A high-powered laser beam (λ=600 nm) with a beam diameter of 10 cm is aimed at the Moon, 3.8 ×

step 1 Hi friends, given wavelength of high power laser beam, 600 nanometer distance is 10 cm, R is equ

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

A high-powered laser beam $(\lambda=600 \mathrm{~nm})$ with a beam diameter of $10 \mathrm{~cm}$ 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 $10 \mathrm{~cm}$ 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

Diffraction

Diffraction is the phenomenon where waves, such as light, bend around obstacles or spread out after passing through an aperture. This effect is inherent to the wave nature of light and becomes significant when the size of the aperture or obstacle is comparable to the wavelength of the light.

Fraunhofer Diffraction

Fraunhofer diffraction, or far-field diffraction, refers to the pattern produced when light passes through an aperture and is observed at a large distance, such that the wavefronts can be treated as planar. For a circular aperture, this results in an Airy pattern, characterized by a bright central disk surrounded by concentric rings of decreasing intensity.

Small-Angle Approximation

In many optical calculations, especially those involving diffraction, the angles involved are very small. The small-angle approximation allows sin(?) to be approximated by ? (in radians), simplifying equations and calculations for determining quantities such as beam spread and spot size.

Beam Propagation and Angular Spread

The relationship between the angular spread due to diffraction and the resulting spot size on a distant surface is a key aspect of beam propagation. By multiplying the angular spread by the distance to the target, one can determine the size of the diffraction pattern (for example, the diameter of the central diffraction disk) on that surface.

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