IB Physics How to Solve: IB Physics HL – Option Topics (Relativity, Astrophysics, Imaging, Engineering Physics)

How to Solve: IB Physics HL – Option Topics (Relativity, Astrophysics, Imaging, Engineering Physics)

Complete Guide

Introduction

"Mastering these option topics can boost your IB Physics HL score by 10–15 marks—enough to push you from a 6 to a 7. Whether it’s calculating time dilation for a spaceship, determining the mass of a black hole, or designing a medical imaging system, these questions appear in Paper 3 and are worth 20% of your final grade. Let’s break them down so you can solve them in under 5 minutes."

WHAT YOU NEED TO KNOW FIRST

Before diving into the options, ensure you understand: 1. Core Physics Concepts – Kinematics, forces, energy, waves, and electromagnetism (SL/HL). 2. Mathematical Skills – Algebra, unit conversions, and interpreting graphs. 3. Problem-Solving Framework – Identify given data, select the right formula, and check units.

KEY TERMS & FORMULAS

1. Relativity (Option A)

Key Terms: - Inertial frame of reference – A non-accelerating frame where Newton’s laws hold. - Proper time (τ) – Time measured by an observer at rest relative to the event. - Relativistic momentum (p) – Momentum at speeds close to c (speed of light). - Rest energy (E₀) – Energy of an object at rest (E₀ = mc²).

Formulas: | Formula | Variables | Memorise? | |---------|-----------|-----------| | Time dilation: Δt = γΔτ | Δt = time observed by moving observer, Δτ = proper time, γ = Lorentz factor | MEMORISE THIS | | Lorentz factor: γ = 1 / √(1 – v²/c²) | v = relative velocity, c = speed of light | MEMORISE THIS | | Length contraction: L = L₀ / γ | L = contracted length, L₀ = proper length | MEMORISE THIS | | Relativistic momentum: p = γmv | m = rest mass, v = velocity | MEMORISE THIS | | Total energy: E = γmc² | E = total energy | MEMORISE THIS | | Energy-momentum relation: E² = p²c² + m²c⁴ | p = momentum | MEMORISE THIS |

2. Astrophysics (Option D)

Key Terms: - Apparent magnitude (m) – Brightness of a star as seen from Earth. - Absolute magnitude (M) – Brightness of a star at 10 pc (parsecs). - Luminosity (L) – Total energy emitted per second. - Blackbody radiation – Emission from a perfect emitter (stars approximate this). - Doppler effect – Shift in wavelength due to relative motion.

Formulas: | Formula | Variables | Memorise? | |---------|-----------|-----------| | Distance modulus: m – M = 5 log(d/10) | d = distance in parsecs | MEMORISE THIS | | Luminosity relation: L = 4πd²b | b = apparent brightness | MEMORISE THIS | | Stefan-Boltzmann Law: L = 4πR²σT⁴ | R = radius, σ = Stefan-Boltzmann constant, T = temperature | MEMORISE THIS | | Wien’s Law: λ_max T = 2.9 × 10⁻³ m·K | λ_max = peak wavelength | MEMORISE THIS | | Doppler shift (non-relativistic): Δλ/λ = v/c | Δλ = change in wavelength, v = radial velocity | MEMORISE THIS | | Hubble’s Law: v = H₀d | H₀ = Hubble constant, d = distance | MEMORISE THIS |

3. Imaging (Option E)

Key Terms: - Focal length (f) – Distance from lens/mirror to focal point. - Magnification (M) – Ratio of image size to object size. - Resolution (θ) – Smallest angle between two distinguishable points. - Spherical aberration – Blurring due to lens shape. - Chromatic aberration – Color distortion due to different wavelengths focusing differently.

Formulas: | Formula | Variables | Memorise? | |---------|-----------|-----------| | Lens formula: 1/f = 1/v + 1/u | v = image distance, u = object distance | MEMORISE THIS | | Magnification: M = v/u = h_i/h_o | h_i = image height, h_o = object height | MEMORISE THIS | | Resolution (Rayleigh criterion): θ = 1.22λ/D | λ = wavelength, D = aperture diameter | MEMORISE THIS | | Power of a lens: P = 1/f | P = power in diopters (m⁻¹) | MEMORISE THIS |

4. Engineering Physics (Option F)

Key Terms: - Stress (σ) – Force per unit area (σ = F/A). - Strain (ε) – Deformation per unit length (ε = ΔL/L). - Young’s modulus (E) – Measure of stiffness (E = σ/ε). - Thermal expansion: ΔL = αL₀ΔT | α = coefficient of linear expansion. - Resonance – Maximum amplitude at natural frequency.

Formulas: | Formula | Variables | Memorise? | |---------|-----------|-----------| | Hooke’s Law: F = kx | k = spring constant, x = extension | MEMORISE THIS | | Young’s modulus: E = σ/ε | σ = stress, ε = strain | MEMORISE THIS | | Thermal expansion: ΔL = αL₀ΔT | α = coefficient of linear expansion | MEMORISE THIS | | Resonance frequency (mass-spring): f = 1/(2π)√(k/m) | k = spring constant, m = mass | MEMORISE THIS | | Damping ratio (ζ): ζ = c/(2√(mk)) | c = damping coefficient | MEMORISE THIS |

STEP-BY-STEP METHOD

General Problem-Solving Framework (All Options)

1. Read the question carefully. Underline key data and what is being asked.
2. Identify the topic. Is it relativity, astrophysics, imaging, or engineering?
3. List knowns and unknowns. Write down all given values and what you need to find.
4. Select the correct formula. Check the formula sheet if unsure.
5. Rearrange the formula (if needed) to solve for the unknown.
6. Substitute values with units. Convert units if necessary (e.g., km to m, years to seconds).
7. Calculate and check units. Ensure the answer makes sense (e.g., time dilation > proper time).
8. Round to significant figures. IB usually expects 2–3 sig figs.
9. Write a concluding statement. Answer the question directly.

