# Electromagnetic Waves

Student Learning Objectives
Lessons / Lecture Notes
Important Equations
Example Problems
Applets and Animations

Student Learning Objectives

• To understand how induced electric and magnetic fields lead to electromagnetic waves.
• To apply the wave model to the electromagnetic spectrum.
• To understand the properties of different types of electromagnetic waves.
• To understand the concept of polarization.
• To calculate the intensity of light transmitted through a series of polarizing filters.

Lessons / Lecture Notes

The Physics Classroom (conceptual)

PY106 Notes from Boston University (algebra-based):

Introductory physics notes from University of Winnipeg (algebra-based):

HyperPhysics (calculus-based)

PHY2049 notes from Florida Atlantic University (calculus-based):

PHY2044 notes from Florida Atlantic University (calculus-based)

General Physics II notes from ETSU (calculus-based)

Important Equations

Example Problems

Problem 1
(a) The average distance to the sun from the earth is 92.58 million miles. How long does it take light from the sun to reach the earth? (Solutions)

(b) The human eye is most sensitive to light with a frequency of about 5.5 × 1014 Hz, which is in the yellow-green region of the electromagnetic spectrum. How many wavelengths of this light can fit across the width of your thumb, a distance of about 2.0 cm? (Solutions)

Problem 2
An initially unpolarized beam of light is sent through a stack of four polarizing sheets, oriented so that the angle between the polarization directions of adjacent sheets is 22o. What fraction of the incident intensity is transmitted by the system? (Solutions)

Applets and Animations
 Radio Waves and EM Fields Broadcast radio waves from KPhET. Wiggle the transmitter electron manually or have it oscillate automatically. Display the field as a curve or vectors. The strip chart shows the electron positions at the transmitter and at the receiver. EM Wave Animation This animation shows an electromagnetic wave, namely a plane polarized wave, which propagates in positive x direction. The vectors of the electric field (red) are parallel to the y axis, the vectors of the magnetic field (blue) are parallel to the z axis. EM Wave A 3 dimensional animation of the "far" fields of an oscillating charge. Electromagnetic Waves The Electromagnetic Wave model displays the electric field and magnetic field of an electromagnetic wave.  The simulation allows an arbitrarily polarized wave to be created. The magnitude of the electric field components and the relative phase between the components of the electric field can all be changed via sliders. Color Vision Make a whole rainbow by mixing red, green, and blue light. Change the wavelength of a monochromatic beam or filter white light. View the light as a solid beam, or see the individual photons. Additive Colors This applets allows the user to add varying amounts of red, green, and blue and see the resulting color. Doppler Effect Explanation Illustrating the classical Doppler Effect for sound waves. Doppler Wave Fronts Illustrating the wave fronts of a wave for a moving source. Doppler Effect The Doppler Effect model displays the detection of sound waves from a moving source and the change in frequency of the detected wave via the Doppler effect. In addition to the wave fronts from the source a graph depicting the time of emission and time of detection of each of the wave fronts is given. Circular Polarization Circular polarization generated from a linearly polarized electromagnetic wave by a quarter-wave plate. Polarizers This applet shows circularly polarized light passing through a series of three polarizers. The user can control the angle of each polarizer. Polarizer The Polarizer program displays the effect of a plane polarizer on an incident electromagnetic wave.   The polarization of the electromagnetic wave and the orientation of the polarizer can be modified. Brewster's Angle The Brewster's Angle model displays the electric field of an electromagnetic wave incident on a change of index of refraction.  The simulation allows an arbitrarily linearly (in parallel and perpendicular components) polarized wave to encounter the change of index of refraction.