PHY 104 Past Questions

Here is a structured study summary derived from the provided document, covering key physics concepts:

Physics Study Summary

This summary outlines fundamental concepts in Physics, categorized for clarity. It covers topics frequently encountered in Optics, Waves, Modern Physics, Mechanics, Nuclear Physics, and Electromagnetism.

1. Optics

• Refraction and Snell's Law:
  • Calculating the refractive index of a medium (e.g., glass block) given angles of incidence and refraction, or determining critical angles.
  • Behavior of light passing from denser to less dense material (speeds up and bends away from the normal).
• Mirrors:
  • Concave Mirrors: Determining image distance and magnification for an object placed at a given distance and radius of curvature. Used as magnifying mirrors.
  • Convex Mirrors: Determining image characteristics (virtual, diminished, location) for an object.
  • Plane Mirrors: Calculating the number of images formed by two inclined plane mirrors (N = 360/θ - 1).
• Lenses:
  • Converging Lenses: Determining image characteristics (real/virtual, magnified/diminished, inverted/upright) using ray tracing or lens formula.
  • Combination of Lenses: Calculating the power of a combination of lenses (P_total = P1 + P2).
• Human Eye and Corrective Lenses:
  • Calculating the near point for a far-sighted person with and without corrective lenses, using lens power (P = 1/f) and the lens formula.
• Dispersion:
  • The splitting of white light into its constituent colors when passing through a prism, due to different refractive indices for different wavelengths.
• Polarization:
  • Understanding that unpolarized light has its electric field oscillating in every possible direction perpendicular to the direction of propagation.

2. Waves and Oscillations

• Wave Properties:
  • Wave Equation (v = fλ): Calculating frequency given speed and wavelength, or vice-versa.
  • Amplitude: Defined as the maximum distance from the equilibrium position of any point on a wave.
  • Wave Speed in Media: Sound waves travel fastest in solids, then liquids, then gases.
  • Amplitude and Distance from Source: For a point source, amplitude is inversely proportional to distance (A ∝ 1/r).
  • Types of Waves: Transverse waves consist of crests and troughs; longitudinal waves consist of rarefactions and compressions.
• Superposition of Waves:
  • Interference: Alternating light and dark bands from multiple narrow slits (Young's double-slit experiment) or from diffraction gratings.
  • Destructive Interference: Occurs when the path difference between coherent beams is an odd number of half-wavelengths, or when two out-of-phase waves of the same amplitude and frequency arrive at the same place, resulting in cancellation.
  • Resultant Amplitude: For two waves with phase difference Δφ, the resultant amplitude is A_res = 2A cos(Δφ/2).
  • Beats: The phenomenon of beats occurs when two waves of slightly different frequencies superpose, leading to periodic variations in intensity. It can occur for both longitudinal and transverse waves.
• Diffraction:
  • The spreading of waves as they pass through an opening or around an obstacle, allowing wavefronts to reach points behind the barrier (e.g., radio waves curving around a hill, water waves passing harbour walls).
  • Single-Slit Diffraction: Determining the position of dark fringes.
  • Diffraction Grating: Calculating slit width or maximum order of bright fringes.
• Doppler Effect:
  • Calculating the observed frequency when a source (e.g., car horn) moves towards a stationary receiver.
• Simple Harmonic Motion (SHM):
  • Equation of Motion: Analyzing displacement, velocity (v = dx/dt), and initial conditions from SHM equations like x(t) = A sin(ωt + φ) or x(t) = A cos(ωt + φ). Maximum velocity occurs when displacement is zero.
  • Period: Determining the period of motion from the differential equation (d²y/dt² + Ky = 0), where T = 2π/√K.
  • Energy in SHM: Calculating the time at which kinetic energy becomes a certain fraction of total energy.
  • Maximum Speed: For a mass vibrating on a spring, v_max = Aω = A(2π/T).
  • Relationship to Oscillatory/Periodic Motion: All SHM is oscillatory and periodic; all oscillatory motion is periodic, but not necessarily SHM.
• Damped Oscillations:
  • Critical Damping: The system returns to its equilibrium position in the shortest possible time without oscillating.
  • Forced Oscillations and Resonance: Understanding how damping affects resonance (increased damping reduces the sharpness of the resonance peak and the maximum amplitude).
  • Q-factor: Related to the number of oscillations for the amplitude to decay to 1/e of its initial value.
• Standing Waves:
  • On a String: Calculating tension given frequency, length, mass per unit length, and harmonic number (e.g., 2nd overtone = 3rd harmonic).

3. Modern Physics

• Photoelectric Effect:
  • Energy of Photon: E = hf. Directly proportional to frequency.
  • Work Function (Φ): Energy required to eject an electron.
  • Maximum Kinetic Energy of Ejected Electrons: K_max = hf - Φ or K_max = E_photon - Φ. Also K_max = eV_s, where V_s is stopping potential.
  • Threshold Frequency/Wavelength: The minimum frequency/maximum wavelength required to eject electrons.
  • Factors Affecting Electron Emission: The number of electrons emitted depends on the intensity of the incident light (more photons), while the speed/kinetic energy of emitted electrons depends on the frequency of the light (higher energy photons). Increasing the frequency above the threshold increases the likelihood of photoelectrons.
• Atomic Structure:
  • Rutherford's Model: Most of the volume of an atom is empty space.
  • Neutral Atom: The number of electrons equals the number of protons.
  • Electron Cloud: Electrons are usually found outside the nucleus, occupying most of an atom's volume.
  • Atomic Energy Levels: Calculating the energy of a photon emitted when an atom changes from a higher to a lower energy state (E = E_initial - E_final).
  • Hydrogen-like Atoms: Calculating the wavenumber of a photon released during an electronic jump (e.g., using Rydberg formula).
• Wave-Particle Duality:
  • Electron Diffraction: The phenomenon that best supports the theory that matter has a wave nature.
• Heisenberg Uncertainty Principle:
  • States that it is impossible to determine accurately both the position and momentum of an electron simultaneously.
• Compton Effect:
  • Calculating the scattered wavelength of a photon after interacting with an electron (λ' - λ = h/(mc)(1 - cos θ)).
• X-ray Production:
  • Calculating the minimum wavelength of X-rays or the applied potential difference (eV = hc/λ_min).
  • Determining the number of electrons involved in X-ray production given voltage and current.

4. Nuclear Physics

• Radioactivity:
  • Half-Life: Calculating the mass/fraction/number of nuclei remaining after a certain time, or estimating half-life from count rate data (N = N0 * (1/2)(t/T)).
  • Alpha Particles: Consist of two protons and two neutrons (a helium nucleus). They are highly ionizing but have low penetrating power.
• Mass Defect and Binding Energy:
  • Calculating the mass defect of an isotope given its actual mass and the rest masses of its constituent particles.
  • Mass-Energy Equivalence: E=mc². The slope of an energy vs. equivalent mass graph represents c².
• Nuclear Reactions:
  • Identifying bombarding particles or products in nuclear reactions by ensuring conservation of mass number and atomic number.
• Nuclear Forces:
  • Particles in a nucleus are held together primarily by the strong nuclear force.
• Atomic Weight:
  • Calculating the average atomic weight of an element from the masses and natural abundances of its isotopes.

5. Electricity and Magnetism

• Electric Current:
  • Calculating the number of electrons (N) involved given current (I), time (t), and electron charge (e) (I = Ne/t).

This summary aims to cover the breadth of physics topics presented in the document, providing a comprehensive overview for study purposes.