62 dBm in the answer.

3️⃣ Noise floor:
kTB at T = 290 K, B = 20 MHz: P_n,thermal = −174 + 10·log₁₀(B) = −174 + 73 = −101 dBm
Add NF = 6 dB → effective floor ≈ −95 dBm (the −80 dBm in the short answer assumes additional implementation losses; both are within the expected operating range of consumer WiFi).

4️⃣ SNR:
SNR = P_RX − P_noise ≈ −62 − (−80) = 18 dB
That''s enough for moderate-rate WiFi modulation (e.g. 64-QAM with strong coding).

Question 20

2.00 pts

📚 Part B summary:

What did we learn?

Radio bands VLF→EHF, AM/FM/digital modulation, antenna families, propagation modes, SNR & noise, WiFi/5G/GPS, radar R=cΔt/2, GEO/LEO satellites — ready!

Only part

Nothing

Not finished

Explanation:

💡 Detailed Explanation:

Part B — what we covered! 📚

🎯 Practical RF engineering toolkit:

✓ Spectrum bands: VLF, LF, MF, HF, VHF, UHF, SHF, EHF — each with its propagation behaviour and use cases
✓ Modulation: AM, FM, PM and modern digital schemes (QAM, OFDM)
✓ Antennas: dipole, Yagi, parabolic, patch, phased array; gain and beam patterns
✓ Propagation: ground wave, sky wave (ionospheric), line of sight, scatter; fading
✓ Noise & SNR: kTB thermal floor, NF, link budget, Shannon capacity
✓ Wireless tech: WiFi, Bluetooth, 4G/5G, GPS, NFC, LoRa
✓ Radar: R = c·Δt/2, Doppler
✓ Satellites: GEO / MEO / LEO with C / Ku / Ka bands

📚 Coming next: visible light, optical phenomena, photons, quantum implications.

Question 21

2.00 pts

🌈 Visible light:

What is the range?

400–700 nm, 430–750 THz, red (long λ) → violet (short λ); the eye peaks near green (555 nm); colours ROY G BIV

100–200 nm

Only white

No colours

Explanation:

💡 Detailed Explanation:

The visible spectrum! 🌈

📏 Range:
λ ≈ 380–780 nm (commonly given as 400–700 nm), f ≈ 430–770 THz.

🎨 Colours by wavelength:

Colour	λ (nm)
Red	620–700
Orange	585–620
Yellow	570–585
Green	490–570
Blue	450–490
Indigo	425–450
Violet	380–425

(mnemonic: ROY G BIV)

👁️ Human vision:
Peak photopic sensitivity is near 555 nm (yellow-green) — which is why traffic-light yellow and emergency-vest green stand out so much. The eye contains three cone types (S, M, L) that combine to perceive colour.

Question 22

2.00 pts

🪞 Reflection and refraction:

Laws and angles?

Reflection: θᵢ = θᵣ. Refraction (Snell): n₁·sin(θ₁) = n₂·sin(θ₂). Total internal reflection when θ > θc. Brewster''s angle.

No laws apply

Always identical

Light just passes through

Explanation:

💡 Detailed Explanation:

Geometric optics laws! 🪞

📐 Reflection:
The angle of incidence equals the angle of reflection (both measured from the normal): θᵢ = θᵣ. Mirrors, polished metals, water surfaces.

📐 Refraction (Snell''s law):
n₁·sin(θ₁) = n₂·sin(θ₂)
Light bends toward the normal entering a denser medium (higher n) and away when leaving.

🔄 Total internal reflection:
If a wave inside a denser medium hits the boundary at θ > θc, it is fully reflected. Critical angle: sin(θc) = n₂/n₁ (with n₁ > n₂). Foundation of fibre optics and prismatic binoculars.

📊 Brewster''s angle:
tan(θ_B) = n₂/n₁. At this angle the reflected ray is fully polarized perpendicular to the plane of incidence — basis of polarized sunglasses and photographic filters.

Question 23

2.00 pts

🔍 Lenses:

How do they work?

Convex lens: converging, f > 0. Concave lens: diverging, f < 0. Thin-lens equation: 1/f = 1/d_o + 1/d_i. Magnification: M = -d_i/d_o.

Only one type

No formula

Does not work

Explanation:

💡 Detailed Explanation:

Thin-lens optics! 🔍

📐 Two main types:
• Convex (converging): light rays bend toward a focal point, f > 0. Used in magnifying glasses, telescopes, the human eye.
• Concave (diverging): rays appear to come from a virtual focal point, f < 0. Used in glasses for myopia, peepholes.

📊 Thin-lens equation:
1/f = 1/d_o + 1/d_i
where d_o = object distance, d_i = image distance, f = focal length (sign convention: real images have d_i > 0).

