An em wave entering a medium.

A wave crossing from vacuum into a medium of chosen εr and μr: same frequency, lower speed 1/√(με), shorter wavelength.

Make the wave travel at 2.0 × 10⁸ m/s inside the medium and confirm its frequency is unchanged.

Thinking the frequency changes in a medium, or that em waves need one.

• Electromagnetic waves are self-sustaining oscillations of E and B in free space. Unlike sound or waves on a string, they need no material medium: nothing material vibrates.
• In vacuum the speed is c = 1/√(μ₀ε₀). With μ₀ = 4π × 10⁻⁷ T m A⁻¹ and ε₀ = 8.854 × 10⁻¹² C² N⁻¹ m⁻², this is about 3 × 10⁸ m/s.
• In a material medium of permittivity ε and permeability μ these replace ε₀ and μ₀, and the speed becomes v = 1/√(με). The speed of light depends on the electric and magnetic properties of the medium.
• The refractive index of one medium with respect to another equals the ratio of the speeds of light in them (taken up in the next chapter).
• Measured with waves of many different wavelengths, the vacuum speed does not depend on wavelength; the results agree to a few m/s out of 3 × 10⁸ m/s. The value is known so precisely that it is used to define the standard of length.
• All electromagnetic waves, from radio waves to gamma rays, travel at the same speed c in vacuum.
• Electromagnetic waves carry energy from one place to another. Radio and TV signals carry energy, and light carries the sun's energy to the earth, which makes life on earth possible.

Teaching this idea? Put the simulation on your own page or LMS with this code.