(I) What is the angular resolution limit (degrees) set by diffraction for the 100-inch (254-cm mirror diameter) Mt. Wilson telescope (λ = 560 nm)

Verified step by step guidance

1. Identify the given values: diameter of the telescope mirror (D) is 254 cm and the wavelength of light (λ) is 560 nm.
2. Convert the diameter from centimeters to meters by dividing by 100, since 1 m = 100 cm.
3. Use the formula for the angular resolution limit due to diffraction, which is given by θ = 1.22 × (λ / D).
4. Convert the wavelength λ from nanometers to meters by multiplying by 1e-9, since 1 nm = 1e-9 m.
5. Calculate θ using the converted values and convert the result from radians to degrees by multiplying by (180/π), since 1 radian = 180/π degrees.

Key Concepts

Diffraction

Diffraction is the bending of waves around obstacles and the spreading of waves when they pass through small openings. In optics, it limits the ability of a telescope to resolve fine details. The extent of diffraction depends on the wavelength of light and the size of the aperture, which in this case is the diameter of the telescope's mirror.

Angular Resolution

Angular resolution is the smallest angle between two point sources that a telescope can distinguish as separate. It is typically measured in arcseconds or degrees. The angular resolution limit due to diffraction can be calculated using the formula θ = 1.22(λ/D), where λ is the wavelength of light and D is the diameter of the telescope's aperture.

Wavelength of Light

The wavelength of light is the distance between successive peaks of a light wave, typically measured in nanometers (nm). Different wavelengths correspond to different colors of light, with 560 nm being in the green part of the spectrum. The wavelength is a critical factor in determining the diffraction limit and, consequently, the angular resolution of optical instruments like telescopes.