Final answer:
The resolving power of a telescope with an objective lens diameter of 1.22m for a wavelength of 4000 Å (400 nm) is calculated to be 400 nanoradians using the formula for angular resolution.
Step-by-step explanation:
To calculate the resolving power of a telescope, we can use the formula θ = 1.22 λ / D, where θ is the angular resolution, λ is the wavelength of light, and D is the diameter of the telescope's objective lens. Given that the objective lens has a diameter of 1.22m and the wavelength of light is 4000 Å (or 400 nm), the resolving power of the telescope can be calculated.
First, convert the wavelength from Ångströms to meters: 4000 Å = 400 nm = 400 × 10-9 m. Then plug the values into the formula:
θ = 1.22 × (400 × 10-9 m) / 1.22 m
The lens diameter cancels out the 1.22 in the numerator, making the calculation simpler:
θ = 400 × 10-9 m / 1 m = 400 × 10-9
The angular resolution, θ, is therefore 400 nanoradians.