# Laser Beam Question

## Homework Statement

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

## Homework Equations

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.

Sincerely,
Travis Walters

dlgoff
Gold Member
Think of it this way. How much energy (watts) do you have through a 2m diam. circle?

Hey there,

For reference, the answer key says 6.4 W/m2 is the correct answer.

The answer I got was 6.4 * 10^-4 W / m^2, so I am just wondering the answer is a typo.

I am not sure where you are getting at dlgoff? Please explain :)