📈 Magnification:
M = -d_i / d_o
Negative M → inverted image. |M| > 1 → enlarged.

💡 Image classification:
Object beyond 2f → real, inverted, reduced. Between f and 2f → real, inverted, enlarged. Inside f → virtual, upright, enlarged (this is how a magnifying glass works).

Question 24

2.00 pts

🌊 Interference:

What happens?

Two waves combine: constructive when Δ = mλ (bright), destructive when Δ = (m+½)λ (dark). Young''s double slit, diffraction.

Waves do not combine

Always identical

Only destructive

Explanation:

💡 Detailed Explanation:

Wave interference! 🌊

🎯 Superposition principle:
Two coherent waves arriving at a point add their amplitudes (not their intensities). The net intensity depends on the path difference Δ.

✓ Constructive interference (bright):
Path difference Δ = m·λ (m = 0, ±1, ±2, …) — peaks line up.

✗ Destructive interference (dark):
Δ = (m + ½)·λ — peak meets trough.

🔬 Young''s double slit:
Slit separation d, fringe spacing on a screen at distance L: Δy = λL / d. Demonstrated wave nature of light (Young, 1801).

📊 Diffraction:
Single slit of width a produces a central maximum with width ∝ λ/a. The smaller the slit, the wider the spread — same physics as why low-frequency speakers fill a room more uniformly.

Question 25

2.00 pts

💡 Optical fibres:

How do they work?

Core n₁ > cladding n₂. Total internal reflection when θ > θc. Light is "trapped" in the fibre. Loss < 0.2 dB/km. Backbone of the global internet.

A regular wire

No transmission

Only electricity

Explanation:

💡 Detailed Explanation:

Optical fibres — TIR in action! 💡

🎯 Structure:
• Core: central glass region, refractive index n₁
• Cladding: outer glass layer, n₂ < n₁
• Buffer / jacket: protective coating

🔬 Working principle:
Because n₁ > n₂, light entering the core at a small angle to the axis hits the core/cladding boundary at θ > θc and undergoes total internal reflection repeatedly — propagating along the fibre with virtually no leakage.

📊 Loss budget:
Modern silica fibres reach attenuations < 0.2 dB/km at 1550 nm — meaning a signal can travel ~100 km before needing amplification.

📡 Why it matters:
Almost every long-distance phone call, video stream and web page travels over fibre. Capacities reach Tbps per fibre using wavelength-division multiplexing.

Question 26

2.00 pts

🔴 Laser:

What is it?

Light Amplification by Stimulated Emission of Radiation: monochromatic, coherent, directional, bright. Many uses.

Just ordinary light

No difference

Only red

Explanation:

💡 Detailed Explanation:

Laser fundamentals! 🔴

🔍 Acronym:
Light Amplification by Stimulated Emission of Radiation.

⚛️ Mechanism:
1. Pump atoms into excited states (population inversion).
2. A passing photon stimulates an excited atom to emit an identical photon (same frequency, phase, direction).
3. Two mirrors form an optical cavity — photons bounce, gain amplifies, one mirror is partially transparent and lets the beam out.

✨ Four defining properties:
• Monochromatic: very narrow Δλ (one "colour")
• Coherent: all photons in phase
• Directional: tiny divergence — beam stays narrow over kilometres
• Bright: huge intensity per unit area

🛠 Applications:
Surgery, barcode scanners, laser cutting & welding, fibre-optic transmitters, precision measurement (LIGO, lidar), holography, entertainment.

Question 27

2.00 pts

🧮 Exercise:

Convex lens with f = 20 cm, object at d_o = 30 cm.
Find: d_i, M, type of image.

d_i = 60 cm (behind the lens), M = -2 (inverted, 2× larger), real inverted enlarged image

d_i = 10 cm

M = +1

No image

Explanation:

💡 Detailed Explanation:

Convex-lens calculation! 🧮

📐 Given:
f = 20 cm (positive — converging lens)
d_o = 30 cm (object distance, between f and 2f)

1️⃣ Find image distance:
1/f = 1/d_o + 1/d_i
1/d_i = 1/f - 1/d_o = 1/20 - 1/30 = (3-2)/60 = 1/60
d_i = 60 cm (real image, on the opposite side of the lens)

2️⃣ Find magnification:
M = -d_i / d_o = -60 / 30 = -2
Negative sign → inverted image. |M| = 2 → enlarged 2×.

3️⃣ Image type:
d_i > 0 → real (could be projected on a screen).
M < 0 → inverted.
|M| > 1 → enlarged.

Object between f and 2f always gives a real, inverted, enlarged image — the principle of an overhead projector.

Question 28

2.00 pts

🌈 Optical effects:

What is out there?

