# 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 ?

May 27, 2016

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 $d$:
${\theta}_{R} = 1.22 \frac{\lambda}{d}$
We have for the first wavelength:
$0.14 = 1.22 \frac{650 \times {10}^{-} 9}{d}$
so that $d = 5.664 \times {10}^{-} 6 m$
For the second wavelengrt we have then a angular separation of:
${\theta}_{R} = 1.22 \frac{150 \times {10}^{-} 9}{5.664 \times {10}^{-} 6} = 0.032$radians