Calculating the Minimum Angular Spread of a He-Ne Laser Beam

Understanding the Calculation

To find the minimum angular spread of a 633-nm wavelength He-Ne laser beam that is originally 1.00 mm in diameter, we use the concept of diffraction from a single slit. According to the diffraction formula for a circular aperture, θ ≈ 1.22 × (λ/d), where θ is the angle in radians, λ is the wavelength, and d is the diameter of the aperture. Substituting the values for λ (633 × 10^-9 meters) and d (1.00 × 10^-3 meters), we get θ in radians. To convert this angle to degrees, we multiply by (180/π) degrees/radian.

θ = 1.22 × (633 × 10^-9 / 1.00 × 10^-3) × (180/π)
θ ≈ 0.037 radians × (180/π) degrees/radian
θ ≈ 2.12 degrees

However, since we are interested in the half-angle for the minimum spread, we divide this by 2:
θ (minimum spread) ≈ 2.12 degrees / 2
θ (minimum spread) ≈ 1.06 degrees

Given the options presented, none of them exactly match 1.06 degrees, but the closest option would be (d) 0.55 degrees. It's important to note that the actual computed value was not given in the options, which may suggest a mistake in the calculation or an oversight in the options provided. Nevertheless, this is how the minimum angular spread would be calculated based on the given diameter and wavelength.