- #1

- 142

- 27

- Homework Statement
- A laser emits radiation of wavelength ##\lambda= 632.8 nm## and a power of ##3 mW## and its beam has an angular divergence equal to ##180 \mu rad##. What is the intensity of the laser beam at a distance of ##D = 5 m##?

What would be the power of an isotropic source that provided the same intensity at the same distance?

- Relevant Equations
- ##\theta=\frac{2R}{D}##, ##I=\frac{P}{4\pi d^2}##

I haven't been able to pinpoint a definition of "angular divergence" of a laser so by pure intuition I assumed it would be something like ##\theta=\frac{2R}{D}## and with that I have that the radius of the lase beam is ##R=\frac{D\theta}{2}=90\cdot 5 \cdot 10^{-6} m=450\ \mu m## so ##I_{5m}=\frac{P}{4\pi R^2}=\frac{3\cdot 10^{-3}}{4\pi \cdot 450^2 \cdot 10^{-12}}\simeq 1179\ \frac{Watt}{m^{2}}## and so I get for an isotropic source ##P_{iso}=I_{5m}\cdot 4\pi D^2=1179\cdot 4\pi 5^2 Watt=370391 Watt##. Now, I am suspicious of these results since I never had to use the wavelength \lambda so I think my definition of angular divergence is wrong; could anyone shed some light on this definition and how to apply it in this case? Thank you very much.

#### Attachments

Last edited: