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1. In this problem, you are going to compare the angular resolution obtained by Keck with that obtained with the Hubble Space Telescope. Remember that the angular resolution (θ) of a telescope is given roughly by θ=λ D; where λ is the wavelength of the light being used for the observations and D is the diameter of the telescope. Also remember that for angular resolution, smaller values of θ are better since they mean that you can see more details in the objects that you are observing.
(a) Each Keck Telescope has a diameter of 10 m, while the Hubble Space Telescope (HST) has a diameter of 2.5 m. What is the ratio of the diffraction limit of HST to the diffraction limit of Keck (θHST/θKeck), assuming that both telescopes are observing at a wavelength of 2 μm?
(b) What is the ratio of the diffraction limit of HST to that of Keck, assuming that HST is observing at 500 nm and Keck is still observing at 2 μm? NOTE: For this part of the problem, you have to convert units so that both wavelengths are measured in the same units, either μm or nm.
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