Question

the diffraction-limited resolution of a telescope 10 m long at a wavelength of 500 nm is 1.22x10-6 radians. the diameter of the collecting lens of the telescope is closest to____

Answer 1

The diameter of the collecting lens of a telescope with a diffraction-limited resolution of 1.22x10^-6 radians at a wavelength of 500 nm is closest to 0.5 meters.

Step-by-step explanation:

The question asks for the diameter of the collecting lens of a telescope given the resolution limit in radians and the wavelength of light. Using the Rayleigh criterion, the resolution limit (θ) can be expressed as θ = 1.22 λ / D, where λ is the wavelength and D is the diameter of the collecting lens. We are given θ = 1.22 x 10-6 radians and λ = 500 nm, hence we can solve for D:

θ = 1.22 λ / D
→ D = 1.22 λ / θ
→ D = (1.22)(500 x 10-9 m) / (1.22 x 10-6)
→ D = (1.22)(500) / (1.22 x 103)
→ D ≈ 0.5 m

Therefore, the diameter of the collecting lens of the telescope is closest to 0.5 meters.