Question2 An electromagnetic wave is propagating along the -x-axis in vacuum. It

Question

Question2 An electromagnetic wave is propagating along the -x-axis in vacuum. It has a wavelength of 14x104 m and the E field is parallel to the y-axis with a maximum magnitude of 1.2 MV/m. a.) Write down the vector equations for both the E and B fields as functions of time and position. b.) Evaluate the radiation pressure of this wave on a mirror. A beam of light emits an initial intensity of 35 W/m2. It then passes through a system of polarizers where the first one is oriented vertically, and the second one is oriented 35° from the vertical. a) What is the intensity of the light beam after passing through the polarizers?

Explanation / Answer

2. given EM wave, propogating along -x direction in vaccum

lambda = 14*10^-4 m

E field is parallel to the y axis, Eo = 1.2 MV/m

a. for a wave travelling in -x direction

E = Eo*sin(kx + wt)

B = Bo*sin(kx + wt)

also

Eo/Bo = c

hence

Bo = Eo/c = 0.004 T

also,

k = 2*pi/lambda = 4487.9895 rad/m

w = 2*pi*f = 2*pi*c/lambda = 1.3463968*10^12 rad/s

hence

E = 1.2*10^6*sin( 4487.9895x + 1.3463968*10^12*t ) j

now Ex B is in direction of wave propogation

j x B = -i

hence B is in -k direction

hence

B = -0.004*sin(4487.9895x + 1.3463968*10^12*t ) k

b. radiation pressure = 2S/c ( for a mirror, where S is intesity)

now, S = Eo^2/2c*muo

where muo/4*pi = 10^-7

hence

P = Eo^2/c^2*muo = (1.2*10^6)^2/(3*10^8)^2 *4*pi*10^-7 = 12.7323954 Pa

Io = 35 W/m^2

first polariser is vertical

secoond is 35 deg from vertical

a. considering the light was unpolarised

intesity passing thourhg first polariser = Io/2 = 17.5 W/m^2

intensity passing through the seonc polariser = (Io/2)cos^2(35) = 11.74267625409 W/m^2

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