Answer:
a)
b)
Explanation:
We are comparing two wavelengths with the radius and diameter constant, and if we want to compare it, we need to use the following formula:
Where represent the angular resolution and the wavelength.
So if we have a fixed resolution and wavelength 1 and we want to find the resolution for a new condition we can solve for and we got
Part a
For this case the subindex 1 is for the color red and we know that:
And the angular resolution for the color red is specified as
And for the infrared case we know that , so if we replace we got:
Part b
For this case the subindex 1 is for the color red and we know that:
And the angular resolution for the color red is specified as
And for the ultraviolet case we know that , so if we replace we got: