A helium-neon laser, radiating at 632.8 nm, has a power output of 3.0 mW. The beam diverges (s

step 1 In this question, we have a helium neon laser. Helium neon laser. Okay. And then it has a power

A helium-neon laser, radiating at 632.8 nm, has a power...

A helium-neon laser, radiating at $632.8 \mathrm{~nm}$, has a power output of $3.0 \mathrm{~mW}$. The beam diverges (spreads) at angle $\theta=0.17$ mrad (Fig. $33-72$ ). (a) What is the intensity of the beam $40 \mathrm{~m}$ from the laser? (b) What is the power of a point source providing that intensity at that distance?

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Key Concepts

Intensity

Intensity is a measure of the power delivered per unit area. In the context of beams such as laser light, it quantifies how much energy is transported through a given area and is typically expressed in watts per square meter. This concept is crucial when assessing the energy distribution over a beam's cross-section as the beam travels and spreads out.

Beam Divergence

Beam divergence refers to the angular spread of a beam as it propagates over a distance. In lasers, even a well-collimated beam gradually widens, and this divergence is commonly described by a small angle. Understanding beam divergence is important because it determines the size of the beam’s cross-sectional area at a given distance, which in turn affects the intensity derived from a fixed power output.

Point Source Radiation and the Inverse-Square Law

For a point source, the emitted power is distributed uniformly in all directions. The intensity at a distance from a point source diminishes according to the inverse-square law, meaning that the intensity is inversely proportional to the square of the distance from the source. This concept is fundamental when comparing the focused energy of a laser beam to that of an idealized point source operating at the same distance.

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