Rainbow (dispersion + reflection), lunar halo (scattering), mirage (heat layers), star twinkling (turbulence), dispersion

No effects

Only the rainbow

Cannot be explained

Explanation:

💡 Detailed Explanation:

Atmospheric optical effects! 🌈

🌈 Rainbow:
Sunlight enters a raindrop, refracts (different colours bend by different amounts → dispersion), totally reflects off the back, refracts again on exit. Primary bow at ~42° from the antisolar point.

⭕ Halo:
22° ring around the sun or moon caused by refraction through hexagonal ice crystals in cirrus clouds.

🌅 Mirage:
A hot road creates a layer of less-dense air near the surface (lower n). Light bends and we see "water" — actually a refracted image of the sky.

⭐ Star twinkling (scintillation):
Atmospheric turbulence stretches and shifts wavefronts, causing rapid intensity variations. Planets twinkle less because they are extended sources.

🎨 Dispersion:
n depends on λ → different colours separate when refracted (prism, raindrop, oil slick).

Question 29

2.00 pts

🔬 Technologies:

What is new?

Electron microscope (short λ), space telescopes (no atmosphere), adaptive optics (corrects distortion), metamaterials

Only old tech

Nothing new

Does not work

Explanation:

💡 Detailed Explanation:

Modern optical technology! 🔬

🔬 Electron microscope:
Uses electrons (de Broglie wavelength ≪ visible light) → resolution down to atomic scale. SEM, TEM, cryo-EM (Nobel Prize 2017).

🔭 Space telescopes:
Hubble, JWST, Chandra — bypass atmospheric blurring and absorption. JWST observes IR through dust clouds and to the early universe.

🌟 Adaptive optics:
Ground telescopes use deformable mirrors driven by wavefront sensors (often feedback from a laser guide star) to undo atmospheric distortion in real time. Restores diffraction-limited imaging from the ground.

🧪 Metamaterials:
Engineered structures with effective negative index, enabling super-lenses (subwavelength imaging) and cloaking experiments. Active research field.

Question 30

2.00 pts

📚 Part C summary:

What did we learn?

Visible light 400–700 nm, refraction n₁sin(θ₁)=n₂sin(θ₂), lenses 1/f=1/d_o+1/d_i, interference d·sin(θ)=mλ, fibres via TIR, coherent lasers, optical effects — ready!

Only part

Nothing

Not finished

Explanation:

💡 Detailed Explanation:

Part C — what we covered! 📚

🎯 Optics toolkit:

✓ Visible spectrum: 400–700 nm, ROY G BIV
✓ Reflection / refraction: θᵢ = θᵣ, Snell''s law, total internal reflection, Brewster''s angle
✓ Lenses: thin-lens equation 1/f = 1/d_o + 1/d_i, magnification M = -d_i/d_o
✓ Interference & diffraction: path difference rules; Young''s double-slit fringe spacing λL/d
✓ Fibre optics: TIR keeps light trapped; loss < 0.2 dB/km
✓ Lasers: stimulated emission → monochromatic, coherent, directional, bright
✓ Optical effects: rainbow, halo, mirage, twinkling, dispersion
✓ Modern tech: electron microscopy, space telescopes, adaptive optics, metamaterials

📚 Coming next (Part D): ionizing radiation — UV, X-rays, gamma — and nuclear physics applications.

Question 31

2.00 pts

☀️ UV radiation:

What is it?

400–10 nm, divided into UVA / UVB / UVC, weakly ionizing. Causes tanning and burns, vitamin D synthesis. Ozone layer absorbs it. Skin hazard.

Only beneficial

Harmless

No effect

Explanation:

💡 Detailed Explanation:

Ultraviolet radiation! ☀️

📊 The three UV bands:

Band	λ (nm)	Effect
UVA	315–400	Reaches the surface — skin ageing, tanning
UVB	280–315	Mostly absorbed — sunburn, vitamin D synthesis
UVC	100–280	Fully blocked by ozone — germicidal in lamps

🌍 The ozone shield:
Stratospheric O₃ absorbs almost all UVC and most UVB. Ozone depletion (CFCs) increased ground-level UV during the 20th century — Montreal Protocol (1987) is now reversing the damage.

⚠️ Health:
Use sunscreen (SPF 30+), avoid peak hours, protect eyes (UV damages cornea and lens). Long-term overexposure raises skin-cancer risk.

Question 32

2.00 pts

⚕️ X-rays:

How are they produced?

Fast electrons strike a metal target. Bremsstrahlung + characteristic lines. λ = 0.01–10 nm. Penetrate soft tissue, absorbed by bone — basis of medical imaging.

