Example Problem
How close do you have to be to a 100 W light bulb to observe light of the same intensity as that from a 5 mW laser with a 3 mm diameter spot size?
For the laser beam the intensity is:
| I |
= |
| Power
|  |
| Area
|
|
= |
| 0.005 W
| |
| pr2
|
|
= |
| 0.005 W
| |
| p (0.0015)2
|
|
This is about 700 W/m2
Assume the light bulb emits energy uniformly in all directions, and that the bulb is about 5% efficient. Most of the energy is given off as heat, so only about 5 W is emitted as visible light.
The energy spreads out uniformly in all directions, so imagine a sphere of radius r centered on the light bulb. The intensity is:
| I |
= |
| Power
| |
| Area
|
|
= |
| 5 W
| |
| 4pr2
|
|
= |
700 W/m2 |
This gives r = 2.4 cm, about as large as the glass enclosing the filament.