Final answer:
The divergence of a HeNe laser beam at 633 nm with a spot size of 0.8 mm is 2.512 x 10^-4 radians. The Rayleigh range is approximately 1.26 meters, and the beam width at a distance of 10 meters from the laser is about 6.35 mm.
Step-by-step explanation:
Divergence, Rayleigh Range, and Beam Width of a Laser Beam
To find the divergence of a Gaussian beam, we use the formula:
Beam divergence (θ) = (λ / π) / (Diameter at waist)
Where λ is the laser wavelength and the diameter at the waist is the minimum spot size of the beam.
For the HeNe laser beam at 633 nm and a spot size of 0.8 mm, the divergence (θ) is calculated as follows:
Divergence (θ) = (633 x 10-9 m) / (π x 0.8 x 10-3 m) = 2.512 x 10-4 radians
The Rayleigh range (zR) is the distance over which the beam's cross-sectional area doubles for a Gaussian beam, and it is defined as:
Rayleigh range (z
R
) = (π x (Diameter at waist / 2)
2
) / λ
Substituting the given values:
Rayleigh range (zR) = (π x (0.8 x 10-3 / 2)2) / (633 x 10-9) ≈ 1.26 meters
Finally, the beam width at a distance (d), for example, 10 meters, is given by:
Beam width (w) = Waist diameter x √(1 + (d / z
R
)
2
)
Beam width at 10 m = 0.8 x 10-3 x √(1 + (10 / 1.26)2) ≈ 6.35 mm