A 3,000 watt co, (A.= I0,555nm) laser produces a circular beam of diameter D=2 m

Question

A 3,000 watt co, (A.= I0,555nm) laser produces a circular beam of diameter D=2 mm. The intensity at the source is great enough to cut through a quarter inch thick plate off stainless steel in 10 seconds Find the beam area at the source and the intensity I. Also, find E max and B max where and cB max = E max In an attempt to use the laser as a weapon, a person points t he laser at a target 1,000 m away. Of course, all beams diverge by some angle B. This means that a distance s from the source, the beam spreads out to circle of radius R where For this laser, the divergence is diffraction limited. This means that Find R, and t he beam area A = pi R' at 1,000 m. From this, find the intensity of the beam at this distance from the source. Also, find Em., and B, ... corresponding to I 1000

Explanation / Answer

a) A= (pi/4)D^2= (pi/4)(2E-3)^2=3.14E-6

so I = P/A = 3000/3.14E-6=9.55 E8

we know I=1/2 c 0 E^2

so 9.55E8 = 0.5 *3E8*8.85E-12*E^2 so E=8.48E5

then B =E/c=2.83E-3

b) so we have tan=R/s

and sin=1.22 /D

so we know sin=1.22 * 10555E-9/2E-3

so =arcsin(1.22 * 10555E-9/2E-3)=0.369 degrees

then tan(0.369)=R/1000

R=6.44 m

so A=R^2 = 130.3

so I = 3000/130.3=23.02

we know I=1/2 c 0 E^2

so 23.02 = 0.5 *3E8*8.85E-12*E^2 so E=131.7

and B=E/c = 131.7/3E8 = 4.39E-7

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