A 10- W laser emits a beam of light 4.0 mm in diameter. The...

A $10-$ W laser emits a beam of light 4.0 mm in diameter. The laser is aimed at the Moon. By the time it reaches the Moon, the beam has spread out to a diameter of $85 \mathrm{km} .$ Ignoring absorption by the atmosphere, what is the intensity of the light (a) just outside the laser and (b) where it hits the surface of the Moon?

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Key Concepts

Conservation of Energy

In the absence of absorption or other losses, the total power (or energy per unit time) emitted by the source remains constant as the beam propagates. This principle allows us to equate the initial power to the power delivered over the larger area after beam spreading, which is key to understanding how intensity decreases over distance.

Area Calculation

Calculating the cross-sectional area over which a beam of light is spread is essential to determine its intensity. For circular beams, the area is determined using the formula A = ?r², where r is the radius of the beam. This calculation helps in quantifying the decrease in intensity as the beam expands.

Beam Divergence

Beam divergence describes the spreading of a light beam as it propagates through space. Due to diffraction and the finite size of the initial beam, the beam’s diameter increases with distance, which in turn causes a reduction in the intensity of the beam because the same power is distributed over a larger area.

Intensity

Intensity is the power per unit area that a light beam delivers. It is calculated by dividing the total power of the source by the area over which the light is spread. This concept is crucial in understanding how light diminishes in brightness as its beam expands over a larger surface.

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