If a 20-W laser beam, which has an initial diameter of 2.0 mm, spreads out to a diameter of 2.0 m after traveling 10,000 m, what is the final intensity of the beam?
A. 20 x 10-4 W/m2
B. 20 x 10-6 W/m2
C. 20 x 10-8 W/m2
D. 6.4 W/m2
E. 6.4 x 10-6 W/m2
I found an equation that states if light hits a surface area A at normal incidence, the intensity I is equal to:
I = <P> / A
The Attempt at a Solution
If I draw this beam out, I have a frustrum of a right circular cone.
The lateral surface area of a frustrum = PI * S * (R + r) where R and r are the radia and s is the diagonal side.
After a little math, I found s to be about 10000. It is a little over but its neglible.
So the surface area would be = PI * 10000 * (.001 m + 1.0 m) = 31447.3 m^2
Wouldnt that mean the intensity I = 20 W / 31447.3 m^2 = .000636 W / m^2
Intensity = 6.4 * 10^-4 W / m^2
Obviously, that is not one of the answers. What am I doing wrong here?
Any help will be greatly appreciated. Thanks in advance.