Intensity of laser beam / Inverse square law

[stimpyzu]

Hello everyone!

I'm having a real tough time with this one, maybe I can get a little help.

A small helium neon laser emits red visible light with a power of 3.2 mW in a beam that has a diameter of 2.5mm. What is the intensity of the laser beam? Does this intensity obey the inverse square law?

Now I have for an answer an intensity of 0.652 W/m2 and that it does not obey the inverse square law (although this could be wrong).

For the intensity, I thought:

I = Power / ( 4 pi ( diameter / 2 ) ^ 2 )

but that gives me an intensity of only 0.163. And I thought that all light obeyed the inverse square law. I've done research for this on the net, but I can't find anything. A shove in the right direction would be appreciated.

Thanks!

 

[Nenad]

You need to lose the 4.
ok, when I did the calculation, I get the right answer, but wrong decimal places. I found the area of the beams cross section. I did this by:
Area = pi(r)^2
= pi(0.00125m)^2
= 4.91exp.-6 (I don't know why you added the 4, the area is only pi(r)^2)
Now I found the powre in watts, 3.2mW = 0.0032W
Now I divided the power by area to get intencity:
I = Power / (pi(r)^2)
= 0.0032W / 4.91exp.-6
I = 652 W/m2
Can someone show me where I went wrong, or is the book wrong. I hope I've been a help.

 

[BobG]

Hello everyone!

I'm having a real tough time with this one, maybe I can get a little help.

A small helium neon laser emits red visible light with a power of 3.2 mW in a beam that has a diameter of 2.5mm. What is the intensity of the laser beam? Does this intensity obey the inverse square law?

Now I have for an answer an intensity of 0.652 W/m2 and that it does not obey the inverse square law (although this could be wrong).

For the intensity, I thought:

I = Power / ( 4 pi ( diameter / 2 ) ^ 2 )

but that gives me an intensity of only 0.163. And I thought that all light obeyed the inverse square law. I've done research for this on the net, but I can't find anything. A shove in the right direction would be appreciated.

Thanks!

I also got 652 using Nenad's equation.

The inverse square law applies to light radiated in all directions. The reduction in intensity is because the same amount of light is covering an ever expanding area. With a laser, you're sending the light in a straight line (theoretically, at least). The light beam covers the same amount of area 10 miles from its source as it did when it first left the laser.

 

[Everett]

All the lasers I know about have some sort of laser cavity where the photons make many circuits (n) between reflective ends. The effective geometry has the photons that do not exit out of the sides of the cavity traveling a distance of n times the length of the cavity before exiting the laser and forming the beam.

For a He-Ne laser, the cavity might have a length of 25 cm and a photon might make 5 circuits on average before joining the beam. The distance traveled is then 2.5 m and since the aperature is 2.5 mm, the beam divergence is 1 milliradian.

I say the laser does obey the inverse square law, but you have to consider the distance traveled within the laser. For the above example, the beam width should double and the beam intensity should go to a quarter at a distance of 2.5 meters from the end of the laser ( 5 meters from the "point" of origin of the photons.)

Note that I am probably off by a factor of two since the photons do not originate from a point source but from an extended source with dimensions probably equal to that of the laser aperature (2.5 mm in the example.)

Regards,

Everett

 

[stimpyzu]

Thanks guys, I really appreciated your input. It helped a lot. What a friendly bunch you guys are in this forum!

Thanks a million!

 

[Claude Bile]

The inverse square law applies only to isotropic light sources. A laser is highly directional and thus does not obey the inverse square law.

Claude.