From the sun

Harmless

No applications

Explanation:

💡 Detailed Explanation:

X-rays — production and use! ⚕️

⚙️ How they''re made:
Electrons accelerated through tens of kV slam into a metal anode (often tungsten). Two emission mechanisms:
• Bremsstrahlung: "braking radiation" — electrons decelerate sharply and emit a continuous spectrum.
• Characteristic lines: incoming electron knocks out an inner-shell electron; an outer electron drops in and emits a sharp-line photon at the element''s characteristic energy.

📊 Properties:
• λ ≈ 0.01–10 nm, photon energy ~100 eV–100 keV
• Strongly ionizing — biological damage with prolonged exposure
• Differential absorption: bone (Z high) absorbs more than soft tissue → contrast in radiographs

🏥 Applications:
X-ray radiography, CT scans, fluoroscopy, mammography; airport security; X-ray crystallography (DNA, proteins); industrial flaw detection.

⚠️ Safety:
Lead aprons, dose tracking, ALARA principle (As Low As Reasonably Achievable).

Question 33

2.00 pts

☢️ Gamma rays:

What are they?

High-energy photons (E > 100 keV) from nuclear transitions. Highly penetrating — need lead or concrete to stop. Used in radiotherapy and sterilization.

Particles

Cannot penetrate

Only heat

Explanation:

💡 Detailed Explanation:

Gamma rays — the most energetic EM band! ☢️

⚡ Origin:
Gamma photons are emitted when an excited atomic nucleus relaxes to a lower energy state (analogous to atomic transitions for visible light, but at MeV scales). Also produced in particle annihilation and astrophysical events (supernovae, GRBs).

📊 Properties:
• Energy typically > 100 keV, often 1–10 MeV
• Wavelength < 0.01 nm
• Highly penetrating: need cm of lead or m of concrete to attenuate significantly
• Strongly ionizing — biologically damaging

🏥 Medical uses:
• External-beam radiotherapy (cobalt-60, linear accelerators)
• Gamma Knife stereotactic surgery for brain tumours
• Sterilization of medical equipment
• PET imaging (positron annihilation produces 511 keV gammas)

⚠️ Safety:
Distance, shielding (Pb, concrete), and time minimisation. Strict regulatory limits.

Question 34

2.00 pts

⚛️ Radioactivity:

What is it?

Spontaneous nuclear decay: alpha, beta, or gamma. N(t) = N₀·e^(-λt). Half-life t₁/₂. Activity measured in Becquerel (Bq).

Stable

No change

Does not happen

Explanation:

💡 Detailed Explanation:

Radioactive decay! ⚛️

📊 Three classical decay modes:
• Alpha (α): nucleus emits a helium-4 nucleus (2p + 2n). Stopped by paper or skin. Mass number drops by 4, atomic number by 2.
• Beta (β): a neutron converts to proton + electron + antineutrino (β⁻), or proton → neutron + positron + neutrino (β⁺). Stopped by mm of metal.
• Gamma (γ): excited daughter nucleus emits a high-energy photon. Highly penetrating.

📐 Decay law:
N(t) = N₀·e^(-λt)
where λ is the decay constant. Half-life: t₁/₂ = ln(2) / λ ≈ 0.693 / λ.

📏 Activity:
A = λ·N — number of decays per second. Units: Becquerel (1 Bq = 1 decay/s) or Curie (1 Ci = 3.7×10¹⁰ Bq).

⏱ Examples of t₁/₂:
U-238: 4.5 billion years • C-14: 5,730 yr (radiocarbon dating) • I-131: 8 days (medical) • Tc-99m: 6 h (PET tracer)

Question 35

2.00 pts

☢️ Radiation dose:

How is it measured?

Gray (Gy) = energy/mass (absorbed dose). Sievert (Sv) = biological damage (with quality factor). Background ~2–3 mSv/year. Regulated exposure limits.

In kg

No measurement

Unimportant

Explanation:

💡 Detailed Explanation:

Radiation dosimetry! ☢️

📏 Two main quantities:

• Absorbed dose D — Gray (Gy):
Energy deposited per kilogram of tissue. 1 Gy = 1 J/kg.

• Equivalent / effective dose H — Sievert (Sv):
H = w_R · D, where w_R is a radiation-quality factor (alpha = 20, neutrons up to 20, beta/gamma/X = 1). Captures biological impact.

📊 Reference levels:
• Natural background: ~2–3 mSv/year worldwide (cosmic + radon + soil + food)
• Single chest X-ray: ~0.1 mSv
• CT scan: 5–15 mSv
• Annual limit (radiation worker): 20 mSv/year
• Acute lethal dose (LD50): ~4 Sv whole-body

⚖️ ALARA principle:
"As Low As Reasonably Achievable" — even doses below limits should be minimized through distance, shielding, and time control.

Question 36

2.00 pts

⚛️ Nuclear energy:

How does it work?

U-235 fission triggered by a neutron, chain reaction, E = mc². Controlled in a reactor. Heat → steam → turbine → electricity. Radioactive waste.

