Understanding the Concepts
* Angular Resolution: This is the smallest angle between two objects that a telescope can distinguish. It's limited by the diffraction of light waves as they pass through the telescope's aperture.
* Rayleigh Criterion: This criterion states that two objects are just resolvable when the center of the diffraction pattern of one object is directly over the first minimum of the diffraction pattern of the other object.
* Diffraction Limit: The minimum angular resolution a telescope can achieve due to diffraction is given by:
* θ = 1.22 * λ / D
* θ = angular resolution (in radians)
* λ = wavelength of light (in meters)
* D = diameter of the telescope (in meters)
Calculations
1. Convert Wavelength to Meters:
* λ = 491 nm = 491 * 10^-9 m
2. Rearrange the Diffraction Limit Formula to Solve for Diameter (D):
* D = 1.22 * λ / θ
3. Plug in the Values:
* D = 1.22 * (491 * 10^-9 m) / (4.64 * 10^-6 rad)
* D ≈ 0.130 m
Answer:
The smallest diameter a telescope can have to resolve this binary star system is approximately 0.130 meters (or 13 centimeters).
