1 in a vacuum the velocity of all electromagnetic waves is c

1) in a vacuum the velocity of all electromagnetic waves is c, what is the velocity in a substance with an index of refraction=1.24 ? if the wavelength of air was 500nm what is the wavelength in the substance ? Show work

2) The E and B fields in electromagnetic waves are oriented perpenndicular to each other. If the Electromagnetic field is oscillating in the x-z plane while traveling in the y direction its displacement is given by: E = 2.4 x 10^-4 Sin(k y - wt).

a) What is the value of amplitude of the magnetic field wave, Bo ?

b) If the wavelength of the wave is 500nm, what is its frequency ?

c) What are the values of k and w ?

Solution

Here ,

1)

wavelength in the substance = wavelength/refractive index

wavelength in the substance = 500/1.24

wavelength in the substance = 403.22 nm

2)

Eo = 2.4 *10^-4 N/C

a) value of amplitude of magentic field = E0/c

value of amplitude of magentic field = 2.4 *10^-4/(3 *10^8)

value of amplitude of magentic field = 8 *10^-13 T

b)

speed of wave = frequency * wavelength

3 *10^8 = 500 *10^-9 * frequency

frequency = 6 *10^14 Hz

c)

k = 2pi/wavelength

k = 2pi/(500 *10^-9)

k = 1.256 *10^7 rad/m

w = 2pi * f

w = 2pi * 6 *10^14

w = 3.77 *10^15 rad/s