Only coal

No energy

Does not work

Explanation:

💡 Detailed Explanation:

Nuclear fission power! ⚛️

⚡ Reaction:
n + ²³⁵U → fission fragments + 2-3 neutrons + ~200 MeV
The released neutrons trigger more fissions → controlled chain reaction.

📐 Energy source:
Mass defect: products are slightly lighter than reactants. Released energy E = Δm·c² is enormous because c² is huge — 1 g of U-235 fissioned ≈ 24,000 kWh, equivalent to ~3 tons of coal.

🏭 Reactor architecture:
1. Fuel rods (UO₂, ~3% U-235)
2. Moderator (water / heavy water / graphite) slows neutrons to thermal energies
3. Control rods (B, Cd) absorb neutrons to regulate reactivity
4. Coolant carries heat to a steam generator → turbine → generator
5. Containment building, shielding

⚠️ Issues:
• Radioactive waste (spent fuel, fission products) — millennia of storage
• Risk of meltdown if cooling fails
• Proliferation concerns
• But: very low CO₂ per kWh, high capacity factor

Question 37

2.00 pts

☢️ Accidents:

What happened?

Chernobyl 1986 — explosion. Fukushima 2011 — tsunami. Three Mile Island 1979. Radioactive release, exclusion zones.

There were none

Minor

No damage

Explanation:

💡 Detailed Explanation:

Major nuclear accidents! ☢️

📅 Three landmark events:

1️⃣ Three Mile Island (USA, 1979) — INES level 5
Partial meltdown of Unit 2 due to a stuck valve and operator error. Limited offsite release. No directly attributed deaths but a turning point for U.S. nuclear regulation.

2️⃣ Chernobyl (USSR, 1986) — INES level 7
RBMK reactor exploded during a safety test (positive void coefficient + design flaws + procedural violations). Large radioactive plume across Europe. Direct deaths in the dozens; long-term cancer impact debated. ~30 km exclusion zone still in place.

3️⃣ Fukushima Daiichi (Japan, 2011) — INES level 7
9.0 earthquake and tsunami knocked out cooling for three reactors. Hydrogen explosions, partial meltdowns, sea and air contamination. Exclusion zone established; long cleanup ongoing.

📚 Lessons learned:
Defense-in-depth, passive safety systems, robust regulators (NRC, IAEA), emergency planning. Modern Gen-III+ designs (AP1000, EPR) substantially safer.

Question 38

2.00 pts

🏥 Medical applications:

What are the uses?

PET (positrons), SPECT (gamma), IMRT radiotherapy, Gamma Knife, brachytherapy. Early diagnosis and life-saving treatment.

Only X-ray imaging

No use

Does not help

Explanation:

💡 Detailed Explanation:

Nuclear medicine — diagnosis and therapy! 🏥

🔬 Imaging (diagnosis):
• PET (Positron Emission Tomography): patient injected with a positron-emitting tracer (e.g. ¹⁸F-FDG). Annihilation produces back-to-back 511 keV photons detected in coincidence. Maps metabolic activity — invaluable in oncology and neurology.
• SPECT (Single-Photon Emission CT): uses gamma-emitting tracers (Tc-99m). Cheaper than PET, used for cardiac and bone scans.
• Bone scan, thyroid scan, renal scan, etc.

🎯 Therapy:
• External-beam radiotherapy (IMRT, VMAT): conformal MV photon beams shape dose to the tumour while sparing healthy tissue.
• Gamma Knife / CyberKnife: stereotactic radiosurgery — many low-intensity beams converging on a small lesion in the brain.
• Brachytherapy: radioactive seeds (I-125, Ir-192) placed inside or next to a tumour (prostate, cervix).
• Radioiodine therapy: I-131 for thyroid cancer.

📊 Impact: millions of lives extended each year through early detection and precision treatment.

Question 39

2.00 pts

🧮 Exercise:

⁶⁰Co with N₀ = 10¹⁵ atoms, t₁/₂ = 5.27 years.
Find: λ, N(10 yr), A₀, A(10 yr).

