Final answer:
The size of the central bright spot caused by light diffraction from a laser beam can be calculated using the Rayleigh criterion. At 1 m, it would be 0.2815 mm in diameter and this size increases linearly with distance. The beam expands as it travels, showing significant growth in size at very large distances such as the Moon.
Step-by-step explanation:
The problem presented is related to light diffraction and how it causes a laser beam to spread out as it travels through space. We use the formula for the diameter of the central bright spot, which is given by the Rayleigh criterion, d = 1.22 λL/D, where λ is the wavelength of the light (461.9 nm), L is the distance from the aperture, and D is the diameter of the aperture (2 mm).
- At 1 m distance, using the given values:
d = 1.22 × 461.9 nm × 1 m / 2 mm = 1.22 × 461.9 × 10-9 m × 1 m / 2 × 10-3 m = 281.5 × 10-6 m = 0.2815 mm
- At other distances, the diameter of the central bright spot is directly proportional to the distance L. So, for a distance of L km, the diameter will be L × 0.2815 mm.
Thus, to find the size of the central bright spot at different distances, one would multiply the size obtained for 1 m by the distance in meters. For the Moon's surface at 400,000 km, the calculation would yield an exceptionally large bright spot, illustrating the significant impact of diffraction over vast distances.