How Is Laser Beam Intensity Calculated?

[ganondorf29]

Homework Statement

A helium-neon laser of the type often found in physics laboratories has a beam power of 3.50 mW at a wavelength of 633 nm. The beam is focused by a lens to a circular spot whose effective diameter may be taken to be equal to 2.00 wavelengths. Calculate the intensity of the focused beam.

Homework Equations

$$<br /> I = P / 4\pi r^2<br />$$

The Attempt at a Solution

$$<br /> I = P / 4\pi r^2<br />$$

P = 3.50mW
I don't know what the radius is. From the problem, I used 633nm as the radius because the diameter = 2*(633nm), I used 633nm as the radius, but after using that value the answer is wrong. If someone can tell me the radius, I think I could get this problem. Thanks

 

[tiny-tim]

Hi ganondorf29!

(have a pi: π )

A helium-neon laser of the type often found in physics laboratories has a beam power of 3.50 mW at a wavelength of 633 nm. The beam is focused by a lens to a circular spot whose effective diameter may be taken to be equal to 2.00 wavelengths. Calculate the intensity of the focused beam.
…
I = P / 4\pi r^2

No, that's the wrong formula …

as you can see, it's the total power divided by the surface area of a whole sphere of radius r …

it applies when the beam is all-round, so the intensity is P/4πr² , and the power through an area A (at distance r) is PA/4πr².

In this case, the total power is confined to the beam, and it all goes through the "effective circle", so the appropriate formula for intensity is … ?