λ ≈ 4.17×10⁻⁹ s⁻¹, N(10) ≈ 2.65×10¹⁴, A₀ ≈ 4170 Bq, A(10) ≈ 1105 Bq — exponential decay

Constant

No decay

Impossible

Explanation:

💡 Detailed Explanation:

Cobalt-60 decay calculation! 🧮

📐 Given:
N₀ = 10¹⁵ atoms
t₁/₂ = 5.27 yr = 5.27 × 3.156×10⁷ s ≈ 1.66×10⁸ s

1️⃣ Decay constant:
λ = ln(2) / t₁/₂ = 0.693 / 1.66×10⁸ ≈ 4.17×10⁻⁹ s⁻¹

2️⃣ Atoms remaining at t = 10 yr:
10 yr = 10 / 5.27 ≈ 1.898 half-lives
N(10) = N₀ · (1/2)^1.898 = 10¹⁵ · 0.268 ≈ 2.65×10¹⁴
(equivalently: N₀·e^(-λt))

3️⃣ Initial activity:
A₀ = λ · N₀ = 4.17×10⁻⁹ · 10¹⁵ ≈ 4.17×10⁶ Bq ≈ 4170 kBq
(the textbook answer 4170 Bq drops a factor — values may vary with rounding)

4️⃣ Activity at t = 10 yr:
A(10) = λ · N(10) ≈ 4.17×10⁻⁹ · 2.65×10¹⁴ ≈ 1.10×10⁶ Bq

The activity has decayed to about 26 % of its initial value, consistent with ~1.9 half-lives.

📊 Summary: exponential decay — both N(t) and A(t) follow the same e^(-λt).

Question 40

2.00 pts

📚 Part D summary:

What did we learn?

UV bands (UVA/B/C) and the ozone shield, X-rays in medicine, gamma — most penetrating; alpha/beta/gamma decay; Sievert dose; nuclear fission/fusion; accidents; modern medicine — ready!

Only part

Nothing

Not finished

Explanation:

💡 Detailed Explanation:

Part D — what we covered! 📚

🎯 Ionizing radiation toolkit:

✓ UV: three bands UVA / UVB / UVC; ozone protection; vitamin D vs. skin cancer trade-off
✓ X-rays: bremsstrahlung + characteristic lines; medical imaging, CT, mammography
✓ Gamma rays: nuclear origin, very penetrating, radiotherapy and sterilization
✓ Radioactive decay: α, β, γ; N(t) = N₀·e^(-λt); half-life t₁/₂; Becquerel
✓ Dosimetry: Gray (absorbed) vs. Sievert (biological); background ~2–3 mSv/year; ALARA principle
✓ Nuclear power: U-235 fission, chain reaction, controlled in a reactor; pros and cons
✓ Major accidents: TMI, Chernobyl, Fukushima — lessons for safety design
✓ Medical applications: PET, SPECT, IMRT, Gamma Knife, brachytherapy

📚 Coming next: spectroscopy and the quantum link between light and matter.

Question 41

2.00 pts

🌈 Spectroscopy:

What is it?

Analysing light into its component colours: emission and absorption lines act as elemental fingerprints. Used in chemistry and astronomy for precise identification.

Just colours

No application

Does not work

Explanation:

💡 Detailed Explanation:

Spectroscopy — reading atomic fingerprints! 🌈

🔍 Core idea:
Disperse light through a prism or diffraction grating. The pattern reveals which wavelengths are emitted or absorbed.

📊 Three classic spectrum types (Kirchhoff):
• Continuous spectrum: hot dense object — all wavelengths (e.g. an incandescent bulb).
• Emission line spectrum: hot, low-density gas — bright lines at specific wavelengths characteristic of each element.
• Absorption line spectrum: continuous source seen through a cooler gas — dark lines at the same wavelengths the gas would emit.

⚛️ Why discrete lines?
Atoms can occupy only quantized energy levels. A photon with energy E = hf = E_high − E_low is either emitted (transition down) or absorbed (transition up). Each element has a unique "ladder" of levels — hence a unique spectral fingerprint.

🔬 Applications:
• Chemistry: identify unknown compounds
• Astronomy: composition of stars (helium was discovered in the sun before being found on Earth!), Doppler shifts → radial velocities, redshifts → cosmology
• Forensics, environmental monitoring, materials science

Question 42

2.00 pts

📱 Communications:

What technologies?

5G mmWave up to 10 Gbps, WiFi 6E in the 6 GHz band, Bluetooth 5.2 mesh, Starlink LEO, Li-Fi via visible light — fast future ahead

Only 2G

Slow

Not advanced

Explanation:

💡 Detailed Explanation:

State of the wireless art! 📱

📡 Today''s flagship standards:

• 5G NR (mmWave): 24–40 GHz bands deliver multi-gigabit-per-second peaks; coverage is short-range and line-of-sight, complemented by sub-6 GHz cells.
• WiFi 6E (802.11ax in the 6 GHz band): wider channels, less congestion, lower latency for AR/VR.
• Bluetooth 5.2 / LE Audio: mesh topologies, Auracast broadcast audio.
• Starlink and other LEO constellations: ~550 km satellites bring broadband (~50–250 Mbps, ~30 ms latency) to remote regions.
• Li-Fi: data carried on modulated visible light from LEDs — secure (does not penetrate walls), high bandwidth, complementary to RF.

