How Far Can a 300 mm Telescope Resolve a Double Star Separated by 10 AU?

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A 300 mm telescope's angular resolution is primarily limited by diffraction, which 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. For visible light, using a wavelength of approximately 550 nm, the resolution can be determined. Given a double star system separated by 10 AU, the maximum distance at which the stars remain resolved can be calculated using the small angle approximation. The final answer will be expressed in light years or parsecs, depending on the calculations. This problem emphasizes the importance of understanding telescope resolution in astronomy.
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Imagine a double star with components separated by 10 astronomical units (10 AU). How far away can such a system be while remaining resolved with a 300 mm telescope? Show workings and give your final answer in either light years or parsecs. (Ignore atmospheric effects).

Thanks.
 
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Since this is obviously a homework problem, it should go into the "Homework and Coursework" section. You're also expected to show your attempts at the problem, as well as any relevant equations.

I'll start you off: what limits the angular resolution of a telescope? (In reality the answer is almost always "atmospheric effects", but the question wants you to ignore that.)
 

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