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A space-based telescope can achieve a diffraction-limited angular resolution of 0.14 for red light (wavelength 650 nm). What would the resolution of the instrument be in the ultraviolet, at 150nm ?

Answer 1

I found #0.032# radians.

I suppose here I am dealing with the Raileigh Criterion that tells us the minimum angular (in radians) separation between two object (emitting light of wavelength #lambda#) to strart to be discriminated (resolvable) by an aperture of diameter #d#: #theta_R=1.22lambda/d# We have for the first wavelength: #0.14=1.22(650xx10^-9)/d# so that #d=5.664xx10^-6m# For the second wavelengrt we have then a angular separation of: #theta_R=1.22(150xx10^-9)/(5.664xx10^-6)=0.032#radians

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Answer 2

Jordan Andrews

The resolution of the instrument in the ultraviolet, at 150nm, would be approximately 0.03 arcseconds.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.