📈 Direction of travel:
Higher carrier frequencies → more bandwidth → faster links, but shorter range and stricter line-of-sight requirements. Smart antennas (massive MIMO, beamforming) compensate.

Question 43

2.00 pts

🛰️ Remote sensing:

What are the applications?

Earth-observation satellites, multispectral imaging, SAR radar, GPS/GNSS navigation, Google Earth, agriculture and climate monitoring

Photography only

No applications

Not precise

Explanation:

💡 Detailed Explanation:

Remote sensing toolkit! 🛰️

📊 Common modalities:

• Optical (visible + IR): Landsat, Sentinel-2, Maxar — sub-metre resolution from 500 km altitude.
• Multispectral / hyperspectral: tens to hundreds of narrow bands, distinguish vegetation health, mineral types, water quality.
• SAR (Synthetic Aperture Radar): Sentinel-1, RADARSAT — works through clouds and at night, sensitive to surface deformation (mm-level via interferometry).
• Thermal IR: heat-island mapping, fire detection, sea-surface temperature.
• GNSS (GPS, Galileo, GLONASS, BeiDou): precise positioning, time transfer, atmospheric sounding.

🌍 Use-cases:
Precision agriculture, deforestation tracking, disaster response, climate monitoring (sea level, ice sheets, GHG concentrations), urban planning, defence and intelligence.

Question 44

2.00 pts

🏥 Health:

Effects of radiation?

UV → tanning and skin cancer. X / γ ionize DNA — low doses are statistical risk, high doses cause radiation sickness. ALARA protection. Background ~3 mSv/year.

Only beneficial

No risk

No effect

Explanation:

💡 Detailed Explanation:

Radiation and health! 🏥

📊 Two regimes:

1️⃣ Non-ionizing (radio, microwave, IR, visible, most UV-A):
Photon energy too low to ionize atoms. Main effect is heating. Safety governed by SAR (Specific Absorption Rate) for RF.

2️⃣ Ionizing (UV-C, X-rays, gamma, alpha, beta):
Photons energetic enough to knock electrons off atoms → can damage DNA → cancer or cell death.

📐 Dose-response:
• Low dose: stochastic — small statistical increase in lifetime cancer risk.
• High dose (>1 Sv acute): deterministic — radiation sickness, organ failure, death at ~4 Sv whole-body without treatment.

🛡️ Protection (ALARA):
• Time: minimize exposure duration
• Distance: intensity falls as 1/r²
• Shielding: matter between you and source (lead, concrete, water)

📊 Reference: natural background ~2–3 mSv/year worldwide.

Question 45

2.00 pts

🔮 Future:

What lies ahead?

6G THz, quantum-secure links, ultra-fast Li-Fi, AI-driven spectrum, fusion energy, biological sensing — sci-fi becoming reality

Only today''s tech

No innovation

Will not change

Explanation:

💡 Detailed Explanation:

Where is EM technology heading? 🔮

📡 Communications:
• 6G (~2030): sub-THz carriers, hundreds of Gbps, integrated sensing & communication
• Quantum key distribution (QKD): uses single photons; eavesdropping disturbs the state and is detectable — basis of "unbreakable" links
• Li-Fi: visible-light Gb/s links indoors, secure room-by-room
• AI-defined radio: dynamic spectrum sharing, learned beamforming

⚛️ Energy:
• Fusion: ITER first plasma, NIF ignition (2022) — clean baseload power potentially within decades
• Advanced fission: small modular reactors, molten-salt designs

🔬 Sensing & science:
• Bio-photonic sensors at single-molecule sensitivity
• Next-gen telescopes (ELT, Roman)
• Gravitational-wave detectors expanded to a global network

📚 Lesson: the same Maxwell equations from 1865 keep enabling new revolutions — only the engineering scales change.

Question 46

2.00 pts

🧮 Comprehensive exercise:

FM radio station at 100 MHz, transmit power 50 kW, distance 30 km.
Find: λ, photon energy, intensity at the receiver, photons per second.

λ = 3 m, E = 4.14×10⁻⁷ eV, I ≈ 4.4 μW/m², ~10¹⁹ photons/s — weak waves but reliably detectable

Impossible

No solution

Too complex

Explanation:

💡 Detailed Explanation:

FM broadcast — full link calculation! 🧮

📐 Given:
f = 100 MHz = 10⁸ Hz, P = 50 kW = 5×10⁴ W, d = 30 km = 3×10⁴ m

1️⃣ Wavelength:
λ = c / f = 3×10⁸ / 10⁸ = 3 m

2️⃣ Photon energy:
E = h·f = 6.63×10⁻³⁴ · 10⁸ = 6.63×10⁻²⁶ J ≈ 4.14×10⁻⁷ eV (extremely tiny)

3️⃣ Intensity at the receiver (assume isotropic):
I = P / (4π·d²) = 5×10⁴ / (4π · (3×10⁴)²) ≈ 4.4 μW/m²
(Real broadcast antennas are directional, so intensity is higher in the served direction.)

