A high-powered laser beam (λ=600 nm) with a beam diameter of 12 cm is aimed at the Moon, 3.8 ×1

step 1 Hi there. So for this problem, we have a laser beam with a wavelength of 600 nanometers. And it

A high-powered laser beam (λ=600 nm) with a beam diameter of...

A high-powered laser beam $(\lambda=600 \mathrm{nm})$ with a beam diameter of $12 \mathrm{~cm}$ is aimed at the Moon, $3.8 \times 10^{5} \mathrm{~km}$ distant. The beam spreads only because of diffraction. The angular location of the edge of the central diffraction disk (see Eq. $36-12$ ) is given by $$\sin \theta=\frac{1.22 \lambda}{d}$$ where $d$ is the diameter of the beam aperture. What is the diameter of the central diffraction disk on the Moon's surface?

A high-powered laser beam $(\lambda=600 \mathrm{nm})$ with a beam diameter of $12 \mathrm{~cm}$ is aimed at the Moon, $3.8 \times 10^{5} \mathrm{~km}$ distant. The beam spreads only because of diffraction. The angular location of the edge of the central diffraction disk (see Eq. $36-12$ ) is given by
$$\sin \theta=\frac{1.22 \lambda}{d}$$
where $d$ is the diameter of the beam aperture. What is the diameter of the central diffraction disk on the Moon's surface?

Key Concepts

Angular Spread in Diffraction Patterns

In diffraction analysis, the angular spread of the light, often determined by an expression like sin? = 1.22?/d, represents the angle at which the intensity falls to its first minimum. This angular spread is a fundamental characteristic of wave diffraction and is critical in determining the size of features such as the central diffraction disk.

Beam Propagation Geometry

The relationship between the angular divergence of a beam and the distance traveled allows one to estimate the physical size of the diffraction pattern on a remote surface. When the angular spread is known, the diameter of the diffraction pattern (or central disk) can be calculated using simple geometric relations based on the distance from the aperture to the target.

Diffraction

Diffraction is the process by which waves bend around obstacles or spread as they pass through an aperture. This phenomenon is an inherent property of wave behavior and explains why even highly collimated beams, such as lasers, inevitably diverge over long distances.

Aperture Effects on Diffraction

The size of the aperture, or the beam diameter in the case of a laser, directly affects the extent of diffraction. A larger aperture results in a narrower diffraction angle, limiting the spread of the beam, whereas a smaller aperture causes the beam to spread more widely due to increased diffraction.

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