WORKED EXAMPLES

Example 1 – Relativity (Basic)

Question: A spaceship travels at 0.8c relative to Earth. If 5 years pass on the spaceship, how much time passes on Earth?

Step-by-Step Solution: 1. Identify topic: Time dilation (Relativity). 2. Knowns:
- v = 0.8c
- Δτ = 5 years (proper time on spaceship) 3. Unknown: Δt (time on Earth). 4. Formula: Δt = γΔτ and γ = 1 / √(1 – v²/c²). 5. Calculate γ:
- γ = 1 / √(1 – (0.8c)²/c²) = 1 / √(1 – 0.64) = 1 / √0.36 = 1/0.6 ≈ 1.667 6. Calculate Δt:
- Δt = 1.667 × 5 = 8.335 years 7. Check units: Years (correct). 8. Round: 8.34 years (3 sig figs). 9. Conclusion: 8.34 years pass on Earth.

What we did and why: - Used time dilation because the spaceship is moving at relativistic speeds. - Calculated γ first because it’s needed for Δt. - Ensured units were consistent (years).

Example 2 – Astrophysics (Medium)

Question: A star has an apparent magnitude of 5 and an absolute magnitude of 2. How far away is it in parsecs?

Step-by-Step Solution: 1. Identify topic: Distance modulus (Astrophysics). 2. Knowns:
- m = 5
- M = 2 3. Unknown: d (distance in parsecs). 4. Formula: m – M = 5 log(d/10). 5. Rearrange for d:
- 5 – 2 = 5 log(d/10)
- 3 = 5 log(d/10)
- log(d/10) = 3/5 = 0.6
- d/10 = 10^0.6 ≈ 3.98
- d ≈ 39.8 parsecs 6. Check units: Parsecs (correct). 7. Round: 40 parsecs (2 sig figs). 8. Conclusion: The star is 40 parsecs away.

What we did and why: - Used the distance modulus formula because we had m and M. - Rearranged the formula to solve for d before substituting. - Remembered that log is base 10.

Example 3 – Imaging (Exam-Style)

Question: A telescope has an aperture diameter of 0.5 m. What is the smallest angular separation it can resolve for light of wavelength 500 nm?

Step-by-Step Solution: 1. Identify topic: Resolution (Imaging). 2. Knowns:
- D = 0.5 m
- λ = 500 nm = 5 × 10⁻⁷ m 3. Unknown: θ (angular resolution). 4. Formula: θ = 1.22λ/D. 5. Substitute values:
- θ = (1.22 × 5 × 10⁻⁷) / 0.5
- θ = 1.22 × 10⁻⁶ radians 6. Convert to arcseconds (optional):
- 1 radian ≈ 206,265 arcseconds
- θ ≈ 1.22 × 10⁻⁶ × 206,265 ≈ 0.25 arcseconds 7. Check units: Radians (or arcseconds, if required). 8. Round: 1.2 × 10⁻⁶ radians (2 sig figs). 9. Conclusion: The smallest resolvable angle is 1.2 × 10⁻⁶ radians.

What we did and why: - Used the Rayleigh criterion for resolution. - Converted nm to m to match units. - Recognized that the answer could be left in radians unless specified otherwise.

Example 4 – Engineering Physics (Exam-Style)

Question: A steel rod (E = 200 GPa) of length 2 m and cross-sectional area 1 × 10⁻⁴ m² is stretched by a force of 10 kN. What is its extension?

Step-by-Step Solution: 1. Identify topic: Stress and strain (Engineering Physics). 2. Knowns:
- F = 10 kN = 10,000 N
- A = 1 × 10⁻⁴ m²
- L₀ = 2 m
- E = 200 GPa = 2 × 10¹¹ Pa 3. Unknown: ΔL (extension). 4. Formulas:
- σ = F/A
- ε = ΔL/L₀
- E = σ/ε → ΔL = (F × L₀) / (A × E) 5. Calculate ΔL:
- ΔL = (10,000 × 2) / (1 × 10⁻⁴ × 2 × 10¹¹)
- ΔL = 20,000 / (2 × 10⁷) = 1 × 10⁻³ m = 1 mm 6. Check units: Meters (correct). 7. Round: 1.0 mm (2 sig figs). 8. Conclusion: The rod extends by 1.0 mm.

What we did and why: - Combined stress, strain, and Young’s modulus. - Converted kN to N and GPa to Pa for consistency. - Used the rearranged formula to solve directly for ΔL.

COMMON MISTAKES

EXAM TRAPS

1-MINUTE RECAP (Night Before the Exam)

"Listen up—this is your 60-second crash course for IB Physics HL Option Topics. For Relativity, remember: time slows down (Δt = γΔτ), lengths shrink (L = L₀/γ), and energy is E = γmc². For Astrophysics, distance modulus (m – M = 5 log(d/10)) and luminosity (L = 4πR²σT⁴) are your best friends. Imaging? Lens formula (1/f = 1/v + 1/u) and resolution (θ = 1.22λ/D). Engineering Physics? Stress (σ = F/A), strain (ε = ΔL/L₀), and Young’s modulus (E = σ/ε). Always write down knowns, pick the right formula, and check units. If you see c, parsecs, diopters, or GPa, you know which option it is. Now go ace that Paper 3!