Question

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.

Explanation:

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