Question

As the above problem refers to !8D.6., I have pasted that question.

Note that E18D6 has been asked as separate question earlier today

E18R.4 What is the upper limit of the intensity of a laser beam in air if it is not to cause the air to ionize? (One can't shine a laser beam through ionized air, because such air is opaque.) (Hint: Note problem E18D.6.)

Answer 1

E18D.6]

Averaging the function $sin^2(\omega t - 2\pi fx)/c$ is to integrate the same function over one full time period (or one full wavelength).

sin (wt

avg-21, Jo

now,

S2n

therefore,

ur avg-2T

hold x to be constant since the integration is happening over time. Taking x = 0, this gives,

avg-2T sin (wt

but

sin(nn) = 0

therefore, $[sin^2(\omega t - 2\pi fx)/c]_{avg} = \frac{1}{2T} [T-0] = \frac{1}{2}$

E18R.4]

Air is a dielectric electric medium and like any other dielectric, it has its own breakdown Electric field strength. This is the field strength when the dielectric is forced to conduct electricity. For air, this is: E_o = 3 x 10⁶ V/m

Now, intensity is time-averaged value of Poynting flux

$I = \frac{1}{T}\int \frac{1}{\mu_oc}E_o^2sin^2(\omega t)dt = \frac{1}{2\mu_oc}E_o^2$

taking E_o = 3 x 10⁶ V/m, this gives, I = 1.1936 x 10 W/m².

This is the upper limit for the intensity of laser beam to not cause breakdown of air.