(1) consider a linearly polarized plane electromagnetic wave traveling in the +x

Question

(1) consider a linearly polarized plane electromagnetic wave traveling in the +x-direction in free space having as its plane of vibration the xy-plane. Given that its frequency is 10 MHz and its amplitude is E0 = 0.08Vm.

(a) Find the period and wavelength of the wave

(b) write an expression for E(t) and B(t)

(c) Find the flux density <s> of the wave

(2) A 1.0mW laser has a beam diameter of 2 mm. Assuming the divergence of the beam to be negligible. compute its energy density in the vicinity of the of the Laser.

(3) A complete absorbing screen receives 300W of light for 100s. compute the total linear momentum transferred to the screen.

(4) A 3.0V flashlight bulb draws 0.25A. converting about 1.0% of the dissipated power into light (wavelength=550nm). If the beam has a cross-sectional area of 10 cm2 and is approximately cylindrical.

(a) How many photons are emitted per second?

(b) How many photons occupy each meter of the beam?

(c) What is the flux density of the beam as it leaves the flashlight?

(5) What is the momentum of a 1019 Hz X-ray photon?

(6) What force on the average will be exerted on the ( 40mX50m) flat, highly reflecting side of a space station wall if it's facing the sun while orbiting earth?

(7) Show that Eq.9 can be writen as

(n2-1)-1 = -C(lambda)-2 + C(Lambda)0-2

Where C= 4pi2c2E0me/ Nqe2

n2(omega) = 1 + (Nqe2 /(E0me)) (1/ (Omega02 __ Omega2) (Eq.9)

(10) If an ultravoilet photon is to dissociate the oxygen and carbon atoms in the carbon monoxide molecule. It must provide 11 eVof energy. what is the minimum frequency of the appropriate radiation?

Explanation / Answer

4.solution

a) How many photons are emitted per second?

For this part you first need to find the overall power in this system, P= IV.

P = 3V * 0.25A = 0.75 Watts

Now multiply that value by 1%.

P = 0.75*(1.0 / 100) = 0.0075 W

With this value, you have what you need to find the number of photons per second using the formula for photon flux:

Photon flux = P/hf = P/hc

photon flux = (0.0075*550*10-9) / (6.626*10-34*3*108 m)

photon flux = 2.07*1016 photons per second

b) How many photons occupy each meter of the beam?

For this part you need to use the number of photons you calculated for part a and divide it by the total volume they fly through.

In order to do this, you need to calculate said volume, which will be ((speed of light) ( 1 second) (10cm^2) ).

volume of beam V = 3*108 m/s *1sec*10*10-4 m2

volume of beam V = 3*105 m3

no of photons for meter = 2.07*1016 / 3*105 = 6.90*1010

c) What is the flux density ( in W/m^2) of the beam as it leaves the flashlight?

Intensity = Power/Area Again, make sure to use the 1% value of power

intensity = 0.0075 W / (10*10-4m2)

intenstity = 7.50 W/m2

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