Physics II: Electromagnetism, Optics, and Relativity – Syllabus Overview and Study Guide

Course Overview

This syllabus outlines the main topics, readings, and laboratory activities for a college-level Physics II course, focusing on electromagnetism, optics, and special relativity. The course follows a logical progression from Maxwell's equations and electromagnetic waves through geometric and physical optics, culminating in an introduction to Einstein's theory of relativity.

Course Topics and Structure

Week	Lecture Dates	Main Topics	Key Readings	Labs
1	1/20, 22	Maxwell’s equations – EM waves	G31.1-7	No Lab
2	1/27, 29	Energy flux – Reflection – Refraction	G31.8-9, 32.1-2, 32.6-9	No Lab
3	2/3, 5	Spherical & plane mirrors – Thin lenses	G32.1, 32.3-5, 33.1-4	Reflection-Refraction (A)
4	2/10, 18	Optical instruments – Polarization	G33.5-10, 34.7	Reflection-Refraction (B)
5	2/17, 25	Interference – Diffraction	G34.1-6, 35.1-5	Geometric optics (A)
6	2/24, 2/26	Resolution limit – Diffraction grating – Invariance of physical laws	G35.6-10, T1.2, 05.1	Midterm 1 Geometric optics (B)
7	3/3, 5	Relativity of simultaneity – Time dilation – Length contraction	T1 all, 05.2-4	Interference-Diffraction (A)
8	3/10, 12	Lorentz transformation – Relativistic velocity transformation	T1 all, 05.5-5.6	Interference-Diffraction (B)

Topic Summaries

Maxwell’s Equations and Electromagnetic Waves

• Maxwell’s Equations: Four fundamental equations describing how electric and magnetic fields are generated and altered by each other and by charges and currents.

• Electromagnetic Waves: Solutions to Maxwell’s equations in free space predict the existence of waves that propagate at the speed of light, $c$.

• Key Equations:

  • Gauss’s Law: $\nabla \cdot \vec{E} = \frac{\rho}{\varepsilon_0}$

  • Gauss’s Law for Magnetism: $\nabla \cdot \vec{B} = 0$

  • Faraday’s Law: $\nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t}$

  • Ampère-Maxwell Law: $\nabla \times \vec{B} = \mu_0 \vec{J} + \mu_0 \varepsilon_0 \frac{\partial \vec{E}}{\partial t}$

• Example: Light is an electromagnetic wave, with oscillating electric and magnetic fields perpendicular to each other and to the direction of propagation.

Energy Flux, Reflection, and Refraction

• Energy Flux: The rate of energy transfer per unit area, described by the Poynting vector $\vec{S} = \frac{1}{\mu_0} (\vec{E} \times \vec{B})$.

• Reflection and Refraction: When light encounters a boundary between two media, part of it is reflected and part is refracted (bent).

• Snell’s Law: $n_1 \sin \theta_1 = n_2 \sin \theta_2$

• Example: Light passing from air into water bends toward the normal due to a higher refractive index.

Spherical & Plane Mirrors, Thin Lenses

• Mirrors: Reflect light to form images; spherical mirrors can be concave or convex.

• Thin Lenses: Refract light to focus or diverge rays; described by the lens equation:

• Lens Equation: $\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$

• Example: A magnifying glass uses a convex lens to produce an enlarged image.

Optical Instruments and Polarization

• Optical Instruments: Devices like microscopes and telescopes use combinations of lenses and mirrors to magnify or resolve images.

• Polarization: Describes the orientation of the electric field vector in a light wave; can be linear, circular, or elliptical.

• Example: Polarized sunglasses block horizontally polarized light to reduce glare.

Interference and Diffraction

• Interference: The superposition of two or more waves leading to regions of constructive and destructive interference.

• Diffraction: The bending and spreading of waves around obstacles and through slits.

• Young’s Double-Slit Equation: $d \sin \theta = m \lambda$

• Example: The colorful patterns seen in soap bubbles are due to thin-film interference.

Resolution Limit, Diffraction Grating, Invariance of Physical Laws

• Resolution Limit: The smallest detail that can be distinguished by an optical instrument, limited by diffraction.

• Diffraction Grating: An optical component with a regular pattern that splits and diffracts light into several beams.

• Invariance of Physical Laws: The principle that the laws of physics are the same in all inertial frames (foundation of relativity).

• Grating Equation: $d \sin \theta = m \lambda$

Relativity of Simultaneity, Time Dilation, Length Contraction

• Relativity of Simultaneity: Events that are simultaneous in one frame may not be in another moving frame.

• Time Dilation: Moving clocks run slower: $\Delta t' = \gamma \Delta t$, where $\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}$

• Length Contraction: Moving objects are shorter along the direction of motion: $L' = L/\gamma$

Lorentz Transformation and Relativistic Velocity Transformation

• Lorentz Transformation: Mathematical equations relating space and time coordinates between two inertial frames moving at constant velocity relative to each other.

• Equations:

  • $x' = \gamma (x - vt)$

  • $t' = \gamma (t - vx/c^2)$

• Relativistic Velocity Transformation: Describes how velocities add in special relativity: $u' = \frac{u - v}{1 - \frac{uv}{c^2}}$

Laboratory Activities

• Reflection-Refraction (A, B): Experiments on the laws of reflection and refraction.

• Geometric Optics (A, B): Investigations with lenses and mirrors.

• Interference-Diffraction (A, B): Hands-on exploration of interference and diffraction phenomena.

• Midterm 1: Assessment covering the first half of the course.

Additional info:

• Readings labeled "G" and "T" refer to sections in the course textbook(s).

• Labs are sequenced to reinforce lecture material and provide practical experience.