A helium-neon laser emitting at \(632.8 \mathrm{~nm}\) light makes a spot with a radius equal to \(100 \mathrm{~mm}\) at \(e^{-2}\) at a distance of \(500 \mathrm{~m}\) from the laser. What is the radius of the beam at the waist (considering the waist and the laser are in the same plane)?

Assume a Gaussian laser beam.