# Extra-thin-line.jpg

One only needs three rather simple equations for all the calculations done in this article. First, if we assume the laser is optimized so that its spreading angle is at its theoretical minimum, then we can calculate its beam divergence (in radians) using this equation.

(The laser's wavelength)/(π × The laser's aperture)

Then a little bit of geometry will give us the size of the final lit spot at the destination.

π × (Beam divergence in radians × Distance)2

Finally, the brightness at the destination is given by dividing the output power of the laser over the area of the spot.

(The laser's power)/(Size of the spot)

If you didn’t make a mistake in your calculations and kept everything in radians, watts and meters, the final number should be in watts per square meter.

The dimmest light visible to the naked eye in perfect darkness is around one ten-billionth of a watt per square meter. However, with the presence of urban light pollution, one usually can’t see stars much dimmer than the North Star, which has an intensity of around four-billionths of a watt per square meter. For comparison, the full moon is almost a million times brighter at one-thousandth of a watt per square meter. Finally, the midday sun is at a whopping 1,000 watts per square meter, about half a million times brighter than the moon.