Last Minute Lecture

Optical Diffraction & Interference Patterns Explained | Chapter 36 of University Physics Chapter 36 delves into diffraction—the bending and spreading of light waves—and the interference patterns that arise when waves overlap. From single-slit fringes to holography, these phenomena reveal the wave nature of light and underpin technologies like spectroscopy and microscopy. Watch the full video summary here for animated demonstrations of diffraction and interference. Fresnel vs. Fraunhofer Diffraction Diffraction can be classified by distance: Fresnel (near-field): wavefronts are curved; pattern depends on source-screen geometry. Fraunhofer (far-field): wavefronts are effectively planar; patterns are simpler to analyze via Fourier optics. Single-Slit Diffraction Light passing through a slit of width a produces a central bright fringe flanked by dimmer side fringes. The minima occur at angles satisfying: a sin θ = m λ , where m = ±1, ±2, … . The intensity distr...

Mechanical Waves – Propagation, Energy & Superposition Explained | Chapter 15 of University Physics Chapter 15 explores how mechanical waves transport energy through media without bulk matter motion. From transverse and longitudinal disturbances to standing wave patterns, this chapter provides the tools to model, analyze, and apply wave behavior across strings, air, and fluids. Watch the full video summary here for detailed derivations and real-world examples. Types of Mechanical Waves Transverse waves – Particle motion ⟂ wave direction (e.g., waves on strings). Longitudinal waves – Particle motion ∥ wave direction (e.g., sound in air). Surface waves – Combine transverse and longitudinal motion (e.g., water waves). Wave Parameters & Periodic Waves Key parameters describe any periodic wave: Amplitude (A): Maximum displacement from equilibrium. Wavelength (λ): Distance between repeating points. Frequency (f): Cycles per second, f = 1/T. P...