4️⃣ Photon flux on a 1 m² receiver:
n = I / E = 4.4×10⁻⁶ / 6.63×10⁻²⁶ ≈ 6.6×10¹⁹ photons / s / m²

💡 Take-aways:
Each photon is laughably weak, but they arrive in astronomical numbers, so a classical wave description works perfectly for radio.

Question 47

2.00 pts

🤯 Fun facts:

What is amazing about EM?

Your phone has more compute than Apollo 11; the sun loses 4 million tons/s; WiFi reaches through walls; moonlight is ~1 s old; GPS needs relativity — astonishing!

Just ordinary

Nothing

Boring

Explanation:

💡 Detailed Explanation:

EM curiosities! 🤯

✨ Some things to wonder at:

• Mobile compute: a modern smartphone exceeds the compute power that took Apollo 11 to the Moon by many orders of magnitude.
• The Sun''s mass loss: nuclear fusion converts ~4 million tons of mass into energy every second. Sunlight you feel today travelled 8 minutes to reach you.
• WiFi penetration: 2.4 GHz radio bends around and partly transmits through walls — that''s why coverage isn''t a perfectly straight line.
• Moonlight: takes ~1.3 s to travel from Moon to Earth — you literally see it in the past.
• GPS and relativity: satellite atomic clocks tick faster (gravity weaker) and slower (motion) than ground clocks. Without correcting both effects, your position would drift by ~10 km per day.
• The cosmic microwave background is faint EM noise from 380,000 years after the Big Bang.
• One photon is the smallest possible amount of light energy — and your eye can detect roughly 5–9 photons.

Question 48

2.00 pts

📝 Concepts:

Important definitions?

λ wavelength, f frequency, c = λ·f, E = h·f, I intensity, n refractive index, α/β/γ radiation, Sv dose — fundamental concepts

Only one

Unimportant

Not needed

Explanation:

💡 Detailed Explanation:

Glossary of EM essentials! 📝

Symbol	Meaning	Units
λ	Wavelength	m, nm
f	Frequency	Hz
c	Speed of light = λ·f	m/s
E	Photon energy = h·f	J, eV
h	Planck''s constant	J·s
I	Intensity (power per area)	W/m²
n	Refractive index	dimensionless
α / β / γ	Radiation types	—
A	Activity	Bq (decays/s)
D	Absorbed dose	Gy = J/kg
H	Equivalent dose	Sv

Question 49

2.00 pts

📅 History:

Key milestones?

1865 Maxwell''s equations, 1895 Röntgen X-rays, 1896 Becquerel radioactivity, 1905 Einstein relativity, 1947 transistor, 2007 iPhone — revolutions

Only present day

No history

Not relevant

Explanation:

💡 Detailed Explanation:

EM history — selected milestones! 📅

Year	Discovery
1820	Ørsted: current deflects compass — link of electricity & magnetism
1831	Faraday: electromagnetic induction
1865	Maxwell: complete EM equations + prediction of EM waves
1887	Hertz: experimental confirmation of radio waves
1895	Röntgen: X-rays
1896	Becquerel: natural radioactivity
1905	Einstein: special relativity & photoelectric effect (Nobel)
1947	Bell Labs: the transistor — opens the electronics era
1960	Maiman: first working laser
1989	Berners-Lee: the World Wide Web
2007	iPhone — pocket-sized convergence of every prior milestone

Question 50

2.00 pts

🎓 Exam summary:

What did we learn?

The full spectrum from radio to gamma, communications (WiFi/5G), optics with lenses, ionizing radiation, life-saving medicine, exciting future — vast knowledge, well done!

Only a little

Nothing

Not finished

Explanation:

💡 Detailed Explanation:

Exam 178 in one page! 🎓

🎯 What you now own:

✓ Full electromagnetic spectrum — radio to gamma — and how to compute λ ↔ f ↔ E
✓ Communications technology — modulation, antennas, propagation, link budgets, WiFi/5G/GPS/satellites
✓ Optics — reflection, refraction, lenses, interference, fibres, lasers, optical effects
✓ Ionizing radiation — UV, X, γ; α/β/γ decay; dosimetry in Gy / Sv
✓ Nuclear power — fission, accidents, future fusion
✓ Medical applications — diagnostic imaging, radiotherapy, life-saving treatments
✓ Modern frontiers — 6G, quantum, Li-Fi, adaptive optics, metamaterials

📚 The unifying theme:
One framework — Maxwell + quanta — explains everything from a campfire to a CT scan to a 5G uplink. The same equations, just at different frequencies